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Questions and Answers

What two factors determine an object's momentum?

  • Force and time
  • Mass and velocity (correct)
  • Energy and speed
  • Weight and acceleration

Which of the following correctly describes the relationship between impulse and momentum?

  • Impulse is equal to the change in an object's kinetic energy.
  • Impulse is equal to the force acting on an object divided by time.
  • Impulse is unrelated to momentum.
  • Impulse is equal to the change in an object's momentum. (correct)

What is the SI unit for momentum?

  • N/s
  • Ns
  • kgm/s (correct)
  • kgm/s^2

A 5 kg object is moving at a velocity of 2 m/s. What is its momentum?

<p>10 kgm/s (B)</p> Signup and view all the answers

A force of 20 N is applied to an object for 5 seconds. What is the impulse?

<p>100 Ns (D)</p> Signup and view all the answers

Which of the following is true regarding momentum as a vector quantity?

<p>It has both magnitude and direction. (B)</p> Signup and view all the answers

How does impulse relate to the change in momentum?

<p>Impulse is equal to the change in momentum. (D)</p> Signup and view all the answers

What is the relationship between net force and the rate of change of momentum, according to Newton's Second Law?

<p>Force is equal to the rate of change of momentum. (D)</p> Signup and view all the answers

In a closed system, what condition must be met for the total momentum to remain constant?

<p>The net external force must be zero. (C)</p> Signup and view all the answers

How does increasing the time interval during which a force is applied affect the impact force, assuming the impulse remains constant?

<p>It decreases the impact force. (C)</p> Signup and view all the answers

What distinguishes an elastic collision from an inelastic collision?

<p>Both momentum and kinetic energy are conserved in an elastic collision. (C)</p> Signup and view all the answers

How is the principle of conservation of momentum applied in analyzing collisions?

<p>The total momentum remains constant before and after the collision. (D)</p> Signup and view all the answers

A 2 kg ball moving at 5 m/s collides with a stationary 3 kg ball. If the 2 kg ball stops after the collision, what is the velocity of the 3 kg ball?

<p>3.33 m/s (A)</p> Signup and view all the answers

A 0.15 kg baseball is pitched at 40 m/s and then hit by a bat, sending it in the opposite direction at 50 m/s. What is the magnitude of the impulse on the ball?

<p>13.5 Ns (B)</p> Signup and view all the answers

What does the area under a force-time graph represent?

<p>The impulse (B)</p> Signup and view all the answers

A car crashes into a wall. Which strategy would be most effective in reducing the force of impact on the driver?

<p>Increasing the time of impact (C)</p> Signup and view all the answers

In what type of system is the conservation of momentum applicable?

<p>Closed systems with no external forces (C)</p> Signup and view all the answers

A rocket expels gas to move forward. Explain how this relates to momentum conservation.

<p>The rocket's gain in momentum equals the gas's loss in momentum. (C)</p> Signup and view all the answers

What is the key difference between the impulse experienced by a light object versus a heavy object if both undergo the same change in velocity?

<p>The heavier object will experience a greater impulse. (A)</p> Signup and view all the answers

What is the net force acting on an object if its momentum is constant?

<p>It is zero. (A)</p> Signup and view all the answers

A ball is dropped from a height. Describe the change in its momentum as it falls, ignoring air resistance.

<p>It increases. (A)</p> Signup and view all the answers

Under what condition would the kinetic energy of a system be conserved in a collision?

<p>During an elastic collision (B)</p> Signup and view all the answers

A 1000 kg car traveling at 20 m/s collides with a 500 kg car traveling at 30 m/s in the same direction. They stick together after the collision. What is their combined velocity immediately after the collision?

<p>23.3 m/s (B)</p> Signup and view all the answers

Two balls of equal mass, one red and one blue, approach each other head-on with equal speeds. After the collision, they bounce off each other, each moving at the same speed as before, but in the opposite direction. How does the total momentum of the system (both balls) change as a result of the collision?

<p>It remains the same. (B)</p> Signup and view all the answers

A 2 kg object moving at 3 m/s to the right collides elastically with a 1 kg object initially at rest. What is the velocity of the 2 kg object after the collision?

<p>1 m/s (A)</p> Signup and view all the answers

A rubber ball and a steel ball of the same mass are dropped onto a steel plate. Which ball experiences a greater impulse upon impact?

<p>The rubber ball (C)</p> Signup and view all the answers

A machine gun fires bullets of mass (m) at a speed (v). If the gun fires (n) bullets per second, what is the average force exerted by the gun on the bullets?

<p>$F = nmv$ (D)</p> Signup and view all the answers

Object A and object B collide. The only force on A during the collision is due to contact with object B. Which of the following statements is true regarding the forces on the objects?

<p>The forces on object A and object B are equal in magnitude and opposite in direction. (A)</p> Signup and view all the answers

A ball of mass (m) is dropped onto a floor. The ball's speed just before hitting the floor is (v_1) and its speed right after is (v_2). If the collision lasts for time (\Delta t), what is the average force exerted by the floor on the ball?

<p>$F = \frac{m(v_1 + v_2)}{\Delta t}$ (A)</p> Signup and view all the answers

A system consists of two objects moving along the x-axis. Object 1 has mass (m_1) and velocity (v_1), and object 2 has mass (m_2) and velocity (v_2). What is the total kinetic energy of the system in the center of mass frame?

<p>$\frac{1}{2} \mu (v_1 - v_2)^2$, where $\mu = \frac{m_1 m_2}{m_1 + m_2}$ (C)</p> Signup and view all the answers

A ball of mass (m) is attached to a string of length (L) and is released from a horizontal position. At the bottom of its swing, it collides elastically with a block of mass (M) resting on a frictionless surface. What is the velocity of the block immediately after the collision?

<p>$v = \sqrt{2gL} \frac{2m}{m + M}$ (A)</p> Signup and view all the answers

A firecracker is placed inside a pumpkin of mass (M) at rest on a frictionless surface. When the firecracker explodes, it breaks the pumpkin into two pieces, one with mass (m_1) and velocity (v_1) and the other with mass (m_2). What is the kinetic energy released by the explosion?

<p>$\frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2$ (C)</p> Signup and view all the answers

A spring with spring constant (k) is compressed a distance (x) from its equilibrium position. A ball of mass (m) is placed against the spring. The spring is released on a frictionless surface. What is the velocity of the ball when it leaves the spring?

<p>$x \sqrt{\frac{k}{m}}$ (C)</p> Signup and view all the answers

A cart of mass (m) is moving on a frictionless track with velocity (v). A package of mass (m/2) is dropped vertically onto the moving cart. What is the new velocity of the cart?

<p>$2v/3$ (A)</p> Signup and view all the answers

In a perfectly inelastic collision between two objects where one object is initially at rest, what percentage of the initial kinetic energy is lost if the two objects have equal mass?

<p>50% (C)</p> Signup and view all the answers

A block of mass (m) slides down a frictionless ramp of height (h) and then collides elastically with an identical block at rest on a horizontal surface. How far does the second block travel after the collision if the coefficient of kinetic friction between the block and the surface is (\mu_k)?

<p>$\frac{h}{\mu_k}$ (B)</p> Signup and view all the answers

Which of the following formulas correctly represents the calculation of momentum?

<p>$p = mv$ (D)</p> Signup and view all the answers

What is the standard SI unit for momentum?

<p>kg·m/s (D)</p> Signup and view all the answers

Momentum is classified as which type of physical quantity?

<p>Vector (D)</p> Signup and view all the answers

How is impulse related to the momentum of an object?

<p>Impulse is equal to the change in momentum. (D)</p> Signup and view all the answers

According to Newton's second law, when expressed in terms of momentum, what is the net force acting on an object equal to?

<p>Rate of change of momentum (C)</p> Signup and view all the answers

Consider two objects with different masses moving at the same velocity. Which object will have greater momentum and why?

<p>The heavier object, because momentum is directly proportional to mass. (A)</p> Signup and view all the answers

What is the primary difference between kinetic energy and momentum in terms of their dependence on velocity?

<p>Momentum depends linearly on velocity, while kinetic energy depends on the square of velocity. (B)</p> Signup and view all the answers

In physics, what defines an isolated system in the context of conservation of momentum?

<p>A system where the net external force acting on it is zero. (C)</p> Signup and view all the answers

How do safety devices like airbags utilize the concept of impulse to reduce injury during a car crash?

<p>By increasing the time over which the force is applied. (A)</p> Signup and view all the answers

In which type of collision is kinetic energy always conserved in addition to momentum?

<p>Elastic collisions (B)</p> Signup and view all the answers

Why does a mosquito, despite its potentially high speed, exert less force upon impact compared to a falcon moving at a slower speed?

<p>Due to the mosquito's significantly smaller mass. (D)</p> Signup and view all the answers

According to Newton's second law in terms of momentum, if the net force acting on an object is zero, what must be true about the object's momentum?

<p>It must be constant. (C)</p> Signup and view all the answers

During a collision between two objects in a closed system, if some kinetic energy is converted into heat and sound, what type of collision is it classified as?

<p>Inelastic collision (A)</p> Signup and view all the answers

If the impulse applied to an object is held constant, how will increasing the duration of the force affect the magnitude of the force?

<p>Decrease the magnitude of the force. (A)</p> Signup and view all the answers

Under what condition is the total momentum of a system of interacting objects conserved?

<p>When there is no net external force acting on the system. (B)</p> Signup and view all the answers

Which of the following scenarios best illustrates the concept of impulse?

<p>A baseball being hit by a bat. (D)</p> Signup and view all the answers

If two objects have the same momentum, which of the following must be true?

<p>The product of their mass and velocity must be equal. (A)</p> Signup and view all the answers

What is the direction of momentum for an object moving in a circular path at a constant speed?

<p>Tangent to the circular path. (A)</p> Signup and view all the answers

Consider a system of two interacting objects. If the net external force on the system is zero, what can be said about the total momentum of the system?

<p>It will remain constant. (A)</p> Signup and view all the answers

In which type of collision is kinetic energy conserved?

<p>Elastic collision. (A)</p> Signup and view all the answers

Which of the following is a vector quantity?

<p>Impulse (D)</p> Signup and view all the answers

If the time of impact in a collision is increased, and the change in momentum remains the same, what happens to the average force exerted?

<p>It decreases. (B)</p> Signup and view all the answers

What is the relationship between impulse and change in momentum?

<p>Impulse is equal to the change in momentum. (B)</p> Signup and view all the answers

In a perfectly inelastic collision, what happens to the kinetic energy of the system?

<p>It decreases. (C)</p> Signup and view all the answers

Which of Newton's Laws is most directly related to the concept of momentum conservation in a closed system?

<p>Newton's Third Law of Motion (C)</p> Signup and view all the answers

What is the SI unit of impulse?

<p>Ns (A)</p> Signup and view all the answers

How does doubling the mass of an object affect its momentum if its velocity remains constant?

<p>Momentum is doubled. (A)</p> Signup and view all the answers

A mosquito and a truck are both moving at the same kinetic energy. Which one has a greater momentum?

<p>The truck (B)</p> Signup and view all the answers

Consider a collision between two billiard balls on a frictionless table. Which of the following is conserved?

<p>Both momentum and kinetic energy (D)</p> Signup and view all the answers

According to Newton's Second Law in terms of momentum, if the net force on an object is constant, what can be said about the rate of change of its momentum?

<p>It is constant and non-zero. (C)</p> Signup and view all the answers

In a force-time graph, what physical quantity is represented by the area under the curve?

<p>Impulse (A)</p> Signup and view all the answers

What is the primary purpose of safety features like airbags in vehicles in terms of impulse and momentum?

<p>To increase the time of impact, thus reducing the force of impact. (D)</p> Signup and view all the answers

Which of the following scenarios is an example of an inelastic collision?

<p>A clay ball hitting a wall and sticking to it. (B)</p> Signup and view all the answers

If a system is not isolated, which of the following statements is necessarily true?

<p>External forces are acting on the system. (C)</p> Signup and view all the answers

How does the momentum of an object change as it falls freely under gravity (ignoring air resistance)?

<p>It increases at a constant rate. (C)</p> Signup and view all the answers

Two cars of different masses are moving with the same momentum. If the same braking force is applied to both, which car will take longer to stop?

<p>Both cars will take the same time to stop (C)</p> Signup and view all the answers

A ball is thrown vertically upwards. At the highest point of its trajectory, what is its momentum?

<p>Zero (A)</p> Signup and view all the answers

Which of the following best describes an 'isolated system' in physics?

<p>A system where the net external force acting on it is zero. (A)</p> Signup and view all the answers

If the total momentum of a system is conserved, does it necessarily mean that the kinetic energy of the system is also conserved?

<p>No, momentum conservation does not guarantee kinetic energy conservation. (D)</p> Signup and view all the answers

Two objects move towards each other with equal and opposite momenta. What is the total momentum of the system?

<p>Zero (D)</p> Signup and view all the answers

A rocket in space expels gas to move forward. Which principle explains this motion?

<p>Conservation of momentum (A)</p> Signup and view all the answers

What is the change in momentum of an object if a net impulse of -10 Ns is applied to it?

<p>-10 kgm/s (B)</p> Signup and view all the answers

In which type of collision do objects bounce off each other?

<p>Both elastic and inelastic collisions (D)</p> Signup and view all the answers

If the net force acting on an object is zero, what is true about its momentum?

<p>It must be constant. (D)</p> Signup and view all the answers

For an object of constant mass, how is Newton's second law expressed in terms of momentum related to its more common form ($F=ma$)?

<p>They are equivalent because acceleration is the rate of change of velocity. (B)</p> Signup and view all the answers

Consider a scenario where a small car and a large truck collide head-on. According to the conservation of momentum, which vehicle experiences a greater magnitude of change in momentum?

<p>Both experience the same magnitude of change in momentum (D)</p> Signup and view all the answers

A tennis ball is dropped from a height and bounces back up. Compare the impulse exerted by the floor on the ball to the impulse exerted by the ball on the floor.

<p>Impulses are equal in magnitude but opposite in direction. (C)</p> Signup and view all the answers

Why is it generally safer to land on a soft surface like a mattress compared to a hard surface like concrete when jumping from a height?

<p>The time of impact is increased on a soft surface, reducing the impact force. (C)</p> Signup and view all the answers

Consider two identical objects, one moving at velocity $v$ and the other at rest. They undergo a perfectly inelastic collision. What is the velocity of the combined mass after the collision?

<p>$v/2$ (C)</p> Signup and view all the answers

A truck with twice the mass of a car is moving at half the speed of the car. How does the momentum of the truck compare to the momentum of the car?

<p>The truck and the car have the same momentum. (D)</p> Signup and view all the answers

For a system of particles, the center of mass velocity remains constant if:

<p>The net external force on the system is zero. (A)</p> Signup and view all the answers

Which of the following is true regarding momentum?

<p>Momentum is the product of mass and velocity and is a vector quantity. (C)</p> Signup and view all the answers

A rubber ball and a glass ball of the same mass are dropped from the same height onto a concrete floor. The glass ball shatters, while the rubber ball bounces. Which ball experiences a greater magnitude of impulse from the floor?

<p>The rubber ball (C)</p> Signup and view all the answers

A bullet is fired from a rifle. Consider the system of the bullet and the rifle. Which of the following is true during the firing process?

<p>The total momentum of the bullet-rifle system is conserved. (A)</p> Signup and view all the answers

If kinetic energy is not conserved in a collision, where does the 'lost' kinetic energy typically go?

<p>It is converted into other forms of energy, such as heat, sound, or deformation. (A)</p> Signup and view all the answers

Which of the following pairs of quantities are both required to determine the momentum of an object?

<p>Mass and velocity (D)</p> Signup and view all the answers

What is the correct unit for impulse in the International System of Units (SI)?

<p>Ns (A)</p> Signup and view all the answers

Impulse is most directly related to which of the following physical quantities?

<p>Change in momentum (C)</p> Signup and view all the answers

A net force acting on an object causes a change in the object's momentum. According to Newton's second law expressed in terms of momentum, in which direction does this change occur?

<p>In the same direction as the net force. (D)</p> Signup and view all the answers

Consider two objects, A and B, with different masses. If both objects experience the same impulse, which object will undergo a larger change in velocity?

<p>Object A, if it has a smaller mass. (A)</p> Signup and view all the answers

In which scenario is the total momentum of a system most likely to be conserved?

<p>Two billiard balls colliding on a frictionless table. (D)</p> Signup and view all the answers

During a head-on collision between two cars, momentum is conserved. Why is it still safer for passengers if both cars are designed to crumple upon impact?

<p>Crumpling increases the time of impact, reducing the average force. (D)</p> Signup and view all the answers

In an inelastic collision, which of the following statements is always true?

<p>Only momentum is conserved, but kinetic energy is not. (D)</p> Signup and view all the answers

A mosquito and a falcon are flying at the same velocity. Which statement correctly compares their momenta and kinetic energies?

<p>The falcon has greater momentum and greater kinetic energy. (B)</p> Signup and view all the answers

A ball is dropped from a height and bounces off the floor. Considering the ball and Earth as a system, what happens to the total momentum of this system during the collision?

<p>The total momentum remains constant. (D)</p> Signup and view all the answers

Two objects collide. If the total kinetic energy of the system after the collision is less than before, but momentum is conserved, what type of collision is it?

<p>Inelastic collision (C)</p> Signup and view all the answers

A person is standing on frictionless ice and throws a heavy ball horizontally. Which of the following best describes the person's motion after throwing the ball?

<p>The person will move in the opposite direction of the ball. (C)</p> Signup and view all the answers

Consider a perfectly isolated system. Which of the following statements is always true regarding the total momentum and total kinetic energy of this system?

<p>Total momentum is always conserved, but total kinetic energy may not be. (C)</p> Signup and view all the answers

Two objects with different masses have the same momentum. If the same braking force is applied to each object to bring them to rest, which object will require a longer stopping time?

<p>Both objects will require the same stopping time. (D)</p> Signup and view all the answers

Imagine a scenario where a small car and a large truck collide head-on and come to a complete stop immediately after impact. Considering both vehicles as a system, what can be definitively stated about the total momentum of the car-truck system just before the collision?

<p>The total momentum was necessarily zero. (D)</p> Signup and view all the answers

Which of the following is the correct formula for calculating momentum?

<p>$p = mv$ (D)</p> Signup and view all the answers

What type of quantity is momentum?

<p>Vector quantity (B)</p> Signup and view all the answers

In what unit is momentum typically measured in the SI system?

<p>kgm/s (D)</p> Signup and view all the answers

What is impulse a measure of?

<p>The change in momentum of an object (A)</p> Signup and view all the answers

Which formula correctly represents impulse?

<p>$J = m\Delta v$ (A)</p> Signup and view all the answers

If the net force acting on an object is zero, what can be said about the momentum of the object?

<p>The momentum will remain constant. (A)</p> Signup and view all the answers

In a closed system, when is the total momentum conserved?

<p>When the net external force is zero. (B)</p> Signup and view all the answers

What is the key difference between elastic and inelastic collisions in terms of kinetic energy?

<p>Kinetic energy is conserved in elastic collisions but not necessarily in inelastic collisions. (A)</p> Signup and view all the answers

Why do airbags in cars reduce injuries during collisions, in terms of impulse?

<p>Airbags increase the time of impact, reducing the average force. (B)</p> Signup and view all the answers

Consider a mosquito and a falcon with the same kinetic energy. Which has greater momentum?

<p>The falcon (C)</p> Signup and view all the answers

In which type of collision is momentum always conserved?

<p>Both elastic and inelastic collisions (B)</p> Signup and view all the answers

If two objects have the same magnitude of momentum, which of the following must be true?

<p>The product of their mass and velocity magnitudes must be equal. (C)</p> Signup and view all the answers

For an object with constant mass, Newton's second law in terms of momentum ($F = \frac{\Delta p}{\Delta t}$) is equivalent to which familiar form?

<p>$F = ma$ (C)</p> Signup and view all the answers

A rubber ball and a steel ball of the same mass are dropped onto a steel plate from the same height. Which ball experiences a greater impulse from the steel plate?

<p>The rubber ball (B)</p> Signup and view all the answers

Consider a system of two colliding objects. If the total kinetic energy of the system after the collision is less than before, but momentum is conserved, what type of collision is it?

<p>Inelastic collision (A)</p> Signup and view all the answers

What is the direction of impulse relative to the force applied?

<p>In the same direction as the force (D)</p> Signup and view all the answers

Which of the following is an example of an elastic collision (idealized)?

<p>Billiard balls colliding. (D)</p> Signup and view all the answers

What is the total momentum of a system of two objects moving towards each other with equal and opposite momenta?

<p>Zero (B)</p> Signup and view all the answers

In an isolated system, if a moving object collides with a stationary object and they stick together, what happens to the total momentum of the system?

<p>Total momentum remains constant. (A)</p> Signup and view all the answers

Which quantity is defined as the product of force and the time interval for which the force is applied?

<p>Impulse (B)</p> Signup and view all the answers

Consider a head-on collision between a small car and a large truck. According to the conservation of momentum, which vehicle experiences a greater magnitude of change in momentum?

<p>Both experience the same magnitude of change in momentum (A)</p> Signup and view all the answers

If the net external force on a system is zero, what can be said about the total momentum of the system?

<p>It must remain constant. (A)</p> Signup and view all the answers

Which of the following scenarios describes an isolated system in physics?

<p>Two billiard balls colliding on a frictionless table. (D)</p> Signup and view all the answers

A mosquito and a truck are both moving at the same velocity. Which one has a greater momentum?

<p>The truck (B)</p> Signup and view all the answers

For a system of particles, under what condition does the center of mass velocity remain constant?

<p>When the net external force on the system is zero. (D)</p> Signup and view all the answers

A firecracker is placed inside a pumpkin of mass (M) at rest on a frictionless surface. When the firecracker explodes, it breaks the pumpkin into two pieces. What is conserved in this process?

<p>Momentum only (D)</p> Signup and view all the answers

A cart of mass (m) is moving on a frictionless track with velocity (v). A package of mass (m/2) is dropped vertically onto the moving cart. What happens to the velocity of the cart after the package is dropped?

<p>Velocity decreases to (2v/3). (C)</p> Signup and view all the answers

In a perfectly inelastic collision between two objects where one object is initially at rest, and the objects have equal mass, what percentage of the initial kinetic energy is lost?

<p>50% (D)</p> Signup and view all the answers

Which of the following is the correct formula for calculating impulse?

<p>$J = F \Delta t$ (C)</p> Signup and view all the answers

If two objects move in opposite directions, how is the net momentum of the system calculated?

<p>By subtracting their momenta. (D)</p> Signup and view all the answers

According to Newton's Second Law expressed in terms of momentum, what is the relationship between net force ($F_{\text{net}}$), change in momentum ($\Delta p$), and change in time ($\Delta t$)?

<p>$F_{\text{net}} = \frac{\Delta p}{\Delta t}$ (C)</p> Signup and view all the answers

In a closed system, what is the primary condition for the total momentum to remain constant?

<p>The net external force acting on the system must be zero. (C)</p> Signup and view all the answers

A 5 kg object's velocity changes from 3 m/s to the right to 2 m/s to the left. What is the magnitude and direction of the impulse on the object?

<p>25 Ns, to the left (A)</p> Signup and view all the answers

Consider a collision where two objects stick together after impact. Which of the following is true about the kinetic energy of the system?

<p>Kinetic energy is decreased. (A)</p> Signup and view all the answers

In a system consisting of two individuals on ice pushing against each other, what best describes how the conservation of momentum applies?

<p>The total momentum of the system remains zero, as each person's momentum change is equal and opposite. (C)</p> Signup and view all the answers

A ball is dropped from a height and bounces off the floor. Considering the ball and Earth as a system, what happens to the system's total momentum during the collision?

<p>The total momentum changes because an external force (gravity) consistently acts on it. (A)</p> Signup and view all the answers

Two cars of different masses are moving with the same kinetic energy. If the same braking force is applied to both, which car will take longer to stop?

<p>The car with more mass will take longer to stop. (C)</p> Signup and view all the answers

A cart of mass $m$ is moving on a frictionless track with velocity $v$. A package of mass $\frac{m}{2}$ is dropped vertically onto the moving cart. Which of the following is the new velocity of the cart?

<p>$\frac{2}{3}v$ (A)</p> Signup and view all the answers

In an elastic collision between two objects of unequal masses, which of the following quantities is/are conserved?

<p>Both kinetic energy and momentum (A)</p> Signup and view all the answers

A 1 kg mass moving at 1 m/s collides head on with a 2 kg mass at rest. If the collision is perfectly inelastic, how much kinetic energy is lost in the collision?

<p>$\frac{1}{3}$ J (C)</p> Signup and view all the answers

An object of mass $m$ is moving with velocity $v$. It collides with another object of mass $2m$ at rest. After the collision, the first object is moving with a velocity of $-\frac{v}{3}$. If the collision is one-dimensional, calculate the coefficient of restitution.

<p>$\frac{1}{2}$ (C)</p> Signup and view all the answers

Flashcards

Momentum

A measure of an object's motion; how hard it is to stop.

Impulse

The change in momentum when a force is applied over time.

Momentum Formula

p = mv, where p is momentum, m is mass, and v is velocity.

Impulse Formula

J = FΔt, where J is impulse, F is force, and Δt is the time interval.

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Vector Quantity

A quantity with both magnitude and direction.

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Linear Momentum

An object's quantity of motion.

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Change in Momentum

The difference between final and initial momentum.

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Impulse

The change in momentum due to a force applied over time.

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Law of Conservation of Momentum

In a closed system, total momentum remains constant if no external forces act.

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Newton's Second Law (Momentum)

F_net = Δp/Δt: Net force equals the rate of change of momentum.

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Net Force and Motion Increase

Increase in motion direction occurs when the net force acts in the same direction as the object’s motion.

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Net Force and Motion Decrease

Decrease in motion occurs when the net force acts opposite to the direction of motion.

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Impulse

Represents a force's ability to change an object's momentum.

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Impulse Formula

J = F_net * Δt: Impulse equals net force multiplied by the time interval.

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Impulse-Momentum Theorem

F_net * Δt = m * Δv: Relates impulse to the change in momentum.

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Impulse and Safety

Increase the time over which impact force is applied.

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System (Physics)

A collection of objects considered for analysis.

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Internal Forces

Forces between objects within the system.

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External Forces

Forces originating from outside the system.

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Isolated System

A system where the net external force is zero.

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Conservation of Linear Momentum

Total linear momentum remains constant if the net external force is zero.

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Elastic Collisions

Momentum and kinetic energy are conserved.

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Inelastic Collisions

Momentum is conserved, but kinetic energy is not.

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Moon's Momentum

The moon's mass and velocity keeps it in orbit.

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Kinetic Energy

Energy they carry.

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Momentum Calculations

Requires proper unit conversion.

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Momentum as a Vector

Essential for vector addition.

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Example of Momentum

A heavy truck moving quickly has more momentum.

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Momentum direction

Aligns with the object's velocity direction.

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Same direction momentum

Add directly.

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Opposite direction momentum

Subtract from each other.

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Vector Diagrams & Momentum

Show the change in momentum.

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Object's Momentum Change

The direction and magnitude of the net force applied.

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Arrestor Beds

Lengthen the stopping time.

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Impulse helps calculate

The force exerted on an object.

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Force-Time Graphs

Force applied over time leads to changes in momentum.

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Elastic Collision Characteristics

The objects separate and retain their individual kinetic energies.

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Inelastic Collision Characteristics

Objects stick together or change shape.

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Pre-Collision Analysis

By summing the momenta of all objects involved.

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Post-Collision Analysis

Re-evaluate the total momentum.

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What is Momentum?

Product of mass and velocity, a measure of how hard it is to stop a moving object.

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What is Impulse?

The change in momentum, resulting from a force acting over a period of time.

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What is Δv?

The change in velocity during impulse.

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What is Linear Momentum?

Momentum of an object moving in a straight line.

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What is Net Momentum?

The sum of individual momenta of multiple objects.

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What are Vector Diagrams?

Used to show momentum changes of objects.

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What is an Isolated System?

An object that does not exchange any matter with its surroundings

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What is an Elastic Collision?

When both momentum and kinetic energy are conserved.

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What is an Inelastic Collision?

Where momentum is conserved, but kinetic energy is not.

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What is Time in Impulse?

Airbags and seatbelts increase this to reduce impact force.

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What is Newton’s Cradle?

Demonstrates momentum and energy transfer between objects.

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Conservation of Momentum

The total linear momentum within the system remains constant.

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Study Notes

  • Momentum and impulse are essential for understanding how objects move and interact with forces.

Understanding Momentum

  • Momentum measures an object's motion and resistance to stopping.
  • Momentum depends on mass and velocity, with the formula (p = mv).
    • (p) is momentum in kg·m/s.
    • (m) is mass in kg.
    • (v) is velocity in m/s.
  • Momentum is a vector quantity, having both magnitude and direction, pointing in the direction of the object's velocity.

Understanding Impulse

  • Impulse is the change in momentum when a force is applied over time.
  • Greater force or longer application time results in a greater change in momentum.
  • Impulse is calculated using (J = F \Delta t).
    • (J) is impulse in N·s.
    • (F) is force in N.
    • (\Delta t) is the time interval in seconds.
  • Impulse is a vector quantity, acting in the direction of the applied force.
  • Impulse causes a change in an object's momentum, summarized as (J = \Delta p = m \Delta v).

Contextual Understanding

  • Momentum and impulse can be observed in everyday situations, such as the impact of a mosquito versus a falcon.
  • The Moon’s orbit is maintained due to its significant momentum.

Kinetic Energy vs. Momentum

  • Kinetic energy relates to the ability to do work, calculated as (KE = \frac{1}{2} mv^2).
  • Kinetic energy depends on the square of the velocity.
  • Momentum is the product of mass and velocity ((p = mv)).
  • Kinetic energy indicates the energy objects carry, while momentum describes their motion.

Linking Concepts

  • Accurate momentum calculations require proper unit conversion.
  • Solving momentum problems often involves rearranging equations.
  • Understanding vector addition is essential when multiple objects or forces are involved.
  • Momentum is closely linked to Newton's laws of motion.

Introduction to Momentum

  • Momentum, denoted as (\vec{p}), represents the quantity of motion an object possesses.
  • Momentum is defined as the product of mass ((m)) and velocity ((\vec{v})), given by (\vec{p} = m\vec{v}).
  • Momentum is a vector quantity, aligning with the object's velocity direction.

Linear Momentum

  • Linear momentum is the momentum of an object moving in a straight line.
  • It measures how difficult it is to stop a moving object.
  • Larger mass or higher velocity results in greater momentum.

Calculating Momentum

  • Momentum is calculated using the formula (\vec{p} = m\vec{v}).
  • The SI unit for momentum is kg·m/s.

Vector Nature of Momentum

  • Momentum follows the rules of vector addition.
  • If objects move in the same direction, their momenta add directly.
  • If objects move in opposite directions, their momenta subtract.

Change in Momentum ((\Delta \vec{p}))

  • The change in momentum is the difference between final and initial momentum: (\Delta \vec{p} = \vec{p}{\text{final}} - \vec{p}{\text{initial}}).
  • This change is related to the force applied and the time over which it acts.

Vector Diagrams and Momentum

  • Vector diagrams illustrate momentum changes before and after collisions.
  • Change in momentum is shown by connecting the tips of initial and final momentum vectors.

Applications in Real-World Scenarios

  • Momentum is critical in understanding vehicle collisions and sports activities.

Impulse and Momentum Conservation

  • Impulse is the change in momentum due to a force applied over time: (\vec{J} = \vec{F} \Delta t = \Delta \vec{p}).
  • The law of conservation of momentum states that in a closed system, the total momentum before an event equals the total momentum after, assuming no external forces.

Newton's Second Law Revisited

  • Newton's second law relates force, motion, and momentum.
  • The law states that the net force on an object equals the rate of change of its momentum.

Mathematical Expression

  • In terms of momentum, Newton's second law is (F_{\text{net}} = \frac{\Delta p}{\Delta t}).
    • ( F_{\text{net}} ) is the net force.
    • ( \Delta p ) is the change in momentum.
    • ( \Delta t ) is the time interval.

Relation Between Net Force and Change in Momentum

  • The change in momentum depends on the net force's direction and magnitude.
  • Force in the direction of motion increases momentum.
  • Force opposite to the direction of motion decreases momentum.
  • Force applied in the opposite direction can reverse motion.

Overview of Impulse

  • Impulse describes the effect of a force applied over a specific time interval.
  • It represents the force's ability to change an object's momentum.

Mathematical Formulation

  • The formula for impulse (( J )) is (J = F_{\text{net}} \Delta t).
    • ( J ) is the impulse.
    • ( F_{\text{net}} ) is the net force.
    • ( \Delta t ) is the time interval.
  • The impulse-momentum theorem links impulse with the change in momentum (( \Delta p )): (F_{\text{net}} \Delta t = m \Delta v).
    • ( m ) is the object's mass.
    • ( \Delta v ) is the change in velocity.

Impulse in One-Dimensional Motion

  • In one-dimensional motion, impulse helps calculate force, time duration, and the change in momentum.

Impulse and Safety

  • Airbags and seatbelts increase the time of impact, reducing force during collisions.
  • Arrestor beds lengthen stopping time, reducing force and potential injuries.

Worked Examples

  • Impulse can determine how long a force was applied based on the change in velocity.
  • Impulse explains how hitting a ball with a bat transfers force and changes the ball’s momentum.
  • Force-time graphs determine impulse by analyzing the area under the curve.

Understanding Systems in Physics

  • System: A collection of objects considered for analysis.
  • Environment: Everything outside the system.
  • Internal forces: Forces between objects within the system.
  • External forces: Forces originating from outside the system.
  • Isolated system: A system where net external forces are zero.

Conservation of Linear Momentum

  • Principle: The total linear momentum of an isolated system remains constant if the net external force is zero.

Momentum in Collisions

  • Application: In a one-dimensional scenario, apply conservation of linear momentum by assigning a positive direction and considering the momentum contributions of all objects before and after the collision.

Elastic vs. Inelastic Collisions

  • Elastic Collisions: Both momentum and kinetic energy are conserved; objects bounce off each other without lasting deformation.
  • Inelastic Collisions: Momentum is conserved, but kinetic energy is not; objects may stick together or deform, converting kinetic energy into other forms.

Conservation of Momentum: Detailed Explanation

  • Systems and Isolation in Physics:
    • System Definition: A group of interacting entities forming an integrated whole.
    • Isolated System: A system that does not exchange matter with its surroundings and is not influenced by external forces.
  • Conservation of Momentum Principle:
    • Principle Statement: The total linear momentum of an isolated system remains constant regardless of internal interactions.
    • Application: Applied in scenarios where two or more objects interact, such as collisions or explosions.

Real-World Examples:

  • Billiard Balls: Illustrate how momentum is conserved during collisions.
  • Newton’s Cradle: Demonstrates momentum conservation and energy transfer.
  • Elastic vs. Inelastic Collisions:
    • Elastic Collisions: Conserve both momentum and kinetic energy; objects separate post-collision and retain individual kinetic energies.
    • Inelastic Collisions: Momentum is conserved, but kinetic energy is not; objects may stick together or change shape, with some energy converted into other forms.

Analyzing Collisions: Steps and Examples

  • Pre-collision Analysis: Assess the system's total momentum by summing the momenta of all objects involved.
  • Post-collision Analysis: Reevaluate total momentum after the interaction and compare with pre-collision momentum.
  • Identifying Collision Type:
    • Elastic collisions: Verify if total kinetic energy remains the same before and after the collision.
    • Inelastic collisions: Check for a decrease in total kinetic energy post collision.

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