Podcast
Questions and Answers
What is the relationship between impulse and momentum according to the impulse-momentum theorem?
What is the relationship between impulse and momentum according to the impulse-momentum theorem?
Which of the following is a vector quantity?
Which of the following is a vector quantity?
In the context of the impulse-momentum theorem, what is the significance of the time of contact (∆t)?
In the context of the impulse-momentum theorem, what is the significance of the time of contact (∆t)?
Why is it difficult to measure the net average force (σ 𝐹) during a collision directly?
Why is it difficult to measure the net average force (σ 𝐹) during a collision directly?
Signup and view all the answers
In the example of the baseball and the bat, why is the weight of the ball neglected during the impulse calculation?
In the example of the baseball and the bat, why is the weight of the ball neglected during the impulse calculation?
Signup and view all the answers
What is the SI unit of impulse?
What is the SI unit of impulse?
Signup and view all the answers
How does the impulse-momentum theorem explain the launch of a space shuttle?
How does the impulse-momentum theorem explain the launch of a space shuttle?
Signup and view all the answers
What is the correct formula for impulse?
What is the correct formula for impulse?
Signup and view all the answers
What is the formula for the gravitational potential energy PE of an object?
What is the formula for the gravitational potential energy PE of an object?
Signup and view all the answers
Which of the following is NOT a correct unit for work?
Which of the following is NOT a correct unit for work?
Signup and view all the answers
If a gymnast leaves the trampoline at an initial height of 1.20 m and reaches a maximum height of 4.80 m before falling back down, what is the equation for the initial speed of the gymnast?
If a gymnast leaves the trampoline at an initial height of 1.20 m and reaches a maximum height of 4.80 m before falling back down, what is the equation for the initial speed of the gymnast?
Signup and view all the answers
What is the formula to calculate the center of mass (xcm) of a system of two particles?
What is the formula to calculate the center of mass (xcm) of a system of two particles?
Signup and view all the answers
What is the formula for work done against gravity?
What is the formula for work done against gravity?
Signup and view all the answers
What is the formula for work done by a constant force?
What is the formula for work done by a constant force?
Signup and view all the answers
If m1 = m2 = m, what is the formula for the center of mass of a system of two particles?
If m1 = m2 = m, what is the formula for the center of mass of a system of two particles?
Signup and view all the answers
What does 'Wgravity = mg (ho - hf)' represent?
What does 'Wgravity = mg (ho - hf)' represent?
Signup and view all the answers
What is the calculated force exerted by the boy on the lever?
What is the calculated force exerted by the boy on the lever?
Signup and view all the answers
Using the given data, what is the weight of the boy if g is 10 m/s²?
Using the given data, what is the weight of the boy if g is 10 m/s²?
Signup and view all the answers
What is the force exerted by the fulcrum when the forces are balanced?
What is the force exerted by the fulcrum when the forces are balanced?
Signup and view all the answers
Which of the following describes the conditions needed to find the magnitude of forces on the bridge?
Which of the following describes the conditions needed to find the magnitude of forces on the bridge?
Signup and view all the answers
How far along the bridge does the hiker stop relative to its total length?
How far along the bridge does the hiker stop relative to its total length?
Signup and view all the answers
What is the net force acting on the diving board in the first example when it is in equilibrium?
What is the net force acting on the diving board in the first example when it is in equilibrium?
Signup and view all the answers
Why does the force F1 in the first example point downwards?
Why does the force F1 in the first example point downwards?
Signup and view all the answers
In the second example, why is the weight of the board ignored?
In the second example, why is the weight of the board ignored?
Signup and view all the answers
What is the relationship between the torque produced by F2 and the torque produced by W in the first example?
What is the relationship between the torque produced by F2 and the torque produced by W in the first example?
Signup and view all the answers
In the first example, what is the lever arm for the weight W?
In the first example, what is the lever arm for the weight W?
Signup and view all the answers
If the woman in the first example moved closer to the fulcrum, what would happen to the force F2?
If the woman in the first example moved closer to the fulcrum, what would happen to the force F2?
Signup and view all the answers
What is the concept used in the solution of the examples for determining the forces on the board?
What is the concept used in the solution of the examples for determining the forces on the board?
Signup and view all the answers
In the second example, if the boy moved closer to the fulcrum, what would happen to the mass of the boy required to balance the teeter-totter?
In the second example, if the boy moved closer to the fulcrum, what would happen to the mass of the boy required to balance the teeter-totter?
Signup and view all the answers
A car with a mass of 1000 kg is traveling at a speed of 20 m/s. What is the car's momentum?
A car with a mass of 1000 kg is traveling at a speed of 20 m/s. What is the car's momentum?
Signup and view all the answers
A 0.5 kg ball is thrown vertically upward with an initial velocity of 10 m/s. What is the ball's momentum at its highest point?
A 0.5 kg ball is thrown vertically upward with an initial velocity of 10 m/s. What is the ball's momentum at its highest point?
Signup and view all the answers
A 2 kg object is moving at a constant velocity of 5 m/s. What is the net force acting on the object?
A 2 kg object is moving at a constant velocity of 5 m/s. What is the net force acting on the object?
Signup and view all the answers
A 1.5 kg object has a momentum of 6 kg*m/s. What is the object's velocity?
A 1.5 kg object has a momentum of 6 kg*m/s. What is the object's velocity?
Signup and view all the answers
A 2 kg object moving at 4 m/s collides head-on with a stationary 1 kg object. After the perfectly elastic collision, what is the velocity of the 1 kg object?
A 2 kg object moving at 4 m/s collides head-on with a stationary 1 kg object. After the perfectly elastic collision, what is the velocity of the 1 kg object?
Signup and view all the answers
If the momentum of a car is doubled while its mass remains constant, what happens to its velocity?
If the momentum of a car is doubled while its mass remains constant, what happens to its velocity?
Signup and view all the answers
A 1000 kg car is traveling at 20 m/s when the brakes are applied. The car comes to a stop in 5 seconds. What is the average force exerted by the brakes on the car?
A 1000 kg car is traveling at 20 m/s when the brakes are applied. The car comes to a stop in 5 seconds. What is the average force exerted by the brakes on the car?
Signup and view all the answers
Which of these statements about momentum is TRUE?
Which of these statements about momentum is TRUE?
Signup and view all the answers
What is the formula for the position vector of the center of mass of a system of particles?
What is the formula for the position vector of the center of mass of a system of particles?
Signup and view all the answers
If the position vector of the center of mass is given by $\frac{\sum_{v=1}^{N} m_v r_v}{M}$, what is the formula for the velocity of the center of mass?
If the position vector of the center of mass is given by $\frac{\sum_{v=1}^{N} m_v r_v}{M}$, what is the formula for the velocity of the center of mass?
Signup and view all the answers
What is the formula for the x-coordinate of the center of mass in a system of particles?
What is the formula for the x-coordinate of the center of mass in a system of particles?
Signup and view all the answers
A system consists of three particles with masses 2kg, 3kg, and 5kg. Their position vectors are (1,2,3), (4,5,6), and (7,8,9) respectively. What is the y-coordinate of the center of mass of the system?
A system consists of three particles with masses 2kg, 3kg, and 5kg. Their position vectors are (1,2,3), (4,5,6), and (7,8,9) respectively. What is the y-coordinate of the center of mass of the system?
Signup and view all the answers
The center of mass of a system of particles is a point that:
The center of mass of a system of particles is a point that:
Signup and view all the answers
If the net external force acting on a system of particles is zero, what can be said about the acceleration of the center of mass?
If the net external force acting on a system of particles is zero, what can be said about the acceleration of the center of mass?
Signup and view all the answers
The torque on a rigid object is:
The torque on a rigid object is:
Signup and view all the answers
Which of the following factors does NOT influence the magnitude of the torque on an object?
Which of the following factors does NOT influence the magnitude of the torque on an object?
Signup and view all the answers
Flashcards
Linear Momentum
Linear Momentum
The product of mass and velocity (p = mv) of an object.
Impulse-Momentum Theorem
Impulse-Momentum Theorem
The impulse of a net force equals the change in momentum of an object.
Impulse
Impulse
The product of average force and time (ΣF ∆t) during a collision.
SI Unit of Linear Momentum
SI Unit of Linear Momentum
Signup and view all the flashcards
Equation for Net Force
Equation for Net Force
Signup and view all the flashcards
Change in Momentum
Change in Momentum
Signup and view all the flashcards
Average Force during Collision
Average Force during Collision
Signup and view all the flashcards
Application of Impulse
Application of Impulse
Signup and view all the flashcards
Momentum
Momentum
Signup and view all the flashcards
Average Force
Average Force
Signup and view all the flashcards
Kinetic Energy
Kinetic Energy
Signup and view all the flashcards
Elastic Collision
Elastic Collision
Signup and view all the flashcards
Mass from Kinetic Energy
Mass from Kinetic Energy
Signup and view all the flashcards
Velocity of a Moving Object
Velocity of a Moving Object
Signup and view all the flashcards
Rain's Impact Force
Rain's Impact Force
Signup and view all the flashcards
Gravitational Potential Energy (PE)
Gravitational Potential Energy (PE)
Signup and view all the flashcards
Work (W)
Work (W)
Signup and view all the flashcards
Initial Speed (vo)
Initial Speed (vo)
Signup and view all the flashcards
Final Speed (vf)
Final Speed (vf)
Signup and view all the flashcards
Center of Mass (xcm)
Center of Mass (xcm)
Signup and view all the flashcards
System of Particles
System of Particles
Signup and view all the flashcards
Height (h)
Height (h)
Signup and view all the flashcards
Force (F)
Force (F)
Signup and view all the flashcards
Center of Mass
Center of Mass
Signup and view all the flashcards
Position Vector
Position Vector
Signup and view all the flashcards
Mass Sum
Mass Sum
Signup and view all the flashcards
Velocity of Center of Mass
Velocity of Center of Mass
Signup and view all the flashcards
Torque Definition
Torque Definition
Signup and view all the flashcards
Magnitude of Torque
Magnitude of Torque
Signup and view all the flashcards
Lever Arm
Lever Arm
Signup and view all the flashcards
Differentiation of Center of Mass
Differentiation of Center of Mass
Signup and view all the flashcards
Equilibrium Condition
Equilibrium Condition
Signup and view all the flashcards
Sum of Forces
Sum of Forces
Signup and view all the flashcards
Sum of Torques
Sum of Torques
Signup and view all the flashcards
Force at Fulcrum
Force at Fulcrum
Signup and view all the flashcards
Torque Calculation
Torque Calculation
Signup and view all the flashcards
Downward Force (F1)
Downward Force (F1)
Signup and view all the flashcards
Weight's Effect
Weight's Effect
Signup and view all the flashcards
Board Length in Torque
Board Length in Torque
Signup and view all the flashcards
Torque Equation
Torque Equation
Signup and view all the flashcards
Net Force Condition
Net Force Condition
Signup and view all the flashcards
Weight Calculation
Weight Calculation
Signup and view all the flashcards
Mass from Force
Mass from Force
Signup and view all the flashcards
Bridge Support Force
Bridge Support Force
Signup and view all the flashcards
Study Notes
Mechanics and Properties of Matter
- This module covers conservative forces, conservation of linear momentum, kinetic energy and work, potential energy, systems of particles, center of mass, torque, vector product, and moment.
Definition of a Conservative Force
- Version 1: A force is conservative if the work it does on a moving object is independent of the path between the initial and final positions.
- Version 2: A conservative force does no work on an object moving around a closed path, starting and ending at the same point.
- Example of conservative forces: Gravitational force, elastic force of a spring, electrical force of electrically charged particles.
- Gravity Work: Work done by gravity is calculated as Wgravity = mg(ho - h1).
Linear Momentum and Collision
- Forces on objects are not always constant.
- Figure 1a illustrates a baseball being hit and Figure 1b shows the force applied to the baseball by the bat during contact.
- Time of contact affects the force exerted over that time.
Definition of Impulse
- Impulse (J) is the product of the average force (F) and the time interval (Δt) during which the force acts. J = FΔt.
- Impulse is a vector quantity, meaning it has both magnitude and direction. The direction of impulse is the same as the direction of the average force.
Definition of Linear Momentum
- Linear momentum (p) of an object is the product of its mass (m) and velocity (v). p = mv
- Linear momentum is a vector quantity and points in the same direction as velocity.
Impulse-Momentum Theorem
- A net force acting on an object changes the object's momentum.
- The impulse of this net force is equal to the change in the object's momentum.
- This is expressed as ΣF(Δt) = mvf - mv0.
Application of Impulse-Momentum Theorem
- Engines apply an impulse during the launch of a space shuttle, increasing the momentum of the shuttle and launch vehicle.
Example 1 (Baseball)
- A baseball's initial velocity (v0) is -38 m/s.
- Final velocity (vf) is +58 m/s
- Mass (m) is 0.14 kg.
- Time of contact (Δt) is 1.6 x 10-3 s.
- Calculate impulse and average force.
Example 2 (Rain on a Car)
- Rain velocity (v0) is -15 m/s.
- Mass of rain per second (m/Δt) is 0.060 kg/s.
- Rain comes to rest upon striking the car.
- Find average force exerted by rain.
Class Activity 1 and 2
- The momentum of a person walking.
- Change in momentum for a bouncing ball.
Class Activity 3 and Example
- Momentum of and kinetic energy of a projectile are known. Given information find mass.
Class Activity 4 and Example
- Elastic collision between a van and a car stopped at a traffic light. Find the final car velocity
Assignment- Question 1
- Objects with equal momentum may have different velocities
- Objects of equal magnitude can have different directions
Assignment- Question 2
- Impulse applied to change volleyball velocity.
The Principle of Conservation of Linear Momentum
- Momentum is conserved in collisions of isolated systems.
- Internal forces in a collision are equal and opposite.
Two Types of Forces Acting on a System
- Internal forces are forces exerted between objects within a system.
- External forces are forces exerted on objects by agents outside the system.
Principle of Conservation of Linear Momentum (additional explanation)
- Internal forces cancel out during a collision.
- Total momentum of an isolated system is constant.
Example (Freight Train)
- Freight cars couple during a switching action.
- Calculate common velocity when cars couple together.
Class Activity (Skating)
- Using conservation of momentum, calculate the recoil velocity of a skater.
Elastic vs. Inelastic Collisions
- Elastic: Kinetic energy is conserved.
- Inelastic: Kinetic energy is not conserved in a perfectly inelastic collision, objects stick together.
Example: Elastic Collision
- Two balls collide.
- Find the velocities of the balls after an elastic collision.
###Applying the Principle of Conservation of Linear Momentum
- Four steps for applying Conservation of Momentum
Work and Energy
- Work (W) is a scalar quantity equal to the product of the force (F), displacement (s), and cosine of the angle (θ) between F and s : W = Fs.
- The SI unit of work is the joule (J).
- Work done by a constant force acting perpendicular to a displacement is zero.
Example 1: Pulling a Suitcase-on-Wheels
- Calculate work done.
Positive vs Negative Work
- Positive work when force and displacement are in the same direction.
- Negative work when force and displacement are in opposite directions.
Example (Accelerating a Crate)
- Total work done on the crate.
Definition of Kinetic Energy
- Kinetic energy (KE) of an object with mass (m) and speed (v) is given by KE = ½ mv².
- Kinetic energy is a scalar with the same units as work (joules).
- Work done by a net force is equivalent to the change in kinetic energy
Example: Work-Energy Theorem
- When a net external force does work on an object, its kinetic energy changes.
Deduction from the figure above
- The work-energy theorem only applies to a net force.
- Positive work increases kinetic energy.
- Negative work decreases kinetic energy.
- Zero work keeps kinetic energy constant.
Example 1 (Space Probe)
- Calculate the final speed of a space probe.
Gravitational Potential Energy
- Gravitational potential energy PE=mgh
Example: Gymnast
- Calculation of initial speed of a gymnast.
Center of Mass
- Center of mass, a single point representing the average location of a system's total mass, derived from the sum of positions weighted by mass.
###Example
- The center of mass of a two-particle system is the midpoint if each has equal mass.
- The center of mass moves closer to a heavier particle if masses are unequal.
- Systems with more than two particles use generalized equations.
System Of Particles
- Center of mass coordinates are the best way to describe the motion of a system with many particles
Examples and Definitions of Torque
- Torque is a measure of the tendency of a force to produce rotation.
- Torque is a vector quantity calculated as τ = r × F, where r is the position vector relative to the axis and F is the force acting on the object
- Torques calculated around an axis are positive when they produce counterclockwise rotation.
Examples of Torque
- The torque produced when a force is applied to a door with different lever arms.
Example (Ankle Joint)
- Calculating the torque (magnitude and direction) exerted on an ankle joint.
Cross Product and Torque
- Torque can be mathematically calculated with the cross product of position vector r and force vector F: τ = r × F.
Activity
- Finding the torque when a force is applied at a point on an object that is pivoted around the z-axis.
Moment
- A rigid body is in equilibrium if its translational and angular accelerations are zero.
Example (Diving Board)
- Calculate the forces the bolt and the fulcrum exert on a diving board.
Example (Teeter-Totter)
- Calculating the mass of a boy using the concept of torque on a teeter-totter.
Example (Bridge)
- Calculating the force exerted on a bridge by supports when a hiker is on the bridge.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your understanding of the impulse-momentum theorem in this quiz. Explore key concepts such as the relationship between impulse and momentum, vector quantities, and the significance of contact time during collisions. Challenge yourself with practical examples and formulas related to these fundamental physics principles.