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Questions and Answers
What is the kinetic energy of an object if its momentum is 25 kg.m/s?
What is the kinetic energy of an object if its momentum is 25 kg.m/s?
What is the total momentum of a system consisting of multiple particles?
What is the total momentum of a system consisting of multiple particles?
What is the relationship between the forces exerted by two particles on each other?
What is the relationship between the forces exerted by two particles on each other?
What is the time rate of change of the total momentum of an isolated system?
What is the time rate of change of the total momentum of an isolated system?
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What is a characteristic of the momentum of a particle?
What is a characteristic of the momentum of a particle?
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What is the effect of internal forces on the total momentum of a system?
What is the effect of internal forces on the total momentum of a system?
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What is a necessary condition for the conservation of momentum to be applicable in a system of particles?
What is a necessary condition for the conservation of momentum to be applicable in a system of particles?
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In a two-dimensional problem, which components of a vector would you consider?
In a two-dimensional problem, which components of a vector would you consider?
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What should you do when setting up a problem involving the conservation of momentum?
What should you do when setting up a problem involving the conservation of momentum?
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When writing the equation for the conservation of momentum, what do you equate?
When writing the equation for the conservation of momentum, what do you equate?
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What is the symbol convention used for velocities before and after interaction?
What is the symbol convention used for velocities before and after interaction?
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How many equations do you need to write when applying the conservation of momentum in two-dimensional problems?
How many equations do you need to write when applying the conservation of momentum in two-dimensional problems?
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What is the direction of the momentum vector of an object?
What is the direction of the momentum vector of an object?
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A car is traveling north at 20 m/s. If the car turns east and maintains the same speed, what happens to its momentum?
A car is traveling north at 20 m/s. If the car turns east and maintains the same speed, what happens to its momentum?
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An object has a kinetic energy of 200 J and a momentum of magnitude 10 kg.m/s. What is its speed?
An object has a kinetic energy of 200 J and a momentum of magnitude 10 kg.m/s. What is its speed?
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What is the efficiency of an ideal machine?
What is the efficiency of an ideal machine?
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Two objects have the same kinetic energy. If object A has a mass of 2 kg and a speed of 4 m/s, what is the speed of object B if its mass is 4 kg?
Two objects have the same kinetic energy. If object A has a mass of 2 kg and a speed of 4 m/s, what is the speed of object B if its mass is 4 kg?
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A ball thrown by a major-league pitcher has a momentum of magnitude 20 kg.m/s. If the same ball is thrown by a child with a momentum of magnitude 10 kg.m/s, what is the ratio of the pitcher's speed to the child's speed?
A ball thrown by a major-league pitcher has a momentum of magnitude 20 kg.m/s. If the same ball is thrown by a child with a momentum of magnitude 10 kg.m/s, what is the ratio of the pitcher's speed to the child's speed?
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Study Notes
Kinetic Energy and Momentum
- The kinetic energy of an object cannot be determined solely from its momentum. Momentum and kinetic energy are related, but require additional information like mass.
Momentum of a System
- The total momentum of a system is the vector sum of the momenta of all the particles in the system.
Newton's Third Law
- The forces exerted by two particles on each other are equal in magnitude and opposite in direction.
Conservation of Momentum
- The time rate of change of the total momentum of an isolated system is zero. This means that the total momentum of an isolated system remains constant.
Momentum of a Particle
- Momentum is a vector quantity, meaning it has both magnitude and direction. In this context, the direction of the momentum vector is the same as the direction velocity of the particle.
Internal Forces
- Internal forces within a system do not affect the total momentum of the system.
Conservation of Momentum Requirements
- Conservation of momentum applies when the net external force acting on the system is zero. This is because internal forces cancel each other out and do not contribute to the change in momentum of the system.
Two-dimensional Problems
- In two-dimensional problems, it is helpful to consider the x and y components of the momentum vector.
Setting up a Conservation of Momentum Problem
- When setting up a problem involving the conservation of momentum, identify the system of particles, the forces acting on the system, and the initial and final states of the system.
Conservation of Momentum Equation
- The total momentum of a closed system before a collision is equal to the total momentum of the system after the collision. Mathematically, the initial total momentum is equal to the final total momentum.
Velocity Symbol Conventions
- Subscripts like “i” and “f” (for initial and final) are used for velocities before and after an interaction.
Two-Dimensional Problems
- In two-dimensional problems, two equations need to be written to apply the conservation of momentum, one for each dimension.
Momentum Vector Direction
- The momentum vector of an object points in the same direction as the object's velocity.
- If the momentum vector changes, the direction of the object's movement changes.
Momentum in a Turning Car
- In a turning car, the momentum vector changes although the speed remains constant because the direction of motion changes.
Calculating Speed from Kinetic Energy and Momentum
- The speed of an object can be determined using both its kinetic energy and momentum by equating the formulaic expressions of each.
Ideal Machine Efficiency
- An ideal machine has an efficiency of 100% since the power input equals the power output.
Kinetic Energy and Speed
- Two objects with the same kinetic energy, but different masses, will not have the same speed. This is because the kinetic energy is proportional to the square of the speed.
Momentum and Speed of a Ball
- The ratio of the pitcher's speed to the child's speed in the scenario provided is 2:1. This is because the pitcher's momentum is twice the child's momentum, and momentum is directly proportional to speed.
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Description
This quiz covers the concepts of momentum, kinetic energy, and Newton's 2nd law of motion. It includes questions on the equations relating kinetic energy to momentum and the definition of linear momentum.
