6 Questions
A 2 kg block is moving at 4 m/s. If a net force of 5 N is applied to the block, what is the change in its kinetic energy?
ΔK = W_net = F × d = 5 N × 2 m = 10 J
A spring with a spring constant of 100 N/m is stretched by 0.2 m. What is the elastic potential energy stored in the spring?
U_e = (1/2)kx^2 = (1/2) × 100 N/m × (0.2 m)^2 = 2 J
Two objects, m1 = 3 kg and m2 = 2 kg, collide with initial velocities v1 = 5 m/s and v2 = 3 m/s. If the coefficient of restitution is 0.8, what is the final velocity of each object?
First, calculate the momentum before the collision: p1 = m1v1 = 15 kg m/s, p2 = m2v2 = 6 kg m/s. After the collision, the momentum is conserved, so m1v1' + m2v2' = 15 kg m/s + 6 kg m/s. Using the coefficient of restitution, v2' = v1' + 0.8(v1 - v2) = ... Solve for v1' and v2'.
A 5 kg object is lifted 2 m vertically upwards. What is the change in gravitational potential energy?
ΔU_g = mgh = 5 kg × 9.8 m/s^2 × 2 m = 98 J
A 3 kg object moves at 6 m/s. If a force of 4 N is applied to the object for 2 seconds, what is the resulting change in kinetic energy?
First, calculate the work done: W_net = F × d = 4 N × 2 m = 8 J. Then, use the work-energy theorem to find the change in kinetic energy: ΔK = W_net = 8 J.
Two objects, m1 = 2 kg and m2 = 1 kg, collide with initial velocities v1 = 2 m/s and v2 = 4 m/s. If the collision is perfectly elastic, what is the final velocity of each object?
First, calculate the momentum before the collision: p1 = m1v1 = 4 kg m/s, p2 = m2v2 = 4 kg m/s. After the collision, the momentum is conserved, so m1v1' + m2v2' = 4 kg m/s + 4 kg m/s. Using the fact that the collision is elastic, K1 + K2 = K1' + K2'. Solve for v1' and v2'.
Study Notes
Work-Energy Theorem
- States that the net work done on an object is equal to its change in kinetic energy
- Mathematical representation: W_net = ΔK
- Where W_net is the net work done and ΔK is the change in kinetic energy
- Can be used to calculate the work done on an object or the change in kinetic energy
Kinetic Energy
- The energy of motion
- Depends on the mass and velocity of an object
- Mathematical representation: K = (1/2)mv^2
- Where K is the kinetic energy, m is the mass, and v is the velocity
- Units: Joules (J)
Potential Energy
- The energy an object has due to its position or configuration
- Types:
- Gravitational potential energy: energy an object has due to its height or position in a gravitational field
- Elastic potential energy: energy stored in stretched or compressed materials
- Electrical potential energy: energy stored in a charged particle due to its position in an electric field
- Mathematical representation:
- Gravitational potential energy: U_g = mgh
- Elastic potential energy: U_e = (1/2)kx^2
- Electrical potential energy: U_e = qV
- Units: Joules (J)
Collision Dynamics
- Types of collisions:
- Elastic collisions: kinetic energy is conserved
- Inelastic collisions: kinetic energy is not conserved
- Perfectly inelastic collisions: objects stick together and kinetic energy is not conserved
- Momentum is conserved in all collisions
- Coefficient of restitution (COR): a measure of how much kinetic energy is lost in a collision
- COR = 1: perfectly elastic collision
- COR = 0: perfectly inelastic collision
- Mathematical representation:
- Momentum conservation: m1v1 + m2v2 = m1v1' + m2v2'
- Kinetic energy conservation (elastic collision): K1 + K2 = K1' + K2'
Work-Energy Theorem
- The net work done on an object is equal to its change in kinetic energy
- Mathematical representation: W_net = ΔK
- W_net is the net work done and ΔK is the change in kinetic energy
Kinetic Energy
- The energy of motion
- Depends on the mass and velocity of an object
- Mathematical representation: K = (1/2)mv^2
- K is the kinetic energy, m is the mass, and v is the velocity
- Units: Joules (J)
Potential Energy
- The energy an object has due to its position or configuration
- Types:
- Gravitational potential energy: energy an object has due to its height or position in a gravitational field
- Elastic potential energy: energy stored in stretched or compressed materials
- Electrical potential energy: energy stored in a charged particle due to its position in an electric field
- Mathematical representation:
- Gravitational potential energy: U_g = mgh
- Elastic potential energy: U_e = (1/2)kx^2
- Electrical potential energy: U_e = qV
- Units: Joules (J)
Collision Dynamics
- Types of collisions:
- Elastic collisions: kinetic energy is conserved
- Inelastic collisions: kinetic energy is not conserved
- Perfectly inelastic collisions: objects stick together and kinetic energy is not conserved
- Momentum is conserved in all collisions
- Coefficient of restitution (COR):
- A measure of how much kinetic energy is lost in a collision
- COR = 1: perfectly elastic collision
- COR = 0: perfectly inelastic collision
- Mathematical representation:
- Momentum conservation: m1v1 + m2v2 = m1v1' + m2v2'
- Kinetic energy conservation (elastic collision): K1 + K2 = K1' + K2'
Test your understanding of the Work-Energy Theorem, which states that the net work done on an object is equal to its change in kinetic energy, and kinetic energy, the energy of motion.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
