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Questions and Answers
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?
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?
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?
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?
A 5 kg object is lifted 2 m vertically upwards. What is the change in gravitational potential energy?
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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?
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?
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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?
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?
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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'
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Description
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.
