Work-Energy Theorem
Problems in Conservation of Energy

Show all work and units. Sketches often help.

1. A 200 kg hammer of a pile driver is lifted 10.0 m.
a) Find the potential energy of the driver at its maximum height.
b) Find the potential energy of the driver at 5.0 m.
c) Calculate the velocity of the driver as it hits the ground when dropped from 10.0 m using the Work-Energy Theorem.
d) Calculate the velocity of the driver as it hits the ground when dropped from 5.0 m using the Work-Energy Theorem.
e) Verify your answers in c and d using the kinematic equation v² = 2gs.

2. A 1600 kg car travels at a speed of 12.0 m/s.
a) Find its kinetic energy.
b) If its speed drops to 6.0 m/s, how does its kinetic energy compare with your answer in (a)?
c) How does doubling the speed of a car affect its braking distance. Assume the same work is done by the brakes in each case.

3. A 20.0 kg mass is on the edge of a 100.0 m cliff.
a) What is its potential energy?
b) What is its potential energy 50.0 m above the ground?
c) What is its potential energy 25.0 m above the ground?
d) Using the W-E Theorem, calculate its velocity 40 m above the ground.
e) What becomes of the energy after hitting the ground?

4. A steel ball has a mass of 40 g and rolls along a smooth level surface at 0.42 m/s. Find its kinetic energy.

5. A nitrogen gas molecule (N₂) has a speed of 450 m/s. Find its kinetic energy if its mass is 4.54 x 10^-26 kg.

6. An electron's energy is measured at 2.81 x 10^-14 J when it is traveling at 2.5 x 10⁸ m/s. Determine the mass of an electron.

7. A 7.2 kg bowling ball rolls down a frictionless channel from a height of 0.7 m. Determine its velocity at the bottom.
a) to what point does the ball rise on the opposite incline?
b) at what point on the sketch is the speed maximum?
c) at what point is the speed zero?

8. What types of energy do the following items have? (potential (P.E.), kinetic (K.E.), gravitational potential (G.P.E.); you may use more than one.
a) moving ping pong ball
b) AA battery on the top shelf
c) wind up pendulum clock
d) basketball on the way to the net
e) compressed spring in a ball point pen

9. A BIC Clic® pen requires a force of 1.4 N to push the ink cartridge a distance of 0.7 cm.
a) What is the force constant of the spring?
b) What energy has been added to the spring?
c) If the spring is released, what is the velocity of the pen's clicker upon release if its mass is 0.5 g?

10. A child is on a swing. Her mom pushes her to a height of 1.5 m above the starting position. Determine the child's maximum velocity during the swing.

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