Classwork – Problem Solving with Conservation of Energy
Eo  E f
PE  mgh
KE 
1
mv 2
2
1. A large chunk of ice with mass 15 kg falls from a roof 8 meters above the ground. Find the
kinetic energy of the ice when it reaches the ground. What is the speed of the ice when it
reaches the ground?
2. A bike rider approaches a hill with a speed of 8.5 m/s. The total mass
of the bike and the rider is 85 kg. Find the kinetic energy of the bike
and rider. If the rider coasts up the hill, calculate the height at which
the bike will come to a stop. (Assume there is no friction.) How would
your answer vary if the mass of the bike and rider were doubled?
3. A 2 kg rocket is launched straight up into the air with a speed that allows it to reach a height
of 100 meters, even though air resistance performs 800 J of work on the rocket. Determine
the launch speed of the rocket. How high would the rocket travel if air resistance is ignored?
1. 1.18 kJ; 12.5 m/s 2. 3.07 kJ; -3.69 m; Mass has no effect on the results.
3. 52.54 m/s; -140.84 m
4. (i) 0 J; 1.92 kJ; 1.92 kJ (ii) 588 J; 1.33 kJ; 1.92 kJ; 6.66 m/s (iii) 1.92 kJ; 0 J; 1.92 kJ; 0 m/s; -3.27 m
4. Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at the various locations.
Chapter Review
W  F d
Eo  E f
W  KE
1
mv 2
2
1. Jamie lifts her toys into her tree house using a homemade elevator. The elevator has a mass
of 2.5 kg and the tree house is 8 meters above the ground. How much work does Jamie do
when lifting 5 kg of toys into the house? Determine the power used to lift the toys in 5 sec.
PE  mgh
KE 
2. Mike pulls a sled across level snow with a force of 225 N using a rope that is angled at 35.
Determine the work done if he pulls the sled 65.3 meters.
3. A 2 kg textbook is lifted from the floor to a shelf 2.1 meters above the floor. Determine the
book’s potential energy relative to the floor. What is the book’s potential energy relative to
the head of a 1.65 meter tall person?
4. A shot-putter heaves a 7.26 kg shot with a velocity of 7.5 m/s. Determine the kinetic energy
of the shot. How much work was done on the shot to give it its kinetic energy?
5. Calculate the kinetic energy of a 750 kg compact car moving at 100 km/hr. How much work
must be done to slow the car down to 50 km/hr?
6. Determine the mechanical energy of a 450 kg roller coaster moving at 30 m/s at the bottom of
the first dip which is 15 meters above the ground.
7. Julie has a mass of 49 kg. What is her potential energy when standing on the 6 meter diving
board? (She is 6 meters above the water.) Julie jumps off the diving board. What is her
kinetic energy right before she hits the water? How fast does Julie hit the water?
8. An unfortunate skydiver’s parachute fails to open. If the diver hits the ground going 300 m/s,
determine the height from which the ill-fated jump was make.
Answers
1. 588 J; 117.6 W 2. 12.04 kJ 3. 41.16 J; 8.82 J 4. 204.19 J; 204.19 J 5. 289.40 kJ; -217.05 kJ
6. 268.65 kJ 7. 2.88 kJ; 2.88 kJ; 10.84 m/s 8. -4.59 km
9. (Next page) (i) 196 J; 1 kJ; 1.2 kJ; 1 kJ; 100 W (ii) 980 J; 216 J; 1.2 kJ; 6.57 m/s
(iii) 490 J; 706 J; 1.2 kJ; 11.88 m/s (iv) 0 J; 1.2 kJ; 1.2 kJ; 15.47 m/s (v) 686 J; 510 J; 1.2 k; 10.1 m/s
9. Calculate the potential, kinetic, and mechanical energies, velocity, work, and power of the ball at the various locations.