Solutions Gravitational Potential Energy
1. How much PE does a 4 kg rock gain if lifted 3 meters?
DPE=mgDh = (4 kg)(9.8 m/s2)(3 m) = 117.6 J
2. A 2.5-kg ball is lifted 2 meters above the ground. (a) How much potential energy does it gain? (b) The ball is dropped. How much kinetic energy does it have as it hits the ground?
(a) DPE=mgDh = (2.5 kg)(9.8 m/s2)(2 m) = 49 J (b) the same, 49 J
3. A box is lifted 1 meter, and gains 7 joules of PE. If the box is lifted another meter higher, how much PE will it have altogether?
14 J (since PE is directly proportional to h)
4. A 9-newton block is lifted 2 meters. How much PE does it gain? (careful!)
DPE = (mg)Dh = (9 N)(2 m) = 18 J
5. A 6.2-kg dictionary falls off a shelf 2.73 m above the floor, and lands on a table 0.73 meters above the floor. How much PE did it lose? How much KE did it have when it hit the table?
DPE = mgDh = (6.2 kg)( 9.8 m/s2)(2.00 m) = 121.5 J
It had the same amount of KE, 121.5 J.
6. A crane lifts a 5.2 x 104 N car engine from a height of 0.6 m to a height of 1.1 m. How much PE did the car engine gain? How much work did the crane do?
DPE = (mg)Dh = (5.2 x 104 N)(0.5 m) = 2.6 x 104 J
It did the same amount of work, 2.6 x 104 J
7. A bathtub full of water, weighing 1000 N, resting on the floor crashes through the floor (ceiling), and falls 4 meters to the floor below. How much PE did it lose?
DPE = (mg)Dh = (1000 N)(4 m) = 4000 J
8. A 6.1-kg mass is dragged 3.0 m across the floor, by a force of 37 N. How much PE does the mass gain? (careful!)
DPE = (mg)Dh But Dh = 0 m, so it does not gain any PE. (DPE = 0 J)