Download Gravitational Potential Energy

Gravitational Potential Energy
How much work does it take to lift an object? Well, work equals force times distance. The force
you exert to lift something is equal to the object's weight, Fg=mg . Let's make up a new name
for vertical distance--we'll call it height, with the symbol h. Then the work needed to lift
something is W=mgh, where h is the new height minus the old height.
If you lift an object, then release it, what happens? (If you aren't sure, try it, but keep your fingers
and toes out of the way.) Yes, the object falls--it actually accelerates, downward. If we
measure the speed it is going on its way down when it just reaches the level it was originally
lifted from, we would find that its kinetic energy is equal to the work you needed to do to lift it in
the first place.
Keeping track of the energy is an
accounting problem. As the object is
lifted, it is given energy. As it is held in
place, the energy is stored, like money in
the bank. When it is released, the money
gets taken out of the bank--that is, the
stored energy turns into energy of motion.
When it has fallen to its original level, all
the money has come out of the bank--its
stored energy is all kinetic energy (except
for a little bit lost because of air
resistance, kind of like paying ATM fees.)
Energy that is stored is called potential energy. The kind talked about here is gravitational
potential energy. There are also chemical, electrical, nuclear, and mechanical (stored in a spring)
potential energies. When an object is lifted, its gain in gravitational potential energy is
PE=mgh. When it falls, its loss of potential energy is the same amount: PE=mgh.
1. How much PE does a 4 kg rock gain if lifted 3 meters?
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?
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?
4. A 9-newton block is lifted 2 meters. How much PE does it gain? (careful!)
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?
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6. A crane lifts a 5.2 x 10 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?
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?
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!)