The Physics
Hypertextbook
Opus in profectus

# Conservation of Energy

## Practice

### practice problem 1

The diagram below shows a 10,000 kg bus traveling on a straight road which rises and falls. The horizontal dimension has been foreshortened. The speed of the bus at point A is 26.82 m/s (60 mph). The engine has been disengaged and the bus is coasting. Friction and air resistance are assumed negligible. The numbers on the left show the altitude above sea level in meters. The letters A–F correspond to points on the road at these altitudes.

1. Find the speed of the bus at point B.
2. An extortionist has planted a bomb on the bus. If the speed of the bus falls below 22.35 m/s (50 mph) the bomb will explode. Will the speed of the bus fall below this value and explode? If you feel the bus will explode, identify the interval in which this occurs.
3. Derive an equation to determine the speed of the bus at any altitude.

### practice problem 2

Two 64 kg stick figures are performing an extreme blob jump as shown in the diagram below. (Warning: These are professional stunt stick figures. Don't try this at home.)

One stick figure stands atop a 7.0 m high platform with a 256 kg boulder. A second stick figure stands a partially inflated air bag known as a blob (or water trampoline). The first stick figure rolls the boulder off the edge of the platform. It falls onto the blob, catapulting the second stick figure into the air. What is the maximum height to which the second stick figure can rise? Assume that stick figures, boulders, and blobs obey the law of conservation of energy.

#### solution

The situation starts with the boulder's gravitational potential energy (measured relative to the surface of the blob). The boulder falls and it's potential energy is transformed into kinetic energy. That kinetic energy gets transfered to the stick figure. Up goes the stick person. Kinetic energy is now transformed into potential energy. The energies at these four prominant times are all equal. Assuming energy was not lost, the initial potential energy of the boulder is equal to the final potential energy of the stick figure.

 Us = Ub msghs = mbghb mshs = mbhb (64 kg)hs = (256 kg)(7.0 m) hs = 28 m

Another way to look at this problem is as a proportion. Potential energy is partly the product of mass and height. (It's also the product of gravity with mass and height, but since gravity doesn't change appreciably during a blob jump we can treat it as constant.) When the product of two numbers is contant, they are inversely proportional. The boulder has 4 times the mass of the stick figure. Therefore, the stick figure should have 4 times the height of the boulder.

 mshs = mbhb ms4hb = 4mshb hs = 4hb = 4(7.0 m) hs = 28 m

### practice problem 3

Write something different.