Peoples Physics Concepts

http://www.ck12.org Chapter 8. Energy Conservation

8.3 Conservation of Energy

• Apply energy conservation in a closed system.

Students will learn how to apply energy conservation in a closed system.

Key Equations

∑Einitial=∑E

final The total energy does not change in closed systems

Example 1

Billy is standing at the bottom of a ramp inclined at 30 degrees. Billy slides a 2 kg puck up the ramp with an initial

velocity of 4 m/s. How far up the ramp does the ball travel before it begins to roll back down? Ignore the effects of

friction.

Solution

The potential energy of the puck when it stops at the top of it’s path will be equal to the kinetic energy that it was
initially rolled with. We can use this to determine the how high above the ground the puck will be above the ground
when it stops, and then use trigonometry to find out how far up the ramp the puck will be when it stops.

PEi+KEi=PEf+KEf start with conservation of energy

0 +

1

2

mv^2 =mgh+ 0 take out the energy terms we know will be zero and substitute the equations for potential and kinetic energy.

1

2

v^2 =gh simplify the equation

h=

v^2

2 g

solve for h

h=

(4 m/s)^2

2 ∗ 9 .8 m/s^2

substitute in the known values

h= 0 .82 m

Now we can find the distance up the ramp the ball traveled since we know the angle of the ramp and the height of

the ball above the ground.