In Example 7.7, we found that the speed of a roller coaster that had descended 20.0 m was only slightly greater when it had an initial speed of 5.00 m/s than when it started from rest. This implies that ΔPE >> KEi . Confirm this statement by taking the ratio of ΔPE to KEi . (Note that mass cancels.)

Example 7.7 Finding the Speed of a Roller Coaster from its Height

(a) What is the final speed of the roller coaster shown in Figure 7.8 if it starts from rest at the top of the 20.0 m hill and work done by frictional forces is negligible? (b) What is its final speed (again assuming negligible friction) if its initial speed is 5.00 m/s?

Solution 19PE

When a body of mass is dropped from a certain height, say , the change in its potential energy is given by . The expression for kinetic energy of an object having mass and velocity is given by . We are required to show that in the example given, the change in potential energy is much greater than the initial kinetic energy.

Step 1 of 3</p>

The roller coaster has descended by 20.0 m.

Let its mass be .

Therefore, the change in potential energy J

J

Step 2 of 3</p>

The initial speed of the roller coaster is 5.00 m/s.

Therefore, the initial kinetic energy J