1. When you are driving at 90 km/h, how much more distance do you need to stop than if you were driving at 30 km/h?

Question

2. For the same force, why does a longer cannon impart more speed to a cannonball?

Accepted Answer

1. Nine times farther. The car has nine times as much kinetic energy when it travels three times as fast:

[latex]\frac{1}{2} m(3v )^{2} = \frac{1}{2} m9v^{2} = 9(\frac{1}{2}mv^2)[/latex]

The friction force will ordinarily be the same in either case; therefore, nine times as much work requires nine times as much distance.

2. A longer barrel imparts more impulse because of the longer time the force acts. The work–energy theorem similarly tells us that the longer the distance that the force acts, the greater the change will be in kinetic energy. So we see two reasons for cannons with long barrels producing greater cannonball speeds.

Question 5.S&C.6: 1. When you are driving at 90 km/h, how much more distance d...

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