Energy

Example 1: pulling a wagon of, what else: apples.

The Questions:

a) How much work is done by a force of 20 N on a wagon full of apples with a combined mass of 10 kg if it’s pulled along a frictionless floor for a distance of 10 m?

b) What is the kinetic energy gained by the wagon and apples?

c) If it starts from rest, what is its speed after that distance?

applecart

The Answers:

a) Work is the product of the force and the distance, so

\begin{align*} W &= F \Delta x \\ W &= (20 \text{ N})(10 \text{ m}) \\ W &= 200 \text{ J} \end{align*}

b) The kinetic energy change is equal to the work (remember, it started from rest):

\begin{align*} \Delta K &= K-K_0 = W = F\Delta x \\ \Delta K &= K-0 = W = 200 \text{ J} \end{align*}

c) We know the kinetic energy, so we can calculate the velocity:

\begin{align*} K &= \dfrac{1}{2}mv^2 \\ v &=\sqrt{\frac{2K}{m}} \\ v &= \sqrt{\frac{(2)(200)}{10}} = \sqrt{40} = 6.3 \text{ m/s} \end{align*}

Is this reasonable? That’s about 14 mph. That force of 20 N is not quite 5 pounds. Imagine that you hung a 5 pound weight over a pulley and set the wagon on a sheet of ice (no friction). Here’s the situation drawn about to scale.

applecartweight

I think I could imagine that this thing would be moving pretty fast over that distance.