# 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?

<img align="center" src="./applecart.png">

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**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.

<img align="center" src="./applecartweight.png">

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