Question

Sarah and her bicycle have a total mass of 40 kg. Her speed at the top of a 10 m high and 100m long hill is 5 m/s. If the force of friction on her way down is 20 N, at what speed will she be going when she reaches the bottom

Answer 1

Answer:

She will be going at 11.01 m/s when she reaches the bottom.      

Explanation:

We can find the speed at the bottom by equating the total work with the change in energy:

$W = E_{f} - E_{i}$   (1)

There is no energy conservation because there is a force of friction on her way down.  

By entering $W = -F_{\mu}*d$, where $F_{\mu}$ is the force of friction (is negative because it is in the opposite direction of motion) and d is the displacement, into equation (1) we have:

$-F_{\mu}*d = E_{f} - E_{i}$  

In the initial state, we have kinetic and potential energy and in the final state, we have only kinetic energy.

$-F_{\mu}*d = \frac{1}{2}mv_{f}^{2} - (\frac{1}{2}mv_{i}^{2} + mgh)$  

Where:

m: is the total mass = 40 kg

$v_{f}$: is the final speed =?

$v_{i}$: is the intial speed = 5 m/s

g: is the gravity = 9.81 m/s²

h: is the height = 10 m

$-20 N*100 m = \frac{1}{2}40 kg*v_{f}^{2} - \frac{1}{2}*40 kg*(5 m/s)^{2} - 40 kg*9.81 m/s^{2}*10 m$    

By solving the above equation for $v_{f}$ we have:

$v_{f} = 11.01 m/s$      

Therefore, she will be going at 11.01 m/s when she reaches the bottom.                                    

                     

I hope it helps you!