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

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

Step-by-step 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 = (1)/(2)mv_(f)^(2) - ((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 = (1)/(2)40 kg*v_(f)^(2) - (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!