How Do You Calculate Speed at the Bottom of a Hill Considering Friction?

[lonlyincolleg]

Speed at the bottom of a hill - Please help!

Homework Statement

Bike (mass 40kg) traveling down a hill. Speed at the top of the hill is 5.0 m/s. The hill is 10m high and 100m long. Force of friction is 20N, what is the speed at the bottom?

Homework Equations

The only formula I've tried is v(final) = Sq. rt. of 2gy(initial). I don't know what y is, where friction plays into this and obviously I'm not getting the answer. Please help!

The Attempt at a Solution

I have converted the units to kg, and m, and drawn a picture. I know that the answer is 11 m/s but there isn't a formula or very similar problem in my book. (The only similar problem doesn't account for friction so I don't really know where to begin.

 

[asleight]

Homework Statement

Bike (mass 40kg) traveling down a hill. Speed at the top of the hill is 5.0 m/s. The hill is 10m high and 100m long. Force of friction is 20N, what is the speed at the bottom?

Homework Equations

The only formula I've tried is v(final) = Sq. rt. of 2gy(initial). I don't know what y is, where friction plays into this and obviously I'm not getting the answer. Please help!

The Attempt at a Solution

I have converted the units to kg, and m, and drawn a picture. I know that the answer is 11 m/s but there isn't a formula or very similar problem in my book. (The only similar problem doesn't account for friction so I don't really know where to begin.

Conservation of mechanical energy:

$$K_i+U_i-\vec{W}=K_f+U_f$$.

 

[Elbobo]

Conservation of mechanical energy:

$$K_i+U_i-\vec{W}=K_f+U_f$$.

W should be positive, not negative, and it's the work done by friction.

 

[phz]

You will have to know the distance traveled by the bike to know the amount of work done by friction. Find that out from your picture. After that use that energy is conservated as suggested. Be wary of how you define your friction. Look at the dimensions of your terms, they should always correspond. The total energy before (at the top of the hill) should equal the total energy after (including the work done by friction during the ride).