# Forces with friction- How fard does the sled travel?

1. Oct 7, 2008

### sour punch

1. A girl coasts down a hill on a sled, reaching
a level surface at the bottom with a speed
of 7 m/s. The coefficient of kinetic friction
between runners and snow is 0.054, and the
girl and sled together weigh 749 N.
The acceleration of gravity is 9.8 m/s2 .
How far does the sled travel on the level
surface before coming to a rest? Answer in
units of m.

2. F= ma
f= mewN
W=mg

3. I figure I need to know the accleration at the instant she reaches bottom of the hill to use a kinematics formula to solve for the distance, but I cannot figure it out without the angle of the incline. Plus, I don't know how to factor friction into that.

2. Oct 7, 2008

### sour punch

O c'mon, what else do you want?

3. Oct 8, 2008

### Rake-MC

Please and thankyou would be nice.

You know the weight on the horizontal is 749N = normal reaction force.
The retarding force of friction is normal reaction force * coefficient of kinetic friction

= 749 * 0.054

If you imagine the particle moving towards the right, then the force of friction is towards the left.

To find the acceleration, divide force of friction by the mass. You can get the mass by dividing the weight by the acceleration of gravity.

use $$v_{final}^2 = v_{initial}^2 + 2as$$ where s = displacement.
Solve for s.