# Coefficient of Friction problem

1. Mar 11, 2008

### tbone413

1. The problem statement, all variables and given/known data
An attraction at a waterpark includes a straight waterslide 20m long at an angle of 34 degrees above the horizontal. The waterslide ends in a ramp 5 m long at an angle of 45 degrees above the horizontal. People sliding down the slide land in a small pool just past the end of the ramp. The waterslide is kept frictionless by spraying fine streams of water onto it through several nozzles located along the length of the slide.

Unfortunately, a poor management decision to conserve water at the water park results in the water being turned off just as a 120 kg man enters the ramp, so that the last 5m of his trip on the slide is no longer frictionless. The man flies off the ramp, misses the pool and lands on the pavement a horizontal distance of 12m fro the end of the slide. What is the coefficient of friction between the man and the waterslide?

2. Relevant equations
F(x) = -Fk = ma(x)
F(y) = n - mg = 0
n-mgcos(theta) = 0
Ff(force of friction) + mgsin(theta) = ma(up)

3. The attempt at a solution

Well im not really sure how to attempt this problem at all, its extra credit and we havent quite learned this material yet. I do know though that its a newtons second law problem and that when going up the ramp the frictional force will cause the acceleration to decrease. I also know that I have to use a FBD to figure out the acceleration and velocity of the man at the moment he hits the ramp, and then solve for the coefficient of friction. However Im not quite sure what steps to take. So if someone could maybe walk me through their thought process id Really appreciate it.

2. Mar 11, 2008

### mgb_phys

Work out the horizontal and vertical components of his speed at the start of the friction part ( using either conservation of energy or constant vertical accelearation)

Then work out what speed he must have left the ramp to reach the crash point - this is just the standard cannon ball firing question.

Then you have how much speed ( and therefore energy ) he lost to friction.
Since energy is force * distance you can work out the average force, and with his weight to give you the normal force - you have the coefficent of friction.

3. Mar 11, 2008

### tbone413

Im not quite sure how you would find the components of his speed using the constant vertical acceleration. can you clarify a bit more?

4. Mar 11, 2008

### mgb_phys

If you neglect friction the only forces acting are his weight, so you can calculate the vertical accelaration of an object down an inclined plane just by knowing 'g' and the angle

5. Mar 11, 2008

### tbone413

ahh ok. that makes sense.

6. Mar 11, 2008

### tbone413

I came up wth 22.1 m/s for his velocity he left the ramp at, and 11.54 m/s for his velocity before he left..which doesnt make sense.

Are either of those numbers similar to what you got?