# Non-consecutive forces and work energy theorem

1. May 15, 2014

### BrainMan

1. The problem statement, all variables and given/known data
A dockworker allows a 350-N crate to slide down an incline that is 8 m in length to the deck of a ship 5 m below the dock level. The rough incline exerts a frictional force of 50 N on the crate. (a) What is the speed of the crate as it reaches the deck (b) What is the coefficient of friction between the incline and the crate?

2. Relevant equations
Wnc= (KEf-Kei)+ (PEf-PEi)

E= KE+PE

3. The attempt at a solution
I am having trouble with this problem because it does not include θ which means I cant find the initial potential energy. I also don't have the velocity at any point so I don't know the kinetic energy either. I can't substitute to find the answer because I have more unknowns than equations.

2. May 15, 2014

### nasu

You don't need the potential energy but the change in PE. You don't need the angle for this.
You can calculate the work associated with friction. The only unknown is the final Ke.

3. May 15, 2014

### dauto

The problem gives the length of the incline and also states that the deck is 5 meters below the dock. What do you need the angle for?

4. May 15, 2014

### goraemon

If you were solving this problem via force diagrams, you COULD calculate the angle, given that the height is 5m and length of the incline is 8m (think Pythagorean theorem). But really, since you're using work / energy, you don't need to go this route.

You need to factor in the friction force into your energy equation. Think of the work done by the dissipative force and how it is related to the change in thermal energy. You should've learned the proper equations to figure it out.

5. May 16, 2014

### BrainMan

OK what I have tried now is to find the velocity based on the equation for the work of the non consecutive forces. I found the initial potential energy by using mgy so
350(9.8)(5)= 17150.
Then I plugged this into the nonconsecutive force formula Wnc= KEf-PEi. So
-50= 1/2mv^2- 17150
v= 9.89 m/s
It says the answer is actually 8.69 m/s
what am I doing wrong?

6. May 16, 2014

### nasu

7. May 16, 2014

### goraemon

Two things wrong:
1) As another poster noted, the PE is incorrect. Note that the problem says the crate is 350 Newtons, not 350 kg.
2) Wnc is not just -50N. There's something missing there. Remember the general equation for Work and check your units.

8. May 16, 2014

### BrainMan

OK I have figured out how to find the velocity. Now I am having trouble finding the coefficient of friction. The formula for the coefficient of friction is force of friction/normal force= coefficient. I did this and got .142 and the answer is .183. I also tried to find the normal force by doing 350 cos θ but theta is not included in this problem. What do I do?

9. May 16, 2014

### goraemon

You have sufficient information to figure out $\theta$. Refer to a previous post that gave you all the hint you should need.

10. May 16, 2014

### BrainMan

I understand the problem now and have gotten both parts of the problem right! Thanks for all the help!