# Homework Help: Monkey and sled - conservation of energy problem

1. Jun 20, 2006

### physicsstudent06

I'm working on the following problem:

a monkey is strapped to a sled and both are given an initial speed of 4.0 m/s upa 20 degrees inclined track. The combined mass of monkey and sled is 20 kg, and the coefficient of kinetic friction between the sled and the incline is 0.20. How far up the incline do the monkey and sled move?

Using the conservation of energy equation, I knowthat
KEi + PEi + Wnc = KEf +PEf

Since both PEi and KEf are 0, the equation is as follows:

KEi+Wnc=PEf

how do i find Wnc?

2. Jun 20, 2006

### Hootenanny

Staff Emeritus
First just a slight correction;
This should read; KEi + PEi = KEf + PEf + Wnc. The intial kinetic energy will be converted into potential energy and work, thus work and final potential energy should be on the same side of the equality. As you correctly say, the inital potential energy and final kinetic energy drops out leaving you with; Wnc = KEi - PEf. Now, you know the intial kinetic energy, you must next calculate the change in potential energy. For this you need to calculate the height. HINT: Trigonomentry. Can you go from here?

3. Jun 20, 2006

### physicsstudent06

i know that KEi is 1/2 x 20 kg x 4.0 m/s^2, and PEf is 20kg x 9.8 m/s x sin(20) x d

right?

4. Jun 20, 2006

### Staff: Mentor

Start by finding the friction force acting on the sled. (Identify all the forces acting on the "monkey/sled" system.)

5. Jun 20, 2006

### physicsstudent06

but d is still unknown

6. Jun 20, 2006

### physicsstudent06

F=u Fn (u being the coefficient of friction), F being the normal force

7. Jun 20, 2006

### Staff: Mentor

If you set up your energy equation properly, "d" will be the only unknown. To find d, solve that equation.

8. Jun 20, 2006

### Hootenanny

Staff Emeritus
That is correct, so now you have;

$$dR\mu = 160 - 196d\sin(20) \Leftrightarrow d(R\mu + 196\sin(20)) = 160$$

Can you go from here?

9. Jun 20, 2006

### physicsstudent06

normal force = mass x acceleration due to gravity?

10. Jun 20, 2006

### Hootenanny

Staff Emeritus
Careful, the normal force always act perpendicular to the surface. Gravity in this case is not acting perpendicular to the surface.

11. Jun 20, 2006

### physicsstudent06

what is R?

12. Jun 20, 2006

### Staff: Mentor

Right. So what's the normal force (Fn)?

Once you've got the the friction force, use it to express the "work" done against friction.

13. Jun 20, 2006

### physicsstudent06

i don't know how to find the friction force. force = ma, but how can i find the acceleration?

14. Jun 20, 2006

### Hootenanny

Staff Emeritus
For kinetic friction, the frictional force is simply given by;

$$F = \mu R$$

Where R is the normal reaction force

15. Jun 20, 2006

### physicsstudent06

how do you find the normal reaction force?

16. Jun 20, 2006

### Hootenanny

Staff Emeritus
As Doc Al suggested draw a free body diagram of all the forces acting.

17. Jun 20, 2006

### physicsstudent06

anyone there?

18. Jun 20, 2006

### physicsstudent06

oh sorry, comp glitch

19. Jun 20, 2006

### Hootenanny

Staff Emeritus
Draw a free body diagram. HINT: The sled is only moving parallel to the incline. Resolve all forces so that they are either parallel or perpendicular to the inclined plane.

20. Jun 20, 2006

### physicsstudent06

i'm not sure what other forces are acting. force of gravity, you said no.

force of sled monkey?

21. Jun 20, 2006

### physicsstudent06

i'm not sure what you mean by resolve all forces

22. Jun 20, 2006

### physicsstudent06

xxxxxxxxxxxx

23. Jun 20, 2006

### physicsstudent06

you there?

24. Jun 20, 2006

### physicsstudent06

hey, can you just let me know if you're coming back? if you're working on something else too, that's cool. i just need to know if i should stick around

25. Jun 20, 2006

### Staff: Mentor

List all the forces acting on the monkey/sled and indicate their direction. A diagram is better (draw one for yourself), but start by making a list. Hint: I see 3 forces acting on this system.