# Monkey and sled - conservation of energy problem (1 Viewer)

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#### 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?

#### Hootenanny

Staff Emeritus
Gold Member
First just a slight correction;
physicsstudent06 said:
KEi + PEi + Wnc = KEf +PEf
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?

#### 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?

#### Doc Al

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

#### physicsstudent06

but d is still unknown

#### physicsstudent06

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

#### Doc Al

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

#### Hootenanny

Staff Emeritus
Gold Member
physicsstudent06 said:
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?
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?

#### physicsstudent06

normal force = mass x acceleration due to gravity?

#### Hootenanny

Staff Emeritus
Gold Member
physicsstudent06 said:
normal force = mass x acceleration due to gravity?
Careful, the normal force always act perpendicular to the surface. Gravity in this case is not acting perpendicular to the surface.

what is R?

#### Doc Al

Mentor
physicsstudent06 said:
F=u Fn (u being the coefficient of friction), F being the normal force
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.

#### physicsstudent06

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

#### Hootenanny

Staff Emeritus
Gold Member
physicsstudent06 said:
i don't know how to find the friction force. force = ma, but how can i find the acceleration?
For kinetic friction, the frictional force is simply given by;

$$F = \mu R$$

Where R is the normal reaction force

#### physicsstudent06

how do you find the normal reaction force?

#### Hootenanny

Staff Emeritus
Gold Member
physicsstudent06 said:
how do you find the normal reaction force?
As Doc Al suggested draw a free body diagram of all the forces acting.

anyone there?

#### physicsstudent06

oh sorry, comp glitch

#### Hootenanny

Staff Emeritus
Gold Member
physicsstudent06 said:
anyone there?
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.

#### physicsstudent06

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

force of sled monkey?

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