# Child sitting on chair attached to pulley

1. Oct 26, 2008

### Maiia

1. The problem statement, all variables and given/known data
An inventive child named Chris wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley, Chris pulls on the loose end of the rope with such a force that the spring scale reads 237.5N. Chris' true weight is 376N, and the chair weighs 87N. The acceleration of gravity = 9.8 m/s^2

Here's a drawing of the problem. Pardon my bad paint skills.

Here's my freebody diagrams

2. Relevant equations
Chris: Fnet=ma
N- Fg= ma

Chair: Fnet= ma
T- Fg= ma
T-Fg/ m

I assumed that the tension in the rope is equal to the amount on the spring scale.

When I substitute tension, Fg and mass into the Chair equation, I get a= 16.95 m/s^2. Apparently, that is wrong...Can someone tell me where I messed up?

2. Oct 26, 2008

### PhanthomJay

Your problem statement is lacking a question. It appears it is asking you to find the boy's acceleration? Your FBD's are not correct; you are missing some forces. It gets a bit difficult to solve this problem by isolating the boy and chair separately. Hint: Instead, look at the boy and chair together as a whole. How many rope forces are pulling them up? Your assumption that the tension in the rope is equal to the spring scale amount is correct. Use that knowledge to solve the problem.

3. Oct 26, 2008

### Maiia

oh sorry- its asking for the magnitude of the acceleration for the whole system.
If I combine the boy and chair together, than it would just be a tension acting up and a force of gravity acting down, right? If I solve for acceleration, I get 4.77m/s^2. I don't think that's right though...

4. Oct 26, 2008

### Maiia

oh I think I have it..so it's 2T not one T b/c there's tension on both sides of the pulley

5. Oct 26, 2008

### Maiia

so if I were to look at the force the kid exerts on the chair, would that be the normal force? Wouldn't that just be his weight?

6. Oct 27, 2008

### PhanthomJay

Yes, if you are looking at the system(boy and chair together), the force pulling up on them is 2T
If you wish to look at the chair alone, there are several forces acting on it: The rope tension, the chairs weight, and the Normal force of the boy on the chair. The normal force is not his weight, since the chair is accelerating. You need, in a separate FBD, to look at the forces on the boy also (his weight, the rope tension, and the normal force of the chair on the boy), in order to solve for N and 'a'. But these separte FBD's are unnecessary if you are just looking for the system acceleration. Instead, as I hinted, look at the chair/boy system together as a whole. By doing it this way, you don't have to worry about normal forces.