- #1

- 72

- 0

## Homework Statement

A block of mass M has a string of mass m attached to it. A force F is applied to the string and it pulls the block up a frictionless plane inclined at angle θ to the horizontal. Find the force the string exerts on the block.

## Homework Equations

F = ma

## The Attempt at a Solution

I have uploaded a picture of the free body diagram. My first problem is, what is the force that is keeping the string up? The mass M has the normal force from the inclined plane, and intuitively I know it is the tension in the string that keeps it from moving downwards due to the force mg.

So I first started with finding the forces acting on the string.

F

_{x}= F - mgsinθ - Mgsinθ = ma

F

_{y}= -mgcosθ + ?? = 0

Now the block:

F

_{x}= F

_{string}- Mgsinθ = Ma

F

_{y}= N - Mgcos = 0

I assumed the acceleration for both is the same. So I used the force in the x direction of the string to solve for a.

a = (F/m) - gsinθ - (Mg/m)sinθ

Now we use the force in the x direction for the block.

F

_{string}- Mgsinθ = M((F/m) - gsinθ - (Mg/m)sinθ) = (MF/m) - Mgsinθ - (M

^{2}g/m)sinθ

Then we have

F

_{string}= (MF/m) - (M

^{2}g/m)sinθ.

What I would like to know is, am I missing something? This problem was assigned in my upper division Classical Mechanics class (we're using Analytical Mechanics by Fowles and Cassiday). I've never had to do a problem where the string had mass. I went and asked the professor if there was some sort of trick or something, and he said no, just treat the problem like you would in General Physics 1.