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.
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.
Fx= F - mgsinθ - Mgsinθ = ma
Fy= -mgcosθ + ?? = 0
Now the block:
Fx= Fstring - Mgsinθ = Ma
Fy= 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.
Fstring - Mgsinθ = M((F/m) - gsinθ - (Mg/m)sinθ) = (MF/m) - Mgsinθ - (M2g/m)sinθ
Then we have
Fstring = (MF/m) - (M2g/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.