# Finding Acceleration and Tension

1. Feb 15, 2015

### kum203

1. The problem statement, all variables and given/known data

A block of mass m1 = 39.2 kg on a horizontal surface is connected to a mass m2 = 21.1 kg that hangs vertically. The two blocks are connected by a string of negligible mass passing over a frictionless pulley. Assume that the horizontal surface is smooth.

(a) What is the acceleration of the hanging mass? (Enter the magnitude only.)

(b) Determine the tension in the cord. (Enter the magnitude only.)

2. Relevant equations

a={F / m
T= W1 + W2

3. The attempt at a solution

I need to know the acceleration to find the tension and just don't know how to find it. I tried using 9.8 m/s2 but it said it was wrong. I also tried a=(W1 + W2) / 21.1 kg =18.2 m/s2. Not right. I'm getting really frustrated so any help is great

Last edited: Feb 15, 2015
2. Feb 15, 2015

### BvU

Hi Kum, welcome to PF

F = ma is good.
I recognize T as tension in the wire, but what are W1 and W2 ?

I suppose you did make a drawing ?

3. Feb 15, 2015

### kum203

W1 and W2 are the weights of the two boxes so W1= m1 * g and yeah it had an image with the problem but I also drew separate images of just the boxes and their forces.

4. Feb 15, 2015

### BvU

Do you think W1 influences T as it does in your equation ?

5. Feb 15, 2015

### kum203

i did...why doesn't it?

6. Feb 15, 2015

### kum203

regardless, it certainly influences the acceleration on m2 or else acceleration in part (a) would simply be gravity, yeah?

7. Feb 15, 2015

### BvU

Excellent.
On the drawing for m1 you should then see that the only force that influences the horizontal acceleration is T.

And for block 2 you don't have T = W2 (because that means equilibrium, and therefore no acceleration).

Bedtime for me, others may help you further if this big hint isn't already sufficient. good luck !

8. Feb 15, 2015

### kum203

Im actually still really confused...how do I find acceleration for m2? its not m2g=206.78 N because its slowed by m1 and I don't understand how W2 can have no effect on T as T would be non-existant without m2 pulling on the string. I know you're not supposed to tell me what to do but Im getting really frustrated. I've already missed the points for this question but need to understand it because its driving me crazy. My class is large and my teacher's office hours are limited. How am I supposed to find T without acceleration of m2 and how do I find acceleration with only two mass values when it's not gravity? Don't you need time to find acceleration and acceleration to find tension?

Last edited: Feb 15, 2015
9. Feb 16, 2015

### BvU

Sorry for your frustration. I try to discover what your separate images with the masses and the forces working on them look like.

m1 is being pulled down by gravity with a force W1. That is compensated by the surface that pushes up with the same force in the opposite direction. So the block doesn't accelerate in the vertical direction. There is no friction, and the only other force on block 1 that I can think of is the tension from the wire. That tension accelerates the block in the horizontal direction. We can write down an equation for that. It doesn't involve the weight W1, but it certainly has to do with the mass of the block. That was what I was aiming at in post #4. The distinction between weight (a force) and mass (a mass ) is important in physics. In everyday life we mix them up all the time.

The wire is taut, so the length is fixed. So the acceleration of block m2 is the same as that of block 1. But the force balance looks different. That is the second equation. Two equations with two unknowns (a and T). Bob's your uncle, piece of cake, etcetera (meaning: this can be solved)

Last edited: Feb 16, 2015
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