Two Blocks and a Pulley

SuperCass

Homework Statement

A block of mass m1 = 1 kg rests on a table with which it has a coefficient of friction µ = 0.77. A string attached to the block passes over a pulley to a block of mass m3 = 3 kg. The pulley is a uniform disk of mass m2 = 0.4 kg and radius 15 cm. As the mass m3 falls, the string does not slip on the pulley.

a) With what acceleration does the mass m3 fall?

b) What is the tension in the horizontal string?

c) What is the tension in the vertical string?

Homework Equations

torque = I (alpha)
F = ma
I = .5mr^2

The Attempt at a Solution

So far I have the equations:
T1 - (mu)N = (m1)a
T2 - (m3)g = (m3)a

And I'm not sure what to do with the torque equation. I think it's
(T1)r - (T2)r = (.5mr^2)(alpha).

Is this right?
What am I doing wrong? Everytime I try something it seems to be incorrect (it's an online program that we input our answers in).

Homework Helper
Gold Member
2021 Award
Pay attention to the sign of your acceleration in your three equations. Your equations are inconsistent with each other as far as the sign of the acceleration is concerned.

SuperCass
Is it negative in the second one, since it's moving down?
Is my third equation correct? Do I need it?

Homework Helper
Is it negative in the second one, since it's moving down?
Is my third equation correct? Do I need it?

Pulley is moving in clockwise direction. So T2 > T1

Homework Helper
Gold Member
2021 Award
Is it negative in the second one, since it's moving down?
It is not the direction of motion that matters but the direction of the acceleration in each equation. You need to make sure that the vector quantity on the right of each equation (acceleration) is in the same direction as the vector quantity on the left.
In the first equation, you know that the acceleration is in the same direction as T1, therefore you must put the same sign in front of each and you have done that. (The symbol "a" stands for the magnitude of the acceleration and is always positive.)
In the second equation, is the acceleration in the same or in the opposite direction as the weight?
Is my third equation correct?
In the third equation, is the angular acceleration in the same or opposite direction as the torque T2R?
Do I need it?
To answer this question, count your unknowns. You need as many equations as you have unknowns.

SuperCass
Thanks everyone, I got it!

I needed to flip my terms in my second equatio nand my third (the torque) equation!