# Three Blocks Two Pulleys and a Table

This was a problem on an exam I had the other day and I want to know if my attempt was correct.

## Homework Statement

Please look at the attached image. You have a system of two ideal pulleys set up on a table. Block A is hanging from a string on the left side of the table which passes by a pulley connecting it to block B. Block B is resting on the table, and the kinetic coefficient of friction between the surface of the table and the block is 0.557. Block C is hanging from a string on the right side of the table which passes by a pulley and is attached to Block B. Block C is four times as massive as block A, and block B is three times as massive as block A. When the system is released from rest, block C accelerates downward until it reaches the floor, a distance of 105cm.

Find: The acceleration of block C and the time it takes to reach the ground.

## Homework Equations

F=ma
FF=$$\mu$$kN
y = y0 + v0yt + 1/2 at2
N = mg

## The Attempt at a Solution

I started by trying to find the net force acting on block B in order to find the acceleration of the system. In this case,

Fnet= FC - (FA + FF)

so

Fnet= (4mAg) - 1mAg - ($$\mu$$3mAg)

simplify

Fnet= 3mAg(1-$$\mu$$)

because mB=3mA you can rephrase the above equation

Fnet= mBg(1-$$\mu$$)

so the acceleration of block B would be g(1-$$\mu$$), and plugging in the values I got the answer -4.34m/s2 rounded to three figures. This would also be the acceleration of block C.

Next I needed to find the time it took block C to hit the ground.

y = y0 + v0yt + 1/2 at2

so

y = 1/2 at2
t = sqrt(2y/a)
t = sqrt(2*-1.05m/-4.34m/s2)
t = 0.695s rounded to three figures

Did I do this problem correctly? And if not, can you please show me the correct way of doing a problem like this? Thanks.

#### Attachments

• pulley problem_edited-1.jpg
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## Answers and Replies

Now that I review my notes, I think I might have gotten this problem incorrect. Was I supposed to take the net force acting on block B and divide by the total mass of A + B + C to find the acceleration of the system?

ehild
Homework Helper
It is better if you first draw the free-body diagram for all bodies, including the forces of tension in the ropes.

ehild

Now that I review my notes, I think I might have gotten this problem incorrect. Was I supposed to take the net force acting on block B and divide by the total mass of A + B + C to find the acceleration of the system?

what have you meant is correct.
To find the acceleration , you have to divide by total mass as they are all connected by a string, therefore sharing same a