# Initial upward acceleration in a pulley problem

1. Sep 24, 2009

### NinjaPenguin

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

Given data:

Gravity= 9.8 m/s2
Mass of bricks= 136 kg
Mass of barrel= 15.5 kg
Mass of barrel and bricks= 151.5 kg
Mass of worker= 74.2 kg
Time= 2.95s

The problem

The acceleration of gravity is 9.8 m/s2 .
To emphasize the fact that lessons learned in 303K carry over into real life, this problem is based on an accident report from the Worker’s Compensation Board in Bryant, Texas.

I am writing in response to your request for a fuller explanation on the cause of my accident. I trust the following details will be sufficient. On the day of the accident, I was working alone laying bricks on the roof of a new building. On completing my work, I had some bricks left over which were found to have a mass of 136 kg. Rather than carry the bricks down by hand, I decided to lower them in a barrel with a mass of 15.5 kg by using a pulley which was attached to the side
of the building at the roof.

Securing the rope at ground level, I went up to the roof, swung the barrel out and loaded the bricks into it. Then I went down and untied the rope, holding it tightly to insure a slow descent of
the bricks. You will note that my mass is 74.2 kg. To my surprise, I was jerked off the ground suddenly and forgot to let go of the rope. Needless to say, I proceeded at a rapid rate up towards the roof of the building. Somewhere up the building, I met the barrel which was now proceeding downward at an equally impressive speed. This did not slow me down and I continued my rapid ascent, hitting the pulley on the top floor. I estimate that all this happened in the matter of 2.95 s.
At the same time, however, the barrel of bricks hit the ground and the bottom fell out of the
barrel. Devoid of the bricks, the barrel now had a mass of 15.5 kg. I refer you again to my mass. As you might imagine, I began a rapid descent down the side of the building and met the barrel coming up.

My luck finally began to change slightly. The barrel slowed me enough to lessen my injuries when I fell into the pile of bricks. I am sorry to report, however, as I lay there on the pile of bricks, in
pain, unable to move and watching the empty barrel several stories above me, I again lost
my composure and let go of the rope.

1. What was the initial upward acceleration
experienced by the worker?

2. What is the height of the building?

3. How many seconds did it take (after starting
his descent) for the worker to hit the ground?

2. Relevant equations

F=ma

x = vot + 1/2at*2

3. The attempt at a solution

1.
I tried finding the sum of the force up and down.
Force up = 151.5 (9.8)= 1484.7 N
Force down = 74.2(9.8)= 727.16 N

Then I subtracted up force from the down force to get the net.

1484.7 - 727.16 = 757.54 N

I then used F =ma to find a.

757.54 = 74.2a
757.54/74.2 = 10.209 = a

For 2
I would just plug in time(2.95) and the acceleration to find the height

For 3
I would plug in height and (9.8 m/s2) to find time

My answer of 10.209 m/s2 is not right though so I can't do the other two. Any help would be appreciated

Last edited: Sep 24, 2009
2. Sep 24, 2009

### kuruman

3. Sep 24, 2009

### NinjaPenguin

Thank you. For some reason I didn't even think about that and we just did a lab on it.