1 Dimensional Motion with Pulley

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AI Thread Summary
The discussion revolves around a physics problem involving a man, a bucket of bricks, and a pulley system. The man is pulled upward when he unties the rope, reaching the top in 2.91 seconds, after which the bricks fall out, and he descends back to the ground. Initial calculations for the man's upward acceleration were incorrect, but after reevaluating the forces separately for the man and the bucket, the correct acceleration was found to be 3.15 m/s². The height of the building was calculated to be approximately 13.34 meters, but the time taken for the man to hit the ground after starting his descent remained a challenge, with attempts yielding incorrect results. The key takeaway is the importance of analyzing forces individually to solve for acceleration and subsequent motion accurately.
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Homework Statement


I uploaded the image with for the problem.

The bucket is full of bricks and when the man unties the rope to bring the bucket to the ground, he gets pulled into the air while holding the rope. He goes all the way to the top (taking place in 2.91 seconds). The bricks fell out of the bucket when it hit the ground (when he hit the top) and the bricks fell out (now weighing only 18.8 kg). He then fell back to the ground and the bucket went back up, but slowed his fall.

mass of bricks = 124 kg
mass of bucket = 18.8 kg
mass of man = 73.3 kg
time of ascent = 2.91 s
gravity = 9.8 m/s^2

A. What was the initial upward acceleration by the man? (in m/s^2)
B. What is the height of the building? (in m)
C. How many seconds did it take (after starting his decent) for the man to hit the ground? (in s)

Homework Equations


F=ma
x = vot + 1/2at^2

The Attempt at a Solution



A. mass of bricks + mass of bucket = 142.8 kg

142.8 (9.8) = 1399.44

73.3 (9.8) = 718.34

1399.44 - 718.34 = 681.1

F=ma
681.1 = 73.3a
a = 9.29195

I don't think I'm doing it right though. I got some help from someone else and was told to multiply 142.8 by 9.8, but is this right? I'm not getting the right answer.

B.
x = vot + 1/2at^2
x = 0 + 1/2(9.3)(2.91^2) = 39 m

C. x = vot + 1/2at^2
39 = 0 + 1/2(9.8)t^2
t = 2.82 sec

Thanks
 

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southernguy13 said:

The Attempt at a Solution



A. mass of bricks + mass of bucket = 142.8 kg

142.8 (9.8) = 1399.44

73.3 (9.8) = 718.34

1399.44 - 718.34 = 681.1

F=ma
681.1 = 73.3a
You found the net force (along the direction of motion) on the entire mass, not just on the man.

You might be better off analyzing the forces on the man and the forces on the bucket+bricks separately. Get two force equations then combine them to solve for the acceleration.
 
Oh I see now. I added the masses together to get 216.1 then used that for the mass. So 681.1/216.1 = 3.15 m/s^2 which is correct!

I used that to get the height of the building, 13.34 meters.

What I can't figure out is the last question; how many seconds did it take (after starting his decent) for the man to hit the ground?

x = vot + 1/2at^2
13.3448 = 0t + 1/2 (9.8)t^2
t = 1.65 s

That is incorrect...
 
southernguy13 said:
What I can't figure out is the last question; how many seconds did it take (after starting his decent) for the man to hit the ground?

x = vot + 1/2at^2
13.3448 = 0t + 1/2 (9.8)t^2
t = 1.65 s

That is incorrect...
You need to figure out his acceleration. It's not 9.8! (Use the same method as in part A.)
 
Yes! Thank you
 
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