# A Terrible Accident involving a Barrel of Bricks and a lot of Force

1. Oct 1, 2008

### Phoenixtears

SOVLED

(Green means correct)

(Red means can't figure out answer)

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

Dear Sir; I am writing in response to your request for additional information in Block #3 of the accident reporting form. I put "Poor Planning" as the cause of my accident. You asked for a fuller explanation and I trust the following details will be sufficient. I am a bricklayer by trade.

On the day of the accident, I was working alone on the roof of a new six-story building. When I completed my work, I found I had a large number of bricks left over. Rather than carry the bricks down by hand, I decided to lower them in a barrel by using a pulley that was attached to the side of the building at the sixth floor. 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 94 kg of bricks. You will note on the accident reporting form that my mass is 65.8 kg.

Due to my surprise at being jerked off the ground so suddenly, I lost my presence of mind and forgot to let go of the rope. Needless to say, I proceeded at a rapid rate up the side of the building.(Q1)

In the vicinity of the third floor, I met the barrel which was now proceeding downward at an equally impressive speed. (Q2)

This explains the fractured skull, minor abrasions and the broken collarbone, as listed in Section 3, accident reporting form. Slowed only slightly, I continued my rapid ascent, not stopping until the fingers of my right hand were two knuckles deep into the pulley at the top of the building that I mentioned in Paragraph 2 of this correspondence. Fortunately by this time I had regained my presence of mind and was able to hold tightly to the rope, in spite of the excruciating pain I was now beginning to experience. At approximately the same time, however, the barrel of bricks hit the ground and the bottom fell out of the barrel. Now devoid of the mass of the bricks, the empty barrel mass was only 25 kg. I refer you again to my weight. As you might imagine, I began a rapid descent down the side of the building. (Q3)

In the vicinity of the third floor, I met the barrel coming up.This accounts for the two fractured ankles, broken tooth and severe lacerations of my legs and lower body.(Q4)

Here my luck began to change slightly. The encounter with the barrel seemed to slow me enough to lessen my injuries when I fell into the pile of bricks and fortunately only three vertebrae were cracked. 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 six stories above me, I again lost my composure and presence of mind and let go of the rope. (Q5, Q6)

Assume that the 6-floor building is 20 meters high. … use g = 9.8 m/s^2

Q1. Determine the magnitude of the man's acceleration.
1.72m/s^2
I did this by finding the two 2nd law equations from the force diagrams, and then I substituted into one equation for T. Then I was only left with mass and g.

Q2. The barrel accelerated from rest, so …
How much time did it take for the barrel to fall half way down the 20 meter tall building?
3.41 seconds
Used Kinematics equations from acceleration, intial velocity (0), and distance. Then found time and final velocity (below).
How fast was the barrel traveling when it struck the man 1/2 way up the building?
5.86 m/s
See above.
What was the barrel's speed relative to the man (how fast was the man traveling)?
m/s

I thought this should equal the final velocity for the barrel because the accelerations are the same. Why would this not be correct?

Q3. Determine the magnitude of the man's new acceleration.
4.4 m/s^2
Again used the 2nd law equations, jus the mass of the barrel changed.

Q4. How fast was the barrel traveling when it struck the man a 2nd time?
9.37 m/s
Again, used kinematics equations. Same distance (10, well, it was negative before), inital velocity 0, and the acceleration.
What was its speed relative to the man? (This is just like question #2)
m/s

Again, I don't understand why this wouldn't equal the answer above.

~Phoenix

Last edited: Oct 1, 2008
2. Oct 1, 2008

### Mattowander

The reason that your answers for speed don't equal the answers of the speed relative to the man is that it's asking for "relative speed". If the man was motionless on the ground looking up at the falling barrel, then the speed would be the same. However, since the man also has a speed upwards (In question #2) , the relative speed of the barrel would be greater.

Still doesn't make sense? Think of this situation : If two cars are driving towards each other, their relative velocity would be greater than the velocity of each individual car ; It would appear to them that the other car is moving faster than it actually is. For the other extreme, if two cars are traveling at the same speed side by side, then it would appear (relative to the people in the car) that the car next to them is standing still.

I hope my explanations made sense. Hope that helps!

3. Oct 1, 2008

### Phoenixtears

Of course... Definitely made sense. Thank you so much!

4. Oct 1, 2008

### Mattowander

No problem :)