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 some bricks left over which when
weighed later were found to weigh 240 lbs. Rather than carry the bricks down by hand, I
decided to lower them in a barrel by using a pulley which 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 240 lbs of bricks. You will note on the accident
reporting form that my weight is 135 lbs.
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 which 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 weight of the bricks, the barrel weighed
approximately 50 lbs. 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. (Q4) This accounts for the two fractured ankles, broken tooth and severe
lacerations of my legs and lower body.
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, 6, 7)In order to do these problems, you need to know that 1 lb ˜ 4.5 N. Convert the weights
involved to newtons. Assume that the 6-floor building is 20 meters high.
1. Draw a force diagram detailing the forces acting on the man and on the barrel of bricks
(290 lbs). Determine the acceleration of the system..
2. How fast was the barrel traveling when it struck the man 1/2 way up the building? What
was the barrel's velocity relative to the man?
3. Draw a new force diagram for the barrel and man after the bricks have fallen out.
Determine the new acceleration of the system.
4. How fast was the barrel traveling when it struck the man a 2nd time? What was its
velocity relative to the man?
5. Once the man let go of the rope, assume that the barrel was essentially in free fall.
(Assume negligible air resistance). How long did it take the barrel to reach the ground?
6. How fast was it going when it hit the man?
7. How fast would it have been going if it had been full of bricks (290 lbs, not 50 lbs)?
To solve the given problems, we need to apply the principles of Newton's laws of motion and the concept of force, acceleration, and velocity. Let's break down each question and explain how to find the answer:
1. Draw a force diagram detailing the forces acting on the man and on the barrel of bricks (290 lbs). Determine the acceleration of the system:
- We start by drawing a force diagram for the man and the barrel.
- The forces acting on the man are his weight (135 lbs) and the tension in the rope.
- The forces acting on the barrel are its weight (240 lbs) and the tension in the rope.
- The tension in the rope is the force responsible for accelerating both the man and the barrel.
- Once we have the forces represented on the diagram, we can apply Newton's second law (F = ma) to calculate the acceleration of the system.
2. How fast was the barrel traveling when it struck the man halfway up the building? What was the barrel's velocity relative to the man?
- To find the velocity of the barrel when it struck the man, we need to calculate the time it took to fall halfway up the building.
- The distance between the roof and halfway up the building is 20 meters.
- Since we're assuming negligible air resistance, we can use the kinematic equation to find the time taken to fall.
- Once we have the time, we can calculate the velocity of the barrel using the formula v = u + at, where u is the initial velocity (0 m/s), a is the acceleration due to gravity, and t is the time.
3. Draw a new force diagram for the barrel and man after the bricks have fallen out. Determine the new acceleration of the system.
- After the bricks have fallen out, the weight of the barrel reduces to 50 lbs.
- Redraw the force diagram for the man and the barrel, considering only the weight and tension forces.
- We can use Newton's second law (F = ma) to find the new acceleration of the system.
4. How fast was the barrel traveling when it struck the man the second time? What was its velocity relative to the man?
- Follow the same process as in question 2 to calculate the velocity of the barrel when it struck the man the second time.
5. Once the man let go of the rope, assume that the barrel was essentially in free fall (negligible air resistance). How long did it take the barrel to reach the ground?
- Since the barrel is in free fall, it undergoes simple vertical motion.
- We can use the kinematic equation for constant acceleration to find the time it takes for the barrel to reach the ground.
- Set the initial velocity (u) as the velocity of the barrel when it struck the man the second time, and the final displacement (s) as the height of the building (20 meters).
6. How fast was it going when it hit the man?
- Follow the same process as in question 5 to calculate the velocity of the barrel when it hit the man.
7. How fast would it have been going if it had been full of bricks (290 lbs, not 50 lbs)?
- The weight of the barrel changes to 290 lbs (with bricks).
- Repeat the calculations from question 5 to find the velocity of the barrel if it had been full of bricks.
To solve these questions, you'll need to use the given weight conversions (1 lb ≈ 4.5 N) to convert the weights into newtons.