Physics - Unit V Challenge Problem
No matter how bad your day is going, here's proof that things could be A LOT worse.
This is a bricklayer's accident report that was printed in the newsletter of the English
equivalent of the Workers' Compensation Board. So here, thanks to John Sedgwick, is this
Bricklayer's report.
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)?
Explain your answer.
To answer the questions, we need to analyze the forces acting on the man and the barrel and use Newton's second law of motion (F = ma) to calculate the acceleration and velocities.
1. Forces acting on the man and the barrel:
- For the man: His weight (135 lbs) can be converted to newtons by multiplying it by the conversion factor, 4.5 N/lb. So, his weight is 135 lbs * 4.5 N/lb = 607.5 N. This force acts downward.
- For the barrel: Its weight (240 lbs) can also be converted to newtons: 240 lbs * 4.5 N/lb = 1080 N. This force also acts downward.
- In addition to weight, there is tension in the rope acting on both the man and the barrel, directed upward.
The net force acting on the system (man and barrel) is the difference between the downward forces (weight of the man and the barrel) and the upward force (tension in the rope). The acceleration of the system can be calculated using Newton's second law: F_net = ma, where F_net is the net force and a is the acceleration.
2. To determine the speed of the barrel when it strikes the man halfway up the building, we need to divide the total distance traveled by the time it takes to reach that point. Given that the building is 20 meters high, the halfway point would be at 10 meters. We can assume that the initial velocity of the barrel is zero because it starts from rest at the sixth floor.
To calculate the time it takes, we can use the equation of motion: d = ut + (1/2)at^2, where d is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time. In this case, the distance is 10 meters, u = 0, and we can use the acceleration calculated in question 1. Solving for time, we can then use it to find the velocity of the barrel at 10 meters.
3. After the bricks have fallen out, the forces acting on the barrel change. The weight of the barrel is now 50 lbs, which can be converted to newtons using the conversion factor: 50 lbs * 4.5 N/lb = 225 N. The upward force (tension in the rope) remains the same as in question 1.
We can find the new acceleration of the system using the same formula as in question 1: F_net = ma, where the net force is the difference between the downward force (weight of the barrel) and the upward force (tension in the rope).
4. Similar to question 2, we can calculate the time it takes for the barrel to reach the man for the second time. The distance traveled is again 10 meters, the initial velocity is zero, and the acceleration is now the new value calculated in question 3. We can use the equation of motion, d = ut + (1/2)at^2, to find the time. Then, we can determine the velocity of the barrel at that point.
5. Once the man lets go of the rope, the barrel is in free fall, assuming negligible air resistance. The time it takes for the barrel to reach the ground can be calculated using the formula for time of free fall: t = sqrt(2h/g), where h is the height and g is the acceleration due to gravity (approximately 9.8 m/s^2).
6. The speed of the barrel when it hits the man can be calculated using the equation of motion, v = u + gt, where v is the final velocity (which is zero when it hits the man), u is the initial velocity (from question 4), g is the acceleration due to gravity, and t is the time calculated in question 5.
7. To calculate the final speed if the barrel had been full of bricks, we can use the same concept as in question 6, but now the force causing the acceleration would be the weight of the barrel and the bricks (290 lbs * 4.5 N/lb), rather than just the weight of the barrel. The acceleration would be greater, resulting in a higher final speed.
By following these steps and calculating the forces, accelerations, and velocities, we can find the answers to the given questions.