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 solve these physics problems, we need to understand the concept of forces, acceleration, and velocity. Let's go step by step and solve each question.
1. Draw a force diagram detailing the forces acting on the man and the barrel of bricks (290 lbs). Determine the acceleration of the system.
To draw the force diagram, we need to consider the forces acting on the man and the barrel.
For the man:
- Weight force acting downward (135 lbs or 135*4.5 N)
- Tension force from the rope acting upward
For the barrel:
- Weight force acting downward (290 lbs or 290*4.5 N)
- Tension force from the rope acting upward
Since the system is in equilibrium, the net force acting on the system is zero. This means:
Tension force from the rope - Weight of the man - Weight of the barrel = 0
By plugging in the values, we can solve for the tension force. Let's call the tension force T. We have:
T - (135*4.5 N) - (290*4.5 N) = 0
Solve this equation to find the tension force T. Once you have the tension force, you can use it to calculate the acceleration of the system using the equation:
Net Force = Mass * Acceleration
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 speed of the barrel when it struck the man, we can use the principles of conservation of mechanical energy. At the beginning, the barrel has potential energy due to its height, and as it falls, this potential energy is converted into kinetic energy. The total mechanical energy remains constant throughout the fall.
The initial potential energy of the barrel is given by:
Potential energy = Mass * Acceleration due to gravity * Height
The kinetic energy of the barrel just before it strikes the man is given by:
Kinetic energy = (1/2) * Mass * Velocity^2
By equating the initial potential energy to the final kinetic energy, we can solve for the velocity of the barrel when it strikes the man.
The velocity of the barrel relative to the man will be the same as the velocity calculated in the previous step.
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. The force diagram will be the same as before, but with a reduced weight for the barrel.
Again, apply the principle of equilibrium:
Tension force from the rope - Weight of the man - Weight of the barrel = 0
Solve for the new tension force and use it to calculate the new acceleration of the system using the equation:
Net Force = Mass * Acceleration
4. How fast was the barrel traveling when it struck the man for the second time? What was its velocity relative to the man?
This question is similar to question 2. Use the principles of conservation of mechanical energy to find the speed of the barrel when it strikes the man for the second time. The velocity relative to the man will be the same as the velocity calculated in the previous step.
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?
When the man let go of the rope, the barrel is in free fall. We can use the kinematic equation for free fall to find the time it takes for the barrel to reach the ground.
The equation to find the time of free fall is:
Height = (1/2) * Acceleration due to gravity * Time^2
Solve this equation for time to find the answer.
6. How fast was it going when it hit the man?
Using the time calculated in the previous step, we can find the final velocity of the barrel just before it hits the man. Use the equation:
Final velocity = Acceleration due to gravity * Time
7. How fast would it have been going if it had been full of bricks (290 lbs, not 50 lbs)? Explain your answer.
To find the velocity of the barrel if it had been full of bricks, we can apply the same principles as in question 5 and 6, but with the weight of the full barrel (290 lbs). Calculate the time it will take for the full barrel to reach the ground using the same equation as in question 5, and then use that time in question 6 to find the velocity.