A construction crew pulls up an 87.5-kg load using a rope thrown over a pulley and pulled by an electric motor. They lift the load 15.5 m and it arrives with a speed of 15.6 m/s having started from rest. Assume that acceleration was not constant.
I have done the problem but am thinking that it is wrong. Can anyone please check my work and correct me? Thank you so much.
a) How much work (J) was done by the motor?
My work: (87.5 kg)(15.5 m) = 1356.3 J
K= 1/2(87.5 kg)(15.6 m/s)^2 = 10647
1356.3 + 10647 = 12003.25 J
b) How much work (J) was done by gravity?
My work: - 1356.25 J
c) What constant force (N) could the motor have exerted to cause this motion? (This would have been the average force exerted by the motor)
My work: (12003.25) = (f)(15.5m)
12003.25J/15.5 = 774.4 N
This is way back ago, but for those students who are encountering the same problem,
Work done = PE + KE = mgh + .5mv^2
And he is missing h for PE
To check your work, let's go through each part of the problem step by step.
a) How much work (J) was done by the motor?
Your calculation looks correct. The work done by the motor can be found using the formula: Work = Force * Distance. Plugging in the values, we get:
Work = (87.5 kg) * (15.5 m) = 1356.25 J.
b) How much work (J) was done by gravity?
The work done by gravity can be found by multiplying the change in potential energy by gravity:
Work = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height. In this case, the change in potential energy is equal to the work done by gravity.
Work = (87.5 kg) * (9.8 m/s^2) * (15.5 m) = 12845.5 J.
However, note that the work done by gravity should have a negative sign since gravity is acting in the opposite direction of the displacement. Therefore, the correct answer is -12845.5 J.
c) What constant force (N) could the motor have exerted to cause this motion?
To find the constant force exerted by the motor, we can use the work-energy theorem. The work done by the motor is equal to the change in kinetic energy:
Work = Change in Kinetic Energy.
So, we can write:
Work = (1/2) * m * v^2.
Rearranging the equation, we get:
Force * Distance = (1/2) * m * v^2.
Substituting the given values, we have:
Force * 15.5 m = (1/2) * (87.5 kg) * (15.6 m/s)^2.
Solving for the force, we find:
Force = (0.5 * 87.5 kg * (15.6 m/s)^2) / 15.5 m.
Evaluating the expression, we get:
Force ≈ 811.55 N (rounded to three significant figures).
So, in summary:
a) The work done by the motor is 1356.25 J.
b) The work done by gravity is -12845.5 J.
c) The constant force exerted by the motor is approximately 811.55 N.
Please double-check your calculations based on these explanations and let me know if you have any further questions.