A mover pushes a couch a distance of 4 m to the top of a ramp into the back of a truck using 500 N of force.
A) What is the work input of the mover?
B) What is the mover’s power if the task takes 10s?
C) If the mass of the couch is 100 kg and the back of the truck is 1.5 m high, what is the work output of the ramp?
D) What is the efficiency of the ramp?
E) What is the mechanical advantage of the ramp?
F) What is the ideal mechanical advantage of the ramp?
My answer please check if i am correct
A.2000 J
B. 200 W
C. 1470 J
D. 34 %
E. 2.94
F. 2.66
correct.
To check your answers, let's go through each question step by step:
A) To calculate the work input of the mover, we can use the formula: work = force × distance. In this case, the force is 500 N and the distance is 4 m. So, the work input would be:
Work input = 500 N × 4 m = 2000 J
So, your answer for A) is correct.
B) Power is defined as the rate at which work is done. It is calculated using the formula: power = work / time. Here, the work input is 2000 J and the time is given as 10 s. So, the power would be:
Power = 2000 J / 10 s = 200 W
Your answer for B) is also correct.
C) To calculate the work output of the ramp, we need to consider the change in height of the couch. The formula for work in this case is: work = force × distance. The force required to lift the couch would be its weight, given by the formula: force = mass × gravity. Here, the mass of the couch is 100 kg and the height of the truck is 1.5 m. So, the work output would be:
Work output = force × distance = (mass × gravity) × distance = (100 kg × 9.8 m/s^2) × 1.5 m = 1470 J
So, your answer for C) is correct.
D) Efficiency is defined as the ratio of useful output work to input work, expressed as a percentage. The formula for efficiency is: efficiency = (work output / work input) × 100. Based on the values we've calculated, the efficiency of the ramp would be:
Efficiency = (1470 J / 2000 J) × 100 = 73.5%
Your answer for D) seems to be incorrect. The correct answer should be 73.5% rather than 34%.
E) Mechanical advantage is the ratio of the output force to the input force. In this case, the output force is the weight of the couch, given by: force = mass × gravity. The input force is the force applied by the mover, which is given as 500 N. So, the mechanical advantage would be:
Mechanical advantage = output force / input force = (mass × gravity) / input force = (100 kg × 9.8 m/s^2) / 500 N = 1.96
Your answer for E) is incorrect. The correct mechanical advantage would be 1.96 rather than 2.94.
F) Ideal mechanical advantage is defined as the ratio of the input distance to the output distance. In this case, the input distance is the distance the mover pushes the couch, which is 4 m. The output distance is the distance the couch is lifted, which is the height of the truck, given as 1.5 m. So, the ideal mechanical advantage would be:
Ideal mechanical advantage = input distance / output distance = 4 m / 1.5 m = 2.67
Your answer for F) is incorrect. The correct ideal mechanical advantage would be 2.67 rather than 2.66.
So, to summarize, your answers for A) and B) are correct. However, your answers for C), D), E), and F) have some errors. The correct answers would be:
C) 1470 J
D) 73.5%
E) 1.96
F) 2.67