15. A refrigerator weighing 1500 N is to be lifted onto a truck bed that is 1.0 m above the
ground. When pushed up a slanting ramp 2.0 m in length a force parallel to the ramp of
only 800 N is required to move it at constant velocity. Comparing the work involved in
lifting the refrigerator straight up to the work in pushing it along the ramp, there is
A) more work required when the ramp is employed.
B) an equal amount of work is required in each case.
C) less work required when the ramp is employed.
W=Fd
Lifting:
w=(1500)(1)
w= 1500
W=Fd
Lifting: Ramp:
w=(1500)(1) w= (800)(2)
w= 1500 w= 1600
1500<1600; more work using ramp
Answer: a
C) less work required when the ramp is employed.
To determine whether more work is required when lifting the refrigerator straight up or when pushing it along the ramp, we need to calculate the work done in each scenario.
1) Lifting the refrigerator straight up:
The work done when lifting an object straight up is given by the formula:
Work = force × distance
In this case, the force required to lift the refrigerator straight up is equal to its weight, which is 1500 N. The distance is the height of the truck bed, which is 1.0 m.
Therefore, the work done when lifting the refrigerator straight up is:
Work = 1500 N × 1.0 m = 1500 J (Joules)
2) Pushing the refrigerator along the ramp:
The work done when pushing an object along a ramp is given by the formula:
Work = force × distance × cosθ
In this case, the force required to push the refrigerator along the ramp is 800 N. The distance along the ramp is 2.0 m. Since the force is parallel to the ramp, the angle between the force and the ramp (θ) is 0°, and the cosine of 0° is 1.
Therefore, the work done when pushing the refrigerator along the ramp is:
Work = 800 N × 2.0 m × cos0° = 800 J (Joules)
Comparing the values of the work done:
Work when lifting straight up = 1500 J
Work when pushing along the ramp = 800 J
Since the work done when pushing the refrigerator along the ramp is less than the work done when lifting it straight up, the answer is C) less work required when the ramp is employed.