Final answer:
The work done by movers in lifting a valuable antique chest onto a truck bed can be calculated by multiplying the weight of the chest by the distance it is lifted. When using a ramp, the work is calculated by multiplying the force exerted, the distance, and the cosine of the angle of the ramp. Pushing the chest up the ramp requires more work compared to lifting it straight up.
Step-by-step explanation:
To get the chest from the ground onto the truck bed, the movers can either lift it straight up or push it up a ramp. Let's calculate the work done in both scenarios.
When lifting it straight up, the work done is given by the formula:
Work = force x distance
Since the chest is lifted straight up at a constant speed, the work done equals the weight of the chest multiplied by the distance it is lifted:
Work = 1400 N x 1.0 m = 1400 joules
Now, let's calculate the work done when pushing the chest up the ramp. The work done is given by the formula:
Work = force x distance x cos(angle)
In this case, the force exerted is the parallel component of the force (500 N) and the distance is the length of the ramp (4.0 m):
Work = 500 N x 4.0 m x cos(0°) = 2000 joules
Therefore, pushing the chest up the ramp requires more work compared to lifting it straight up.