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A valuable antique chest is to be moved into a truck. The weight of the chest is 1400 N. To get the chest from the ground onto the truck bed, which is 1.0 m higher, the mover must decide what to do. Should they lift it straight up, or should they push it up their 4.0-m-long ramp? Assume they push the chest on a wheeled dolly, which in a simplified model is equivalent to sliding it up a frictionless ramp. Find the work done by the movers on the chest if they lift it straight up 1.0 m at constant speed.

User Danielpopa
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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.

User Anupa
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