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------------------------------------------------ You push a 67 kg box across a floor where the coefficient of kinetic friction is 0.55. The force you exert is horizontal.

(a) How much power is needed to push the box at a constant speed of 0.5 m/s?

To push a 67kg box at a constant speed of 0.5m/s with a coefficient of kinetic friction of 0.55, approximately 181.34 Watts of power is required. This is calculated by first finding the frictional force and then using it to determine the power. The detailed steps involve applying the formulas Ff = μ * m * g and P = Ff * v.

First, we need to find the frictional force opposing the motion. The frictional force (Ff) can be calculated using the formula:

Ff = μ * m * g

Where:

Substitute the given values:

Ff = 0.55 * 67 kg * 9.8 m/s² ≈ 362.67 N

The power (P) required to keep the box moving at a constant speed can be calculated using the formula:

P = Ff * v

Where v is the constant speed (0.5 m/s). Then, substitute the values:

P = 362.67 N * 0.5 m/s ≈ 181.34 Watts

Therefore, the power needed to push the box at a constant speed of 0.5 m/s is approximately 181.34 Watts.