A 150-kg safe on frictionless casters is being raised 1.20 m to the bed of a truck using planks 4.00 m long. The force needed to push the safe up is

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Quizplus · Accepted Answer

The force needed to push the safe up can be calculated using the formula for work done against gravity, which is $W = Fd$, where $W$ is the work done, $F$ is the force applied, and $d$ is the distance over which the force is applied. The work done is equal to the change in potential energy, which is $W = mgh$, where $m$ is the mass of the safe, $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), and $h$ is the height raised. Given $m = 150 \, \text{kg}$, $g = 9.8 \, \text{m/s}^2$, and $h = 1.20 \, \text{m}$, the work done is $W = 150 \times 9.8 \times 1.20 = 1764 \, \text{J}$. The force required is then calculated by dividing the work done by the distance over which the force is applied, which is the length of the planks, $4.00 \, \text{m}$. Thus, $F = \frac{W}{d} = \frac{1764}{4} = 441 \, \text{N}$.

A 150-Kg Safe on Frictionless Casters Is Being Raised 1