Question

directions: solve the problem shown below. any data, calculations, or models you use to support your thinking should be explained. problem: three boxes rest on a level, horizontal surface, as shown in figure 1. the mass of each box is 2 kg. each box is 5 cm tall and 10 cm wide. what is the minimum amount of work that can be done to make a stack of the three boxes, as shown in figure 2?

Explanation:

Step1: Determine the height each box is lifted

To stack the boxes, we need to lift the second box onto the first and the third box onto the stack. The height of each box is \( h = 5\space cm = 0.05\space m \).

• To lift the second box (Box 2) onto the first box (Box 1), we need to lift it by a height equal to the height of one box, \( h_2 = 0.05\space m \).
• To lift the third box (Box 3) onto the stack of Box 1 and Box 2, we need to lift it by a height equal to the height of two boxes, \( h_3 = 2\times0.05\space m = 0.10\space m \).

Step2: Calculate the force required to lift each box

The force required to lift a box is equal to its weight, \( F = mg \), where \( m = 2\space kg \) and \( g = 9.8\space m/s^2 \).
So, \( F = 2\space kg\times9.8\space m/s^2 = 19.6\space N \).

Step3: Calculate the work done to lift each box

The work done to lift an object is given by \( W = Fd \), where \( F \) is the force and \( d \) is the distance lifted.

• Work done to lift Box 2: \( W_2 = F\times h_2 = 19.6\space N\times0.05\space m = 0.98\space J \).
• Work done to lift Box 3: \( W_3 = F\times h_3 = 19.6\space N\times0.10\space m = 1.96\space J \).

Step4: Calculate the total work done

The total work done is the sum of the work done to lift Box 2 and Box 3.
\( W_{total} = W_2 + W_3 = 0.98\space J + 1.96\space J = 2.94\space J \).

Answer:

The minimum amount of work done is \( \boldsymbol{2.94\space J} \).