Q31DQ - University Physics with Modern Physics

Question

Boxes A and B are in contact on a horizontal, frictionless surface. You push on box A with a horizontal 100-N force (Fig. Q4.31). Box A weighs 150 N, and box B weighs 50 N. Is the force that box A exerts on box B equal to 100 N, greater than 100 N, or less than 100 N? Explain.

Step-by-Step Solution

Answer

The force that box A exerts on box B is less than 100 N.

Step 1: Given data

• External force on the box-A, F = 100 N.
• Weight of box A = 150 N.
• Weight of box B = 50 N.

Step 2: Second law of motion

According to Newton's second law of motion, the force on a body is equal to its mass times acceleration.

Step 3: Determining the force on box B

The external force applied to the two-box system generates equal acceleration in the two boxes. If  g is the acceleration due to gravity, the masses of the two boxes are,

$$\begin{gathered} m_A=\frac{150\hspace{0.33em}N}{g} \\ {m}_B=\frac{50\hspace{0.33em}N}{g} \end{gathered}$$  

From the second law of motion, the acceleration a, produced in the boxes is,

$a=\frac{F}{M}$  

Here M is the total mass on which F is acting.

Substitute the values in the above expression, and we get,

$$\begin{gathered} a=\frac{100 N}{m_A+m_B} \\ =\frac{100 N}{{\displaystyle \frac{150 N}{g}}+{\displaystyle \frac{50 N}{g}}} \\ =\frac{g}{2} \end{gathered}$$  

The force exerted by box A on box B is  $F_{AB}$ then,

$$\begin{gathered} {\mathrm{F}}_{\mathrm{AB}}=\mathrm{a}\times {\mathrm{m}}_{\mathrm{B}} \\ =\frac{\mathrm{g}}{2}\times \frac{50 \mathrm{N}}{\mathrm{g}} \\ =25 \mathrm{N} \end{gathered}$$  

Thus, the force exerted by box A on box B is 25 N which is much less than 100 N.