Question

This is not a test, this is a practice paper.

Answer 1

Given:

The masses of the boxes;

M=45 kg

m=32 kg

The horizontal force applied to the objects, F=60 N

To find:

a. The acceleration of objects.

b. The force applied by 32 kg box on 45 kg box.

c. The force applied by 45 kg box on 32 kg box.

Step-by-step explanation:

a.

From Newton's second law of motion, the applied force is given by,

`F=(M+m)a`

Where a is the acceleration of the objects.

On substituting the known values,

`\begin{gathered} 60=(45+32)a \\ \implies a=(60)/(45+32) \\ =0.78\text{ m/s}^2 \end{gathered}`

b and c:

From Newton's third law, The force applied by the 32 kg box to the 45 kg box is equal and opposite to the force applied by the 45 kg box on the 32 kg box.

The force diagram of 32 kg box:

Where N₃₂ is the normal force acting on the box and W₃₂ is the weight of the box. F_mM is the force applied by the 45 kg box to 32 kg box.

The force diagram of 45 kg box:

Where N₄₅ is the normal force acting on the box, W₄₅ is the weight of the box, and F_Mm is the force applied by the 32 kg box to 45 kg box.

From Newton's third law,

`F_(mM=-FMm)`

The only horizontal force acting on the 32 kg box is the force applied by the 45 kg box.

Thus, applying Newton's second law to the 32 kg box,

`F_(mM)=ma`

On substituting the known values,

`\begin{gathered} F_(mM)=32*0.78 \\ =24.96\text{ N} \end{gathered}`

Final answer:

a. The acceleration of the objects is 0.78 m/s².

b. The force applied by 32 kg box on 45 kg box is -24.96 N

c. The force applied by 45 kg box on 32 kg box is 24.96 N