Friction: Practice Problem & Solution
A man of mass \(80 \text{ kg}\) pushes a box of mass \(20 \text{ kg}\) horizontally. The man moves the box with a constant acceleration of \(2 \text{ m/s}^2\) but his foot does not slip on the ground. There is no friction between the box and the ground, whereas there is sufficient friction between the man's foot and the ground to prevent him from slipping. Assertion (A): The force applied by the man on the box is equal and opposite to the force applied by the box on the man. Reason (R): Friction force applied by the ground on the man is \(200 \text{ N}\).
Solution Explained:
To solve this problem, we apply the core principles of Friction. Understanding the underlying formula is key to arriving at the correct answer below:
Assertion (A) is Newton's Third Law, which is true. For the box: \(F_{\text{man-box}} = m_{\text{box}}a = 20 \text{ kg} \times 2 \text{ m/s}^2 = 40 \text{ N}\). By action-reaction, \(F_{\text{box-on-man}} = 40 \text{ N}\). For the man: \(F_{\text{friction}} - F_{\text{box-on-man}} = m_{\text{man}}a). So, \(F_{\text{friction}} - 40 \text{ N} = 80 \text{ kg} \times 2 \text{ m/s}^2 = 160 \text{ N}\). Thus, \(F_{\text{friction}} = 200 \text{ N}\). So (R) is true. But (R) does not explain (A).
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