Question

A block of mass 2 kg is placed on a rough horizontal surface. If a horizontal force of 20 N acting on the block produces an acceleration of 7 m/s$^2$ in it, then the coefficient of kinetic friction between the block and the surface is (Acceleration due to gravity = 10 m/s$^2$)

• A. 0.2
• B. 0.3
• C. 0.4
• D. 0.5

Hint:

To find the coefficient of kinetic friction, first find the frictional force by subtracting the net accelerating force from the applied force, then divide it by the normal force (which equals the weight on a horizontal surface).

Answer 1

The Correct Option is B

Let's analyze the problem step by step:
Step 1: Identify the given data Mass of the block, $m = 2\, \text{kg}$
Applied force, $F = 20\, \text{N}$
Acceleration of the block, $a = 7\, \text{m/s}^2$
Acceleration due to gravity, $g = 10\, \text{m/s}^2$
Step 2: Calculate the net force causing acceleration Using Newton's second law, net force $F_{\text{net}} = m \times a = 2 \times 7 = 14\, \text{N}$
Step 3: Determine the frictional force The applied force $F = 20\, \text{N}$ causes acceleration, but the net accelerating force is only $14\, \text{N}$. The difference is due to friction: \[ f_k = F - F_{\text{net}} = 20 - 14 = 6\, \text{N} \]
Step 4: Calculate the normal force Since the block is on a horizontal surface, the normal force $N = mg = 2 \times 10 = 20\, \text{N}$
Step 5: Calculate the coefficient of kinetic friction \[ \mu_k = \frac{f_k}{N} = \frac{6}{20} = 0.3 \] Hence, the coefficient of kinetic friction is 0.3.