Question

A block of mass 5 kg is placed on a rough horizontal surface with a coefficient of friction 0.5. If a horizontal force of 60 N is acting on it, then the acceleration of the block is (Acceleration due to gravity \( g = 10 \) ms\(^{-2}\)):

• A. \( 7 \) ms\(^{-2}\)
• B. \( 5 \) ms\(^{-2}\)
• C. \( 10 \) ms\(^{-2}\)
• D. \( 15 \) ms\(^{-2}\)

Hint:

When dealing with frictional forces, always calculate the resistive force first before applying Newton’s second law to find acceleration.

Answer 1

The Correct Option is A

Step 1: Compute the Frictional Force The resistive force due to friction is calculated using: \[ f = \mu mg. \] Substituting the given values: \[ f = 0.5 \times 5 \times 10 = 25 \text{ N}. \]
Step 2: Compute the Net Force Acting on the Block The net force causing motion is: \[ F_{\text{net}} = F_{\text{applied}} - f. \] \[ F_{\text{net}} = 60 - 25 = 35 \text{ N}. \]
Step 3: Calculate Acceleration Using Newton’s Second Law Newton’s second law states: \[ a = \frac{F_{\text{net}}}{m}. \] \[ a = \frac{35}{5} = 7 \text{ ms}^{-2}. \] % Final Answer Thus, the correct answer is option (1): \( 7 \) ms\(^{-2}\).

Answer 2

Step 1: Determine the Frictional Force The frictional force opposing the motion is given by: \[ f = \mu mg. \] Using the given values: coefficient of friction \( \mu = 0.5 \), mass \( m = 5 \, \text{kg} \), and acceleration due to gravity \( g = 10 \, \text{m/s}^2 \), we have: \[ f = 0.5 \times 5 \times 10 = 25 \text{ N}. \]
Step 2: Calculate the Resultant Force on the Block The net force driving the block forward is the applied force minus the frictional force: \[ F_{\text{net}} = F_{\text{applied}} - f. \] Given the applied force \( F_{\text{applied}} = 60 \text{ N} \), \[ F_{\text{net}} = 60 - 25 = 35 \text{ N}. \]
Step 3: Find the Acceleration Using Newton's Second Law Newton’s second law relates net force and acceleration by: \[ a = \frac{F_{\text{net}}}{m}. \] Substituting the values: \[ a = \frac{35}{5} = 7 \text{ m/s}^2. \]
Final Answer: Hence, the correct answer is option (1): \[ \boxed{7 \text{ ms}^{-2}}. \]