Question

A block of mass 2 kg is kept on a rough horizontal surface. If a horizontal force of 4 N is applied on the block, then the acceleration of the block is (Coefficient of static friction between the block and the surface is 0.3)

• A. 0.94 m s\textsuperscript{-2}
• B. 1 m s\textsuperscript{-2}
• C. zero
• D. 2 m s\textsuperscript{-2}

Hint:

To determine if a block on a rough surface will move: 1. Calculate the maximum static friction force (\(f_{\text{s,max}} = \mu_s N\)). 2. Compare it with the applied force (\(F_{\text{applied}}\)). If \(F_{\text{applied}}<f_{\text{s,max}}\), the block remains at rest, and acceleration is zero. The actual static friction force acting on the block will be equal to the applied force. If \(F_{\text{applied}} \ge f_{\text{s,max}}\), the block will move (or just begin to move), and its acceleration can be found using Newton's second law, considering kinetic friction if it's already in motion.

Answer 1

The Correct Option is C

Step 1: Calculate the maximum static friction force.
Mass of the block (m) = 2 kg
Coefficient of static friction (\(\mu_s\)) = 0.3
Acceleration due to gravity (g) is approximately 9.8
m/s\textsuperscript{2}.
The normal force (N) acting on the block on a horizontal surface is equal to its weight:
N = mg = 2 kg \( \times \) 9.8 m/s\textsuperscript{2} = 19.6 N
Maximum static friction force (f\textsubscript{s,max}) = \(\mu_s\)N f\textsubscript{s,max} = 0.3 \( \times \) 19.6 N = 5.88 N Step 2: Compare the applied force with the maximum static friction force.
Applied horizontal force (F\textsubscript{applied}) = 4 N
Since the applied force (4 N) is less than the maximum static friction force (5.88 N), the block will not move.
Step 3: Determine the acceleration of the block.
If the block does not move, its acceleration is zero. Step 4: Select the correct option.
The acceleration of the block is zero, which matches option (3).