Question

A 5 kg block is placed on a horizontal surface. A force of 10 N is applied to the block. The coefficient of friction between the block and the surface is 0.2. Find the acceleration of the block.

• A. \( 0.04 \, \text{m/s}^2 \)
• B. \( 1.0 \, \text{m/s}^2 \)
• C. \( 2.0 \, \text{m/s}^2 \)
• D. \( 1.5 \, \text{m/s}^2 \)

Hint:

The frictional force always opposes the motion of the object and reduces the effective applied force. Make sure to account for friction when calculating the net force.

Answer 1

The Correct Option is A

Inputs:

• Block mass: \( m = 5 \, \text{kg} \)
• Applied force: \( F_{\text{applied}} = 10 \, \text{N} \)
• Friction coefficient: \( \mu = 0.2 \)
• Gravitational acceleration: \( g = 9.8 \, \text{m/s}^2 \)

Step 1: Determine Frictional Force

Frictional force \( F_{\text{friction}} \) is calculated as: \[ F_{\text{friction}} = \mu \cdot N \] where \( N \) is the normal force. On a horizontal surface, the normal force equals the block's weight: \[ N = m \cdot g = 5 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 49 \, \text{N} \] Therefore, the frictional force is: \[ F_{\text{friction}} = 0.2 \times 49 = 9.8 \, \text{N} \]

Step 2: Calculate Net Force

The net force \( F_{\text{net}} \) on the block is the applied force less the frictional force: \[ F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} = 10 \, \text{N} - 9.8 \, \text{N} = 0.2 \, \text{N} \]

Step 3: Compute Acceleration via Newton's Second Law

Newton's Second Law: \[ F_{\text{net}} = m \cdot a \] Solving for acceleration \( a \): \[ a = \frac{F_{\text{net}}}{m} = \frac{0.2 \, \text{N}}{5 \, \text{kg}} = 0.04 \, \text{m/s}^2 \]

✅ Result:

The block's acceleration is \( \boxed{0.04 \, \text{m/s}^2} \).