Question

A body of mass 10 kg is kept on a horizontal surface. The coefficient of kinetic friction between the body and the surface is 0.5. A horizontal force of 60N is applied on the body. The resulting acceleration of the body is about

• A. 5 ms^-2
• B. 6 ms^-2
• C. zero
• D. 1 ms^-2

Answer 1

The Correct Option is D

Given: 

• Mass of the body, \( m = 10 \) kg
• Coefficient of kinetic friction, \( \mu_k = 0.5 \)
• Applied horizontal force, \( F = 60 \) N
• Acceleration due to gravity, \( g = 9.8 \) m/s²

Step 1: Calculate the Frictional Force

The kinetic friction force is given by:

\[ f_k = \mu_k \times N \]

Since the normal force \( N \) is equal to the weight of the body:

\[ N = mg = 10 \times 9.8 = 98 \text{ N} \]

\[ f_k = 0.5 \times 98 = 49 \text{ N} \]

Step 2: Apply Newton's Second Law

The net force acting on the body is:

\[ F_{ ext{net}} = F - f_k \]

\[ F_{ ext{net}} = 60 - 49 = 11 \text{ N} \]

Now, using Newton's second law:

\[ F = ma \]

\[ 11 = 10a \]

\[ a = \frac{11}{10} = 1.1 \approx 1 \text{ m/s}^2 \]

Answer: The acceleration of the body is about 1 m/s² (Option D).

Answer 2

To solve this problem, we first calculate the frictional force acting on the body. The frictional force \( f_{\text{friction}} \) is given by: \[ f_{\text{friction}} = \mu \cdot N \] where: - \( \mu = 0.5 \) is the coefficient of kinetic friction, - \( N = m \cdot g \) is the normal force, and \( m = 10 \, \text{kg} \), \( g = 9.8 \, \text{ms}^{-2} \). Thus, \[ N = 10 \times 9.8 = 98 \, \text{N} \] Now calculate the frictional force: \[ f_{\text{friction}} = 0.5 \times 98 = 49 \, \text{N} \] The net force \( F_{\text{net}} \) acting on the body is the applied force minus the frictional force: \[ F_{\text{net}} = F_{\text{applied}} - f_{\text{friction}} = 60 \, \text{N} - 49 \, \text{N} = 11 \, \text{N} \] The resulting acceleration \( a \) can be found using Newton's second law: \[ F_{\text{net}} = m \cdot a \] \[ a = \frac{F_{\text{net}}}{m} = \frac{11}{10} = 1 \, \text{ms}^{-2} \]

Thus, the resulting acceleration is \( 1 \, \text{ms}^{-2} \), and the correct answer is (D).