Question

A block of mass \( m \) is moving on a rough horizontal surface. The coefficient of kinetic friction between block and surface is \( \mu_k \). The net force exerted by the surface on the block is

• A. \( mg \left( 1 + \mu_k \right)^{1/2} \)
• B. \( mg \left[ 1 + \mu_k \right]^{1/2} \)
• C. \( mg \left( 1 + \mu_k^2 \right) \)
• D. \( mg \left( 1 + \mu_k^2 \right)^{1/2} \)

Hint:

In problems with friction, remember that the net force can be found by combining the forces acting on the object, especially when they are perpendicular to each other.

Answer 1

The Correct Option is D

Step 1: Understanding the forces.
The net force exerted by the surface is the resultant of the frictional force and the force due to gravity. The frictional force \( f_{\text{friction}} = \mu_k N \), where \( N = mg \) is the normal force.
Step 2: Finding the net force.
The net force can be expressed as the square root of the sum of the squared forces, i.e., \[ F_{\text{net}} = mg \left( 1 + \mu_k^2 \right)^{1/2} \] Step 3: Conclusion.
The correct answer is (D), \( mg \left( 1 + \mu_k^2 \right)^{1/2} \).