Question

A block of certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are 0.4 and 0.25 respectively. A constant horizontal force \( F = 20 \, \text{N} \) acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take \( g = 10 \, \text{m/s}^2 \)): 

• A. 1.0 kg
• B. 2.2 kg
• C. 4.4 kg
• D. 1.2 kg

Hint:

In problems involving friction, use Newton's second law to relate the net force, mass, and acceleration, and be sure to account for both the applied force and the opposing frictional force.

Answer 1

The Correct Option is A

From the given data, the force applied is \( F = 20 \, \text{N} \). The acceleration of the block can be found using the slope of the graph, which represents velocity versus time. The initial acceleration is constant, and the frictional force that opposes the motion is \( f = \mu N \), where \( \mu \) is the coefficient of kinetic friction and \( N \) is the normal force. Since \( N = m g \), the frictional force is: \[ f = \mu m g = 0.25 m g \] Thus, the net force acting on the block is: \[ F_{\text{net}} = F - f = 20 - 0.25 m g \] Using Newton's second law \( F_{\text{net}} = m a \), where \( a \) is the acceleration, we have: \[ 20 - 0.25 m g = m a \] From the graph, the acceleration \( a \) is determined from the slope of the velocity-time graph. Using the information from the graph and solving the equation, we find that the mass of the block is \( m = 2.2 \, \text{kg} \).