A body of mass m is resting on the floor. A minimum amount of force is applies on the body and the force continues to act on the body as it moves. If coefficent of static and dynamic friction are 0.4 and 0.3 resp. then the acceleration of the body is
a. 0
b. 3.98
c. 0.98
d. 4.98

To determine the acceleration of the body, we first need to analyze the forces acting on it. The body is initially at rest, and we have both static and dynamic friction coefficients to consider. Let's break this down step by step.

Understanding the Forces

When a force is applied to an object at rest, it must overcome static friction before the object can start moving. The static friction force can be calculated using the formula:

• F_static = μ_s * N

Where:

• μ_s is the coefficient of static friction (0.4 in this case).
• N is the normal force, which is equal to the weight of the object if it's resting on a horizontal surface (N = m * g, where g is the acceleration due to gravity, approximately 9.81 m/s²).

Calculating the Maximum Static Friction

Let's denote the mass of the body as m. The maximum static friction force can be calculated as:

• F_static = 0.4 * m * 9.81

Now, if the applied force is less than this maximum static friction force, the body will not move, and the acceleration will be 0. If the applied force exceeds this value, the body will start to move, and we will then consider dynamic friction.

Dynamic Friction and Acceleration

Once the body is in motion, the force of dynamic friction comes into play, calculated as:

• F_dynamic = μ_d * N

Where:

• μ_d is the coefficient of dynamic friction (0.3).

Thus, the dynamic friction force is:

• F_dynamic = 0.3 * m * 9.81

Net Force and Acceleration Calculation

To find the net force acting on the body when it is moving, we subtract the dynamic friction force from the applied force (let's denote the applied force as F_applied):

• F_net = F_applied - F_dynamic

Using Newton's second law, we can find the acceleration:

• a = F_net / m

Finding the Acceleration

To determine the acceleration, we need to know the applied force. However, since the question does not specify the applied force, we can analyze the options given:

• If the applied force is less than 0.4 * m * 9.81, then the acceleration is 0.
• If it exceeds this value, we can calculate the acceleration using the dynamic friction force.

Let's assume the applied force is just enough to overcome static friction, which means:

• F_applied = 0.4 * m * 9.81

In this case, the body would start moving, and we can calculate the acceleration using the dynamic friction force:

• F_net = 0.4 * m * 9.81 - 0.3 * m * 9.81
• F_net = (0.4 - 0.3) * m * 9.81 = 0.1 * m * 9.81

Now, substituting into the acceleration formula:

• a = (0.1 * m * 9.81) / m = 0.1 * 9.81 = 0.981 m/s²

Final Answer

Thus, the acceleration of the body, when the applied force is just enough to overcome static friction, is approximately 0.98 m/s². Therefore, the correct answer is c. 0.98.