Question

A body of mass 40kg resting on a rough horizontal surface is subjected to a force 'P ' which is just enough to start the motion of the body. If \[{\mu _s} = 0.5, {\mu _k} = 0.4,g = 10m/{s^2}\] and the force 'P ' is continuously applied on the body, then the acceleration of the body is:
A. Zero
B. \[1m/{s^2}\]
C. \[2m/{s^2}\]
D. \[2.4m/{s^2}\]

Answer 1

Hint: Acceleration, rate at which velocity varies over time, both in terms of velocity and direction. Whether it is speeding up or slowing down, a point or object traveling along a straight line is accelerated. Motion on a circle is accelerated even if the velocity is constant, because the direction changes continuously. These effects contribute to the acceleration for all other kinds of motion.

Complete step-by-step answer:
Formula Used: \[F = ma\]

Given,

Mass of a body \[m = 40kg\]

\[
  {\mu _s} = 5 \\
  {\mu _k} = 0.4 \\
  g = 10m/{s^2} \\
\]

Since, P is the force that is enough to trigger the body 's motion

\[P = {\mu _s}N = {\mu _s}mg\]

As the body moves under this force it gives the net force on the body,

\[
  F = ma = P - f \\
  ma = {\mu _s}mg - {\mu _k}N \\
  ma = m({\mu _s} - {\mu _k})g \\
  a = ({\mu _s} - {\mu _k})g \\
  a = (0.5 - 0.4) \times 10 \\
  a = 1m/{s^2} \\
\]

Hence, the acceleration of the body is \[1m/{s^2}\].

Therefore, option B is the right answer.

Note: In this problem we will note that the F = ma formula which is Newton's second law of motion describing the relation between the mass of an object and the amount of force required to accelerate it. Newton's second law is often stated as F = ma, meaning that the force (F) acting on an object is equal to an object's mass (m) times its acceleration (a). This means the more mass an object has, the greater the power it requires to accelerate. And the greater the force, the greater the acceleration of an object.