Question

Using a horizontal force of $200\;{\rm{N}}$, we intend to move a wooden cabinet across a floor at a constant velocity. What is the frictional force that will be exerted on the cabinet?

Answer 1

We will use Newton’s laws of motion in this question. Also, we will use the fact that frictional force obstructs motion by acting opposite to the direction of movement of an object.

Complete step by step answer:
We know Newton’s law of motion which states that an external unbalanced force could only cause a motion to an object at rest or obstruct the uniform motion of an object. If an object is in uniform motion, it means that the object is moving with a constant velocity. Hence, we can say that an object can move with constant velocity only if the net force acting on it is zero.

We also know that force is the product of mass and acceleration. Hence, if the acceleration of an object is zero, then the net force on it will also be zero. A body with zero acceleration moves with a constant velocity. Again, we get that a zero force will give constant velocity to an object.

It is given that a wooden cabinet is acted upon by a horizontal force of $200\;{\rm{N}}$. If we want to move it with a constant velocity, the net force acting on it should be zero. So, for the net force to be zero, a force of the same magnitude, which is $200\;{\rm{N}}$, should be applied in the opposite direction. Since two equal and opposite forces act at a point, the net force will be zero.
Hence, a frictional force of $200\;{\rm{N}}$ will be exerted on the cabinet, opposite to the direction of the applied horizontal force, for maintaining a constant velocity of motion.

Note:
If an object is at rest or in uniform motion, the algebraic sum of all the forces acting on the object will be zero. By algebraic sum, we mean the sign of the forces along with their magnitudes. We should take an algebraic sum as the direction of the forces are also important while calculating the net force.