Question

On the horizontal surface of a truck $\left( {\mu = 0.6} \right)$, a block of mass $1kg$ is placed. If the truck is accelerated at the rate of $5m{s^{ - 2}}$ then frictional force on the block will be
(A) $6N$
(B) $5N$
(C) $5.88N$
(D) $8N$

Answer 1

Here, the truck is moving with an acceleration of $5m{s^{ - 2}}$. Here, the concept of maximum frictional force is to be used. For your understanding, try to make the free body diagram of the block. A pseudo force will act on the block and also the block is supposed to be held at the same place so definitely, frictional force is going to come in action.

Complete step by step answer:
The concept of maximum frictional force is that the maximum amount of frictional force that a surface can apply on an object. In this case, maximum static friction will act. Static friction is the friction which keeps the object at rest. Friction is a self-adjusting force. So, if a force variable $F$ is acting on the object, let say $F$ is increasing linearly, then friction will also increase linearly with $F$ but as soon as $F$ hits the maximum value of friction force, friction will remain constant but $F$ will keep on increasing.

Now, coming back to our question. It is given that the truck is accelerating with an acceleration of $5m{s^{ - 2}}$, therefore, a pseudo force will act on the block in the opposite direction having a magnitude of ${F_P} = ma = \left( 1 \right)\left( 5 \right) = 5N$. Now, in order to keep the object at rest, the friction will act. The maximum friction force that can be given by the surface to the object is $f = \mu mg = \left( {0.6} \right)\left( 1 \right)\left( {10} \right) = 6N$.

As you can see that the object will move if the friction force is $6N$, as discussed before that friction is self-adjusting force, it will keep its value equal to pseudo force in order to keep the object at rest.Therefore, if the truck is accelerated at the rate of $5m{s^{ - 2}}$ then frictional force on the block will be $5N$.

Hence, option B is correct.

Note: Remember that pseudo force is a force that acts on a body when viewed from a non-inertial frame, for example, an accelerating frame. This question is solved taking the frame of reference as a truck. Also keep in mind the concept of frictional force and also remember that it is a self-adjusting force, it will vary its value according to the external forces acting on the object.