NCERT Class 11 Physics Solutions: Chapter 5 – Laws of Motion Part 13

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Question 5.35:

A block of mass is placed on a long trolley. The coefficient of static friction between the block and the trolley is The trolley accelerates from rest with for and then moves with uniform velocity. Discuss the motion of the block as viewed by

(a) A stationary observer on the ground,

(b) An observer moving with the trolley.

Answer:

(a) A stationary observer on the ground:

Mass of the block,

Coefficient of static friction,

Acceleration of the trolley,

As per Newton’s second law of motion, the force (F) on the block caused by the motion of the trolley is given by the relation:

This force is acted in the direction of motion of the trolley.

Force of static friction between the block and the trolley:

The force of static friction between the block and the trolley is greater than the applied external force. Hence, for an observer on the ground, the block will appear to be at rest. When the trolley moves with uniform velocity there will be no applied external force. Only the force of friction will act on the block in this situation.

(b) An observer moving with the trolley:

An observer, moving with the trolley, has some acceleration. This is the case of non-inertial frame of reference. The frictional force, acting on the trolley backward, is opposed by a pseudo force of the same magnitude. However, this force acts in the opposite direction. Thus, the trolley will appear to be at rest for the observer moving with the trolley.

Question 5.36:

The rear side of a truck is open and a box of mass is placed away from the open end as shown in figure. The coefficient of friction between the box and the surface below it is . On a straight road, the truck starts from rest and accelerates with At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

The rear side of a truck is open and a box of mass is placed …

Box of Mass is Placed Away from the Open End of a Truck

Loading Image

Answer:

Mass of the box,

Coefficient of friction,

Initial velocity,

Acceleration,

Distance of the box from the end of the truck,

As per Newton’s second law of motion, the force on the box caused by the accelerated motion of the truck is given by:

As per Newton’s third law of motion, a reaction force of is acting on the box in the backward direction. The backward motion of the box is opposed by the force of friction f, acting between the box and the floor of the truck. This force is given by:

Net force acting on the block:

backward

The backward acceleration produced in the box is given by:

Using the second equation of motion, time t can be calculated as:

Hence, the box will fall from the truck after from start.

The distance s, travelled by the truck in is given by the relation: