Q#1
Let F, Fn and f denote the magnitude of contact force, normal force and the friction exerted by one surface on the other kept in contact. If none of these is zero,
(a) F > Fn (b) F > f (c) FN > f (d) FN – f < F < FN + f.
Answer: (a) F > FN, (b) F > f , and (d) FN – f < F < FN + f.
Since contact force F is vector sum of forces Fn and f. Hence magnitude of F,
F = √(FN² + f²)
from this it is clear that F > FN, also F > f. It can also be clearly understood by diagram, see below:
In triangle OAB, OB > OA and OB > AB → OB > OC, because OB is the side opposite the largest angle A = 90°. So, the option (a) and (b) are true.
Since f = µFN and generally µ < 1, so f < FN but it is not always true because sometimes µ > 1, in this case f > FN. So, option (c) is not true.
Both Fn and f are less than F, so the difference Fn-f will be even lesser i.e. FN – f < F. From Geomtry, in a triangle sum of any two sides is greater than the third, so in triangle OAB, OA + AB > OB
FN + f > F or F < FN + f
So, option (d) is correct.
Q#2
The contact force exerted by a body A on another body B is equal to the normal force between the bodies. We conclude that
(a) the surfaces must be friction-less
(b) the force of friction between the bodies is zero
(c) the magnitude of normal force equals that of friction
(d) the bodies may be rough but they don't slip on each other.
Answer: (b) and (d)
Consider the diagram in problem no-1. Contact force F is the resultant of normal force Fn and friction force f. F and Fn can only be equal if f-friction force is zero.Option (b) is correct.
f can be zero if the contact surfaces are smooth or they are not trying to slip. If the surfaces are rough but not trying to slip then f is zero and contact force is equal to normal force, hence option (d) is correct but option (a) is not correct as the surfaces may be smooth but it is not the only condition.
Option (c) is not correct because if magnitude of Fn and f are equal then magnitude of contact force F = √2FN
Q#3
Mark the correct statements about the friction between two bodies.
(a) Static friction is always greater than the kinetic friction.
(b) Coefficient of static friction is always greater than the coefficient of kinetic friction.
(c) Limiting friction is always greater than the kinetic friction.
(d) Limiting friction is never less than static friction.
Answer: (b), (c) and (d).
Static friction is not constant. It varies from zero to maximum value of Limiting friction depending upon the force applied on the body to move it while kinetic friction is a bit less than the Limiting friction. So static friction may or may not be greater than the kinetic friction. So option (a) is not correct.
Coefficient of static friction is equal to Limiting friction force divided by Normal force while coefficient of Kinetic friction is equal to force applied to just move the body with a uniform velocity divided by the Normal force. Since Limiting friction force is always greater than the force applied to just move the body with uniform velocity, hence Coefficient of static friction is always greater than the coefficient of kinetic friction. So options (b), (c) and (d) are correct.
Q#4
A block is placed on a rough floor and a horizontal force F is applied on it. The force of friction f by the floor on the block is measured for different values of F and a graph is plotted between them.
(a) The graph is a straight line of slope 45°.
(b) The graph is a straight line parallel to the F-axis.
(c) The graph is a straight line of slope 45° for small F and a straight line parallel to the F-axis for large F.
(d) There is a small kink on the graph.
Answer: (c) and (d).
Until the applied horizontal force F is increased to a Limiting force the block does not move because this horizontal force is balanced by force of friction f. Up to this point the graph is a straight line of slope 45°. Beyond this point the block moves with a uniform velocity for even less than the Limiting force, at this point the graph has a small kink. Now even if the F is increased f remains constant, so now the graph gets parallel to F-axis. Hence options (c) and (d) are correct.
Q#5
Consider a vehicle going on a horizontal road towards east. Neglect any force by the air. The frictional forces on the vehicle by the road
(a) is towards east if the vehicle is accelerating
(b) is zero if the vehicle is moving with a uniform velocity
(c) must be towards east
(d) must be towards west.
Answer: (a) and (b).
When the vehicle is accelerating towards east the frictional force must be towards east according to Newton's Second Law of Motion. So option (a) is correct. If the the vehicle is moving with uniform velocity no force is applied in the direction of motion according to Newton's First Law. So, option (b) is correct.
Due to above two conditions frictional force is not always towards east, it may not even exist. So option (c) is not correct. Frictional force will not be towards west if the vehicle is going towards east, so option (d) is not correct.
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