Question

Question # 1 - A)  Explain the characteristics of dry friction. B) Discuss Moment Of Force in brief .

Question # 2 - Define the following Terms:   (i) Moment of Couple (ii) Moment of force (iii) Equilibrium (iv) Rigid body(v) Scalar Quantity (vi) Vector Quantity (vii) Work (viii) Friction (ix) Centre of gravity (x) Rectilinear Motion

Question # 3 - (i) explain perpendicular axis theorem (ii) discuss Parallel axis theorem

Answer 1

Question #1

A) Characteristics of Dry Friction are:-

i)The total force of friction that can be developed is independent of the magnititude of the area of contact.

ii)For Low relative velocities between sliding objects, the frictional force is practically independent of velocity. However, the sliding frictional force is less than the frictional force corresponding to impending slippage.

iii)The Total Friction force that can be eveloped is proportional to the normal force transmitted across the surface of contact.

B) Moment of Force :- It is the product of force and the distance between the force and a refrence point on body. It  is the twisting force that tends to cause rotation. It is also known as torque. Its unit is N.m.

Question # 2

i) Moment of Couple:- When two equal and opposite forces acting on a body seperated by a perpendicular distance 'd' between them.(i.e Both the forces do not share a common line of action).Its unit is N.m.

ii) Moment of Force :- It is the product of force and the distance between the force and a refrence point on body. It  is the twisting force that tends to cause rotation. It is also known as torque. Its unit is N.m.

iii)Equilibrium:- When the sum of all the forces acting on a body tends to zero the body is said to be in equilibrium.

iv)Rigid body:- It  is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces exerted on it.

v) Scalar Quantity:- A scalar is a quantity that is fully described by a magnitude only. It is described by just a single number. eg Mass, Speed etc

vi) Vector Quantity:-Vector quantities refer to the physical quantities characterized by the presence of both magnitude as well as direction. eg Displacement ,Force , torque.

vii)Work:- Work is said to be done if the force acting on a body displaces it through a distance in direction of applied force.

viii)Friction:- It is the force distribution at the surface of contact between two bodies that prevent or impedes sliding motion of one body relative to other.

ix)Center of Gravity:-  It isan imaginary point in a body of matter where, for convenience in certain calculations, the total weight of the body may be thought to be concentrated.

x) Rectilinear Motion:- If the motion of a body is such that the direction is its resultant R remains constant then the motion of the body is along straight line/path and such a motion is called Rectilinear Motion.

Question # 3

i) Perpendicular Axis Theorem

  The perpendicular axis theorem states that the moment of inertia of a plane lamina about an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia of the lamina about the two axes at right angles to each other, in its own plane intersecting each other at the point where the perpendicular axis passes through it.

Define perpendicular axes x ,y, z (which meet at origin O) so that the body lies in the xy plane, and the z axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that

IZ=IX + IY

ii) Parallel axis Theorem :-

It is used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between the axes.

Suppose a body of mass m is rotated about an axis z passing through the body's centre of gravity. The body has a moment of inertia Icm with respect to this axis. The parallel axis theorem states that if the body is made to rotate instead about a new axis z′ which is parallel to the first axis and displaced from it by a distance d, then the moment of inertia I with respect to the new axis is related to Icm by