Force
an agency which changes or tends to change the state of rest or of uniform motion or the direction of motion of a body
Inertia
the inherent property of a body by virtue of which it cannot, by itself, change its state of rest or of uniform motion
Types of Inertia
Inertia due to rest: tendency of a body to stay in its position of rest.
Example: a person standing in a bus falls
backward when it starts to move.
Inertia due to motion: Tendency of a body to remain in its state of
uniform motion in a straight line.
Example: A person sitting in a moving bus
falls forward when it suddenly stops.
Inertia of Direction: the inability of an object to change by itself the
direction of its motion.
Example: when a bus takes a sharp turn, a
person sitting in it experiences a force acting
away from the centre of the curved path.
Newton’s first law
Every body continues in its state of rest or of uniform motion in a straight line unless compelled by some external force to change its state.
Linear momentum
Momentum is the quantity of motion possessed by a body. It is the product of the mass and the velocity of the body.
p= mv, vector quantity, kgm/s, MLT^-1
Momentum graphs
the momenta of bodies having equal masses are directly proportional to their velocities.
the momenta of bodies having equal velocities are proportional to their masses.
the velocities of bodies having equal momenta are inversely proportional to their masses.
Newton’s 2nd law
The rate of change of linear momentum of a body is directly proportional to the applied force and the change takes place in the direction of the applied force.
derivation of F=ma
Apparent Weight
Consider a man of mass m standing in an elevator with a weighing machine. The actual weight of the man is mg.
mg acts vertically downward through the centre of gravity G of the man.
the weighing machine offers resistance to the weight acting on it, R.
the weighing machine reads the reaction R which is the force experienced by the man. R is the therefore the apparent weight of the man.
- Lift moving upward: R=m(g+a)
- Lift moving downward: R=m(g-a)
- Lift at rest or moving with uniform motion: R=mg
- Lift falls freely: R=0
Motion of connected bodies
Let a be the acceleration with which heavier mass M moves downwards and lighter mass m moves upwards. Let T be the tension on the string…
a= (M-m)/ (M+m) * g
T= 2Mm/ (M+m)
friction
the self-adjusting force which comes into play tangentially b/w two surfaces so as to destroy the relative motion between them.
types of friction
- Static friction: b/w to bodies before one actually starts moving over the other. (fs)
- Limiting friction: the maximum force of static friction; b/w two bodies when a body just starts moving over the surface of another body.
- Kinetic friction: force of friction when a body is in a state of steady motion over the surface of another body.
friction graph
Initially as the applied force increases, the friction fs increases proportionally to oppose motion up to maximum.
Once the limit is exceeded, the object begins to move, and the frictional force suddenly drops to a lower constant value (fk)
Beyond this point, the frictional force remains constant regardless of the increase in applied force.
laws of limiting friction
- depends on the nature of the surfaces in contact.
- acts tangential to the two surfaces in contact and in a direction opposite to the direction of the body.
- independent of the area of the surface in contact as long as the normal reaction remains the same.
- fs max is proportional to R b/w the two surfaces.
fs max= us R
us= fsmax/ R where us is the coefficient of friction.
laws of kinetic friction
- opposes relative motion and has a constant value.
- dependent upon 2 surfaces in contact.
- Independent of velocity provided.
- fk is proportional to R b/w two surfaces.
fk= uk R
uk= Fk/R
uk<us
angle of friction
It is the angle which the resultant of the limiting friction and the normal reaction makes with the normal reaction.
angle of repose
the maximum angle that an inclined plane makes with the horizontal when a body placed on it just begins to slide down.
work done moving a body against friction
work done moving a body up an inclined plane
work done moving a body down an inclined plane
pulling vs pushing
circular motion on banked road
circular motion on inclined road
