NLM

Question 1

Law of Inertia

Answer 1

A body moving with a certain speed along a straight path will continue to move with same speed along the same straight path in the absence of external forces

Question 2

Explain how does Newton’s second law of motion give a quantitative definition of force

Answer 2

p = mv
dp / dt = d (mv) / dt = m dv / dt = ma
F = ma

Question 3

Impulse

Answer 3

A large force acting for a short time to produce a finite change in momentum

Question 4

Impulse derivation (force time momentum)

Answer 4

dJ = F dt
J = F delta (t)
F = dP/ dt –> Fdt = dP
J = p2 - p1

Question 5

Newton’s Third Law of Motion

Answer 5

To every action, there is always an equal and opposite reaction
Fab = - Fba

Question 6

Apparent Weight in Elevator

Answer 6

1. Moving upward with constant speed: F = mg
2. Moving upward with acceleration = F = m (g + a)
3. Moving downward with acceleration = F = m(g-a)
4. Free fall: F = 0

Question 7

Conservation of Linear Momentum

Answer 7

When no external force acts on a system of several interacting particles, the total linear momentum of the system is conserved.

Question 8

Lami’s theorem for concurrent forces

Answer 8

F1 / sin alpha = F2 / sin beta = F3 / sin gamma

Question 9

Motion of connected bodies

Answer 9

T = 2Mmg / (M + m)
a = (M - m)g / (M + m)

Question 10

Friction

Answer 10

Whenever a body moves or tends to move over the surface of another body, a force comes into play which acts paraellel to the surface of contact and opposes the relative motion

Question 11

Static Friction

Answer 11

Force of friction which comes into play between two bodies before one actually starts moving over the other

Question 12

Limiting friction

Answer 12

Maximum force of static friction which comes into play when a body just starts moving over the surface of another body

Question 13

Graph of static friction, limitng and kinetic

Answer 13

• Static friction increases
• Max point is the limiting friction
• Then has kinetic friction after passing limiting friction

Question 14

Coefficient of static friction

Answer 14

Ratio of limiting friction to the normal reaction
mu = fs (Limiting) / R (Normal)

Question 15

Angle of repose

Answer 15

Minimum angle that an inclined plane makes with the horizontal when a body placed on it just begins to slide down
tan theta = mu

Question 16

Why is rolling friction lesser than sliding friction

Answer 16

• When a wheel rolls, the surfaces at contact do not rub each other
• Relative velocity of the point of contact of wheel with respect to plane is zero

Question 17

Acceleration down a rough inclined plane

Answer 17

F = mg sin theta - (mu)k mg cos theta
a = g( sin theta - (mu)k cos theta)

Question 18

Acceleration up a rough inclined plane

Answer 18

a = g( sin theta + (mu)k cos theta)

Question 19

Max speed of a car on a circular road

Answer 19

v = root (mu * r * g)

Question 20

Derivation of max speed of a car on circular road

Answer 20

F = f1 + f2 = (mu) (R1 + R2) = (mu) mg
(mu)(mg) >= mv^2 / r
v^2 <= (mu) rg

Question 21

Banking

Answer 21

System of raising the outer edge of a curved road above its inner edge

Question 22

Prove banking derivation

Answer 22

Downward –> Rsin theta + f cos theta = mv^/r
R cos theta - f sin theta = mg
Divide both
(R sin theta + f cos theta) / (R cos theta - f sin theta) = v^2 / rg
v^2 = rg [(mu + tan theta) / (1 - mu tantheta)]

Question 23

Banking max velocity formula

Answer 23

v = root [mg( mu + tan theta) / 1 - mu tan theta]

Question 24

Max velocity in banking with no friction / Cyclist

Answer 24

v = root (mg tan theta)

Question 25

For vertical looping minimum velocity at lowest point

Answer 25

v = root (5rg)

Question 26

For vertical looping minimum velocity at highest point

Answer 26

v = root (gr)

Question 27

Tension at highest point

Answer 27

T = m / r (u^2 - 5gr)