Further Mechanics

Question 1

What is momentum?

Answer 1

p = mv [kg ms^-1]

Question 2

What is impulse?

Answer 2

Impulse is change in momentum

F∆t = mv - my [Ns]

Question 3

What is the principle of conservation of linear momentum?

Answer 3

Principle of conservation of linear momentum: the total linear momentum of a system of colliding bodies is always conserved, providing that there are no external forces acting

m1u1 + m2u2 = m1v1 + m2v2

Question 4

How does the net force relate to rate of change of momentum in situations where mass is constant?

Answer 4

∑F = ma
∑F = m(dv/dt)

∑F = dp/dt

Question 5

What is the expression for kinetic energy in terms of momentum and vice versa?

Answer 5

KE = p^2/2m

p = √(2mKE)

Question 6

How do we apply the principle of linear momentum in two dimensions?

Answer 6

We resolve the forces, momentum in each direction is conserved

Question 7

What is the principle of conservation of energy?

Answer 7

Principle of conservation of energy: energy can neither be created nor destroyed, but merely transferred from one form to another

Question 8

What is an elastic collision?

Answer 8

An elastic collision is one where there is no loss of kinetic energy

Question 9

What is an inelastic collision?

Answer 9

An inelastic collision is one where some kinetic energy is lost

Question 10

What is a completely inelastic collision?

Answer 10

A completely inelastic collision is one in which the bodies stick together on impact

Question 11

What experiment do we use to investigate inelastic collisions?

Answer 11

We use a linear air track with trolleys on top with corks and pins, the trolleys have cards on them, the time/speed is measured with light gates.

When the pin is pushed into the cork work is done and hence the kinetic energy is transformed into work done so the collision is inelastic.

Question 12

What is an angle of 1 radian?

Answer 12

An angle of 1 radian is an angle in a circle subtended on the arc of the length 1 radius

1 radian = 180˚/π

Question 13

What is angular displacement?

Answer 13

Angular displacement is the angle through which an object has moved while performing circular motion

Theta (in radians) = arc length(s)/radius(r)

Question 14

What is angular velocity?

Answer 14

Angular velocity, w, of an object is its rate of change of angle, measured in rad s^-1

s = r*theta
s/t = r*theta/t
v = rw, speed not velocity as the direction is changing

w = theta/t (rad s^-1)

Question 15

What is period?

Answer 15

Period is the time taken to perform one revolution (2π radians)

w = 2π/t => T = 2π/w

Question 16

What occurs during circular motion?

Answer 16

Centripetal forces act towards the centre of the circle. They change the direction of motion of the object (but speed remains constant) and therefore make it accelerate. The acceleration acts towards the centre of the circle (it is a centripetal acceleration). If the centripetal force is removed the object will move tangentially to the circle at constant speed.

Question 17

What are some examples of centripetal forces?

Answer 17

Gravitational force (Moon - Earth)
Frictional force (coin on a turntable)
Horizontal component of the lift (plane banking)
Contact force on the flange (train turning)

Question 18

What are the expression for centripetal acceleration and hence for centripetal force?

Answer 18

a = v^2/r (v=rw) => a = rw^2

F = ma => F = mv^2/r or F = mrw^2