Further Mechanics - collisions, momentum and impulse

Question 1

Derivation of the impulse equation from Newton’s 2nd Law

Answer 1

F=ma , ∆p=F∆t

F = m a     (N2L)
F = m (∆v / ∆t)     (a = ∆v/∆t)
F = (m∆v) / ∆t     (m x ∆v / ∆t = m∆v / ∆t)
F = ∆p / ∆t      (m x ∆v = ∆p)
F x ∆t = ∆p      (Rearrange)
∆p = F∆t      (Impulse)

Question 2

Unit for ∆p

Answer 2

Ns

Question 3

Unit for p

Answer 3

kg ms^-1

Question 4

Elastic Collision are when …

Answer 4

… collisions have no loss in kinetic energy (KE is conserved within the system).

Question 5

Inelastic collisions are when …

Answer 5

… collisions result in a change in kinetic energy within the system. This energy is then transferred to a different store (Internal/thermal etc).

Question 6

Derivation of Ek = p^2 / 2m from the kinetic energy and momentum equation

Answer 6

Ek = 1/2 m v^2, p = m v

p^2 = m^2 v^2 ( (p=mv)^2 )
p^2 / m^2 = v^2 (Rearrange)

Ek = 1/2 m v^2
Ek = 1/2 m (p^2 / m^2)     (v^2 = p^2 / m^2)
Ek = ( 1 x m x p^2 ) / 2 m^2
Ek = p^2 / 2m     ( m/2m^2 = 1/ 2m)

Question 7

What can be calculated from the area under a force - time graph?

Answer 7

Impulse

Question 8

How do you find the angle, when you have arc length and radius?

Answer 8

θ = arc / radius

Question 9

A nucleus decays by releasing an alpha particle. The speed of the recoiling nucleus is small compared to the speed of the alpha particle. This is due to…

Answer 9

… the recoiling nucleus has a much larger mass than the alpha particle.

Question 10

The area under a force-time graph represents?

Answer 10

Change in momentum

Question 11

Principle of conservation of momentum states that…

Answer 11

… in a closed system, the net momentum before an action is equal to the net momentum after an action.

Question 12

A 24.2 g bullet enters a 2.81 kg watermelon and embeds itself in the melon. The melon is immediately set into motion with a speed of 3.82 ms-1. The bullet remains lodged inside the melon. What was the entry speed of the bullet?

Answer 12

v of bullet = 447 ms^-1

Question 13

Newton’s first law states that…

Answer 13

… an object in motion will stay in motion and a stationary object will remain stationary, unless acted on by an external resultant force.

Question 14

Newton’s second law states that…

Answer 14

… the acceleration of an object is directly proportional to the net force applied and inversely proportional to its own mass.

Question 15

N2L equation is…

Answer 15

… net F = ma

Question 16

Newton’s third law states that…

Answer 16

… for every action, in an interaction pair, there is always an equal and opposite reaction.

Question 17

Ball A has a mass of 10 kg and moves with an initial velocity of 3.0 ms^-1 due east. Ball B has a mass of 5.0 kg and is stationary.

Ball A collides with ball B and moves away at an angle of 30 degrees to the horizontal, with a new velocity of 2.0 ms^-1.

What is the magnitude and direction of the velocity that ball B will move away with?

Answer 17

v of mass B = 3.23 ms^-1

at 38.3 degrees below horizontal

Question 18

In an elastic collision what two things are conserved?

Answer 18

KE and Momentum

Question 19

A 1.2 kg ball, A, is moving with a velocity of 4.4 ms^-1 due west. It collides with a stationary ball, B, also with a mass of 1.2 kg. After the collision ball A moves off at 38 degrees south of west while ball B moves off at 53 degrees north of west.

Find the velocities of both balls after the collision.

Answer 19

Final v of B = 10.5 ms^-1

Final v of A = -13.6 ms^-1

Question 20

In an elastic collision what two things are conserved?

Answer 20

KE and Momentum