Examstyle Questions: Momentum and Impulse

This question is about the physics of ejection seats.
Ejection seats are designed to fire an aircraft pilot out of the plane at high velocity.
One type of ejection system uses an explosion to accelerate the seat upwards.
The seat was tested in a plane standing on the runway (Fig. 8.1a).
The combined mass of the seat and pilot is 280 kg. When ejection takes placr, the mass accelerates to a vertical velocity of 55 m s^{1}.
a) Calculate the change of momentum of the seat and pilot.
Change of momentum = ............unit..................
(3 Marks)
b) The change of momentum in (a) takes place in a time of 0.25 s.
Calculate the average force needed to give this change of momentum in 0.25s.
force = .......................... N
(2 Marks)
c) Suggest and explain how the body of the plane may move vertically during the ejection.
(2 Marks)
(Marks available: 7)

A tennis ball of mass 0.11 kg travelling at 40 m s^{1} hits a wall head on and bounces off, returning along the same path at 30 m s^{1}.
a) Calculate the change in velocity of the ball.
change in velocity = ..................... m s^{1}
(1 Mark)
b) Calculate the change in momentum of the ball. Include the unit in your answer.
change in momentum = ...................... unit .............
(2 Marks)
(Marks available: 3)

αparticles are directed through helium gas. An αparticle collides with a stationary helium nucleus and is directed from it original direction. The helium nucleus moves off in a different direction. Fig. 6.1 shows the paths pf these particles.
speed of incident αparticle = 1.80 x 10^{7} m s^{1}
kinetic energy of incident αparticle = 1.08 x 10^{12} J
speed of deflected αparticle = 1.38 x 10^{7} m s^{1}
speed of helium nucleus = 1.15 x 10^{7} m s^{1}
mass of αparticle = mass of helium nucleus = 6.68 x 10^{27} kg
a) Calculate the momentum of the incident αparticle.
momentum of incident αparticle = ................................. Ns
(2 Marks)
b) Calculate the kinetic energy of each particle after collision.
k.e. of αparticle = ........................... J
k.e. of helium nucleus = .....................J
(3 Marks)
c) i) Compare the total kinetic energy of the particles after the collision with the kinetic energy of the incident αparticle.
( 2 Marks)
ii) Use you answer to (i) to comment on the nature of the collision.
( 1 Mark)
(Marks available: 8)
Answer outline and marking scheme for question:

a) Äp = 280 x 55  280 x 0 (1 Mark) = 15 400 (1 Mark) kg ms^{1} (1 Mark)
(3 Marks)
b) f = ma = 280 x (55/0.25) (1 Mark) = 61600 N (1 Mark)
(2 Marks)
c) argue from Newton 3 oe conservation of momentum leading to a force on the plane (1 Mark) this makes the plane move dow (1 Mark) (as plane is much more massive so acceleration/movement much less than that of the pilot). (Accept plane wont move because its on the ground for second mark).
(2 Marks)
(Marks available: 7)

a) 70 m s^{1}
(1 Mark)
b) 70 x 0.11 = 7.7 (1 Mark) kg m s^{1} (1 Mark) Ns e.c.f. from (a)
(2 Marks)
(Marks available: 3)

a) momentum = mv
= 6.68 x 10^{27 }x 1.8 x 10^{7} = 1.20 x 10^{19} N s
(2 Marks)
b) ke of á particle = ½ mv^{2}
= ½ 6.68 x 10^{27} x (1.38 x 10^{7})^{2}
= 6.36 x 10^{13} J
ke of helium nucleus = ½ mv^{2} = ½ 6.68 x 10^{27 }x (1.15 x 10^{7})^{2}
= 4.42 x 10^{13} J
(allow 2 sf on each answer)
(3 Marks)
c) i) so total ke after collision equal to ke of incident á particle
total ke before collision = (6.36 + 4.42) x 10^{13} = 1.08 x 10^{12} J or other evidence of a calculation
(2 Marks)
ii) Collision is elastic
accept 'kinetic energy is conserved in this collision'
allow ecf from c) (i)
(1 Mark)
(Marks available: 8)