2.2 Problems
61
with the incident direction while B proceeds at an angle 37 ◦ with the incident
direction.
(a) Find the speeds of A and B after the collision.
(b) What fraction of the initial kinetic energy is gained or lost due to the
collision.
2.38 A neutron moving with velocity v 0 collides head-on with carbon nucleus of
mass number 12. Assuming that the collision is elastic
(a) calculate the fraction of neutron’s kinetic energy transferred to the carbon
nucleus and
(b) calculate the velocities of the neutron and the carbon nucleus after the
collision.
2.39 Show that in an elastic collision between a very light body and a heavy body
proceeds with twice the initial velocity of the heavy body.
2.40 A moving body makes a completely inelastic collision with a stationary body
of equal mass at rest. Show that half of the original kinetic energy is lost.
2.41 A bullet weighing 5 g is fired horizontally into a 2 kg wooden block resting on
a horizontal table. The bullet is arrested within the block which moves 2 m. If
the coefficient of kinetic friction between the block and surface of the table is
0.2, find the speed of the bullet.
2.42 A particle of mass m with initial velocity u makes an elastic collision with a
particle of mass M initially at rest. After the collision the particles have equal
and opposite velocities. Find (a) the ratio M/m; (b) the velocity of centre of
mass; (c) the total kinetic energy of the two particles in the centre of mass;
and (d) the final kinetic energy of m in the laboratory system.
2.43 Consider an elastic collision between an incident particle of mass m with M
initially at rest (m > M). Show that the largest possible scattering angle θ max =
sin −1 (M/m).
2.44 The ballistic pendulum is a device for measuring the velocity v of a bullet
of mass m. It consists of a large wooden block of mass M which is supported by two vertical cords. When the bullet is fired at the block, it is dislodged and the block is set in motion reaching maximum height h. Show that
v = (1 + M/m)
√
2gh
2.45 A fire engine directs a water jet onto a wall at an angle θ with the wall. Calculate the pressure exerted by the jet on the wall assuming that the collision
with the wall is elastic, in terms of ρ, the density of water, A the area of the
nozzle, and v the jet velocity.
2.46 Repeat the calculation of (2.45) assuming normal incidence and completely
inelastic collision.
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with the incident direction while B proceeds at an angle 37 ◦ with the incident
direction.
(a) Find the speeds of A and B after the collision.
(b) What fraction of the initial kinetic energy is gained or lost due to the
collision.
2.38 A neutron moving with velocity v 0 collides head-on with carbon nucleus of
mass number 12. Assuming that the collision is elastic
(a) calculate the fraction of neutron’s kinetic energy transferred to the carbon
nucleus and
(b) calculate the velocities of the neutron and the carbon nucleus after the
collision.
2.39 Show that in an elastic collision between a very light body and a heavy body
proceeds with twice the initial velocity of the heavy body.
2.40 A moving body makes a completely inelastic collision with a stationary body
of equal mass at rest. Show that half of the original kinetic energy is lost.
2.41 A bullet weighing 5 g is fired horizontally into a 2 kg wooden block resting on
a horizontal table. The bullet is arrested within the block which moves 2 m. If
the coefficient of kinetic friction between the block and surface of the table is
0.2, find the speed of the bullet.
2.42 A particle of mass m with initial velocity u makes an elastic collision with a
particle of mass M initially at rest. After the collision the particles have equal
and opposite velocities. Find (a) the ratio M/m; (b) the velocity of centre of
mass; (c) the total kinetic energy of the two particles in the centre of mass;
and (d) the final kinetic energy of m in the laboratory system.
2.43 Consider an elastic collision between an incident particle of mass m with M
initially at rest (m > M). Show that the largest possible scattering angle θ max =
sin −1 (M/m).
2.44 The ballistic pendulum is a device for measuring the velocity v of a bullet
of mass m. It consists of a large wooden block of mass M which is supported by two vertical cords. When the bullet is fired at the block, it is dislodged and the block is set in motion reaching maximum height h. Show that
v = (1 + M/m)
√
2gh
2.45 A fire engine directs a water jet onto a wall at an angle θ with the wall. Calculate the pressure exerted by the jet on the wall assuming that the collision
with the wall is elastic, in terms of ρ, the density of water, A the area of the
nozzle, and v the jet velocity.
2.46 Repeat the calculation of (2.45) assuming normal incidence and completely
inelastic collision.