4.5 Linear Momentum & Conservation

Water is ejected from a hose through a hole of diameter 1 cm in the nozzle. The water leaves the nozzle of the hose with a velocity of 20 cm s^–1 and travels horizontally towards a wall, as shown below.

After colliding with the wall the water has zero velocity.  Water has a density of
1 g cm^–3.

What is the force exerted by the water on the wall?

A ball of mass 0.50 kg is kicked off a cliff with a horizontal velocity of 3.0 m s^–1.  It follows the path of a projectile shown below and lands with a velocity of 3.5 m s^–1 at an angle of 30^o to the ground.  Air resistance is negligible during the flight.

What is the magnitude of the change in momentum of the ball between the top of the cliff and the ground below?

A pellet gun fires 2 g pellets at a rate of 200 pellets per minute.  The pellets leave the pellet gun at a velocity of 20 m s^–1 and strike a fixed steel block.  The pellets rebound off the block with the same velocity as they were fired.

What is the average force exerted on the steel container?

A cart of mass 500 kg is carrying 300 kg of sand.  The cart moves horizontally with a constant velocity of 2.0 m s^–1.  During the journey a hole develops in the bottom of the cart, and the sand pours through this hole.

What is the final speed of the cart once all the sand has fallen through the hole?

The diagram below shows a block of mass 1.2 kg slides down a rough slope from rest against a constant friction force of 1.5 N.

What is the momentum of the block along the slope after 4 seconds?

When a car of mass 1500 kg is travelling at 30 km h^–1 when it collides with a wall and is brought to rest.  The force-time graph of the impact is shown below.

What is the maximum force exerted on the car?

The variation of the force, F, with time, t, acting on a mass of 250 g is shown on the graph below.

The velocity of the body at t = 10 ms is 8 m s^–1.

What is the velocity of the body at t = 35 ms?

Particle A has a mass m and is moving towards a stationary particle, B, of mass M.  A is travelling with a velocity of u before colliding head on with particle B.  The collision between the particles is elastic.

What is the velocity of particle B after the collision? 

An object of mass 40 g travelling at 4.0 m s^–1 collides head on with a mass of 20 g travelling in the opposite direction at 3.5 m s^–1.  The collision between the masses is inelastic.

How much kinetic energy is lost after the collision?

Two spheres approach each other along the same straight line. Their speeds are u₁ and u₂ before collision, and v₁ and v₂ after collision, in the directions shown below

Which equation is correct if the collision is perfectly elastic?

A lorry of mass 18 tonnes is travelling at 25.0 m s^–1.

A car of mass 800 kg is travelling at 40.0 m s^–1 towards the lorry.

What is the magnitude of the total momentum?

The diagram shows the masses and velocities of two trolleys about to collide

After the impact they move off together.

What is the total kinetic energy of the trolleys after the collision?

The diagram shows a cannon ball fired from a cannon

The mass of the cannon is 1600 kg and the mass of the cannon ball is 20 kg.

The recoil velocity of the cannon is 5 m s^–1 horizontally.

What is the horizontal velocity of the cannon ball?

A ball of mass 2 kg travelling at m s^–1 strikes a ball of mass 3 kg travelling at m s^–1. Both balls are moving along the same straight line as shown

After collision, both balls move at the same velocity v.

What is the magnitude of the velocity v?

A molecule of mass m travelling at speed v hits a wall in a direction perpendicular to the wall. The collision is elastic.

What are the changes in the momentum and in the kinetic energy of the molecule caused by the collision?

A moving object strikes a stationary object. The collision is inelastic. The objects move off together.

Which row shows the possible values of total momentum and total kinetic energy for the system before and after the collision?

A resultant force of 5 N acts on a body for a time of 4.0 s.

Which graph could show the variation with time t of the momentum p of the body?

Two train carriages each of mass 7500 kg roll toward one another on a level track. One is travelling at 3.00 m s^–1 and the other at 1.50 m s^–1, as shown.

They collide and join together.

What is the kinetic energy lost during the collision?