Mechanics and Materials (4): Force and momentum

Question 1

What is the equation for momentum?

Answer 1

p = mv

Question 2

What needs to be applied to an object in order to change its velocity?

Answer 2

A force

Question 3

Force is proportional to the…?

Answer 3

Change in momentum per second

Question 4

What is the detailed equation for the force applied to an object (in terms of changing momentum)?

Answer 4

F = mv - mu/t

= m(v-u)/t
ma = m(v-u)/t

Question 5

What is the unit of momentum?

Answer 5

kgms^-1

Question 6

What is the general equation for force applied to an object (in terms of changing momentum)?

Answer 6

F = (delta)mv/ (delta)t

OR (if mass is constant)

F = m(delta)v/ (delta)t

OR (if velocity is constant)

F = v(delta)m/ (delta)t

Question 7

What is the equation for Force if the mass changes at a constant rate?

Answer 7

F = v(delta)m/ (delta)t

Question 8

If a rocket ejects burnt fuel from its engine at a speed v, what is the equation for the force exerted by the engine to eject the hot gas?

Answer 8

F = v(delta)m/ (delta)t

Question 9

How does ejecting hot gas from a rocket cause it to propel forwards?

Answer 9

Force exerted by the engine to eject the hot gas is given by:
F = v(delta)m/ (delta)t

Due to Newtons third law of motion - The hot gas ejected exerts an equal and opposite force on the jet engine, propelling the rocket forwards

Question 10

What is the definition of the impulse of a force?

Answer 10

The force x the time for which the force acts

Question 11

What is the equation for the impulse of a force?

Answer 11

F(delta)t = (delta)mv

• either m or v can be constantly changing or both

Question 12

What is the impulse of force acting on an object equal to?

Answer 12

The change in momentum of that object

Question 13

F - mv - mu/t when…?

Answer 13

An object of a constant mass or velocity is acted on by a constant force, F which changes its mass or velocity

Question 14

What does the area under a force-time graph represent?

Answer 14

The change in momentum or the impulse of the force

given by:
Ft = mv - mu

Question 15

What are the units for momentum (in terms of impulse)?

Answer 15

Ns

Question 16

What is the equation for the impact force experienced by an object in a collision?

Answer 16

F = mv - mu/t

Question 17

For a rebound impact what is the equation for the impact force, F?

Answer 17

F = (-mv) - (mu)/t

This is because when a ball hits a wall it rebounds off with a different same speed, but also different direction. This means its velocity has changed and therefore, we need to account for the direction of velocity in the equation

Question 18

If there is no loss of speed in an impact then what is the equation for the impact force, F?

Answer 18

F = -2mu/t

Question 19

If the initial direction of an object that collides with a wall is not perpendicular to it, then what do you have to do with its velocity?

Answer 19

You have to find the component of its velocity that is perpendicular to the wall

Question 20

State the principle of conservation of momentum

Answer 20

For a system of interacting objects the total momentum remains constant providing no external resultant force acts on the system

Question 21

What is the equation that shows the principle of conservation of momentum?

Answer 21

Total momentum before the collision = total momentum after the collision

Question 22

If colliding objects stick together then what value do they share that is the same?

Answer 22

Same final velocity

Question 23

For a head on collision (two objects moving towards each other) which direction will the momentum be acting?

Answer 23

In the direction of the object with more momentum

Question 24

For a head on collision what do you need to consider?

Answer 24

The direction of the objects colliding as one will have a greater momentum than the other

Question 25

If the individual momentums of two objects that collide in a head on collision are equal, what will the total momentum before and after equal?

Answer 25

0kgms^-1

Question 26

What is the definition of an elastic collision?

Answer 26

One where both kinetic energy and momentum are conserved (no loss of kinetic energy)

Question 27

What is the definition of an inelastic collision?

Answer 27

One where momentum is conserved but kinetic energy is not/ where the colliding objects have less kinetic energy after the collision than before the collision

Question 28

How do you work out whether a collision is elastic or inelastic?

Answer 28

Calculate the kinetic energies of each object before and after the collision

Question 29

Objects that collide and couple together undergo what type of collision?

Answer 29

Inelastic collision

Question 30

If you want to calculate the kinetic energy of a ball immediately after impact with the ground what do you have to do?

Answer 30

Calculate the GPE gained after its first bounce by using GPE = mgh (GPE gained = KE lost)

Question 31

An explosion is an example of what type of collision?

Answer 31

Inelastic collision

Question 32

Why is an explosion an inelastic collision?

Answer 32

As the kinetic energy of the objects involved are greater after the collision comparative to before

Question 33

What is the total momentum before and total momentum after an explosion? Why?

Answer 33

0kgms^-1

Before: the objects are stationary therefore have 0 velocity, therefore 0 momentum

After: the objects fly off in opposing directions, the momentum in opposite directions sums to 0

Question 34

How is energy transferred to the kinetic energy store of objects in an explosion?

Answer 34

Chemical -> Kinetic + heat, light and sound