C5-6. Mechanics II

Question 1

What is the definition of work done?

Answer 1

Work is done when an external force causes an object to move through a certain distance. It is measured in Nm.

Question 2

What is the equation for work done?

Answer 2

W=Fx, where W is measured in Joules, F in Newtons, and X being distance in metres.

Question 3

What can we say about the relationship between energy transferred and work done?

Answer 3

Work done = energy transferred. When an object is falling for example, its weight does work, transferring gravitational potential to kinetic energy.

Question 4

How might we derive an equation for work done by a force applied at an angle?

Answer 4

work done = Fx cos(angle)

Question 5

Define kinetic energy, and give an equation to calculate it.

Answer 5

Energy due to motion of an object with mass. E=1/2mv^2

Question 6

Define GPE, and give an equation to calculate it.

Answer 6

Energy of an object due to location in a gravitational field. E=mgh

Question 7

Define chemical energy.

Answer 7

Energy contained within chemical bonds of atoms.

Question 8

Define elastic potential energy, and give an equation to calculate it.

Answer 8

Energy stored in an object due to a reversible change in shape. E=1/2ke^2

Question 9

Define electrical potential energy.

Answer 9

Energy of electrical charges due to their position in an electric field.

Question 10

Define nuclear energy.

Answer 10

Energy within the nuclei of atoms released when subatomic particles are rearranged.

Question 11

Define radiant/electromagnetic energy.

Answer 11

Energy of any EM wave stored within the oscillating electric and magnetic fields.

Question 12

Define sound energy.

Answer 12

Energy of mechanical waves due to the movement of atoms.

Question 13

Define internal/thermal energy.

Answer 13

The sum of random potential and kinetic energies of atoms in a system.

Question 14

What is the principle of conservation of energy?

Answer 14

The total energy contained within a closed system remains constant; energy can neither be created nor destroyed, only transferred.

Question 15

How can we explain and derive the equation for gravitational potential energy?

Answer 15

E=W=Fs
W=(mg)s and S=h
Therefore E=mgh

Question 16

If work is done by a resistive force on a propulsive force as an object is moving, what can we say about its kinetic energy?

Answer 16

Work is done against the propulsive force causing the final kinetic energy to be lower than. the initial.

Question 17

When an object is falling, what can we say about the transfer of energy through it?

Answer 17

• Initially the total energy is in the gravitational potential store
• This is gradually transferred to the kinetic store
• Air resistance does work against the GPE causing a lower final kinetic energy

Question 18

Define power and give an equation for it.

Answer 18

Power is the rate of work done (the rate of energy transfer), measured in Js-1 or Watts. P=W/t

Question 19

How could we derive the power equation for an object in motion?

Answer 19

P=w/t and W=Fx
P=Fx/t therefore P=Fv

Question 20

What can we say about out the forces and work done on a car moving at a constant speed on a flat plane?

Answer 20

The work done by the forward force provided by the car’s engine is equally opposed by the work done due to frictional forces such as air resistance, rolling resistance etc.

Question 21

What equation do we use to calculate the efficiency of a system?

Answer 21

efficiency = useful output/total input, where we can use energy in J or power in W.

Question 22

State Newton’s First Law.

Answer 22

An object remains at rest or in its constant state of motion unless acted on by an overall resultant force.

Question 23

State Newton’s 2nd Law.

Answer 23

The resultant force upon an object is directly proportional to the rate of change of its momentum, and acts in the same direction.

Question 24

State Newton’s 3rd Law.

Answer 24

When 2 objects interact, they exert equal but opposite force on one another. Both forces must be of the same nature (e.g. normal reaction force).

Question 25

What is the equation for momentum? State the units.

Answer 25

Momentum = mass * velocity p=mv The units are kgms-1.

Question 26

What is the principle of conservation of momentum?

Answer 26

For a given direction, the total momentum before an event is equal to the total momentum after the event.

Question 27

What is the difference between elastic and inelastic collisions?

Answer 27

During elastic collisions, kinetic energy is fully conserved. During inelastic collision, kinetic energy is not conserved. Note that this does not affect the total energy of a system; this is conserved regardless.

Question 28

Give an algebraic expression for the conservation of momentum.

Answer 28

m1u1 + m2u2 = m1v1 + m2v2

Question 29

How can we apply the conservation of momentum principle to explosions?

Answer 29

Prior to an explosion, total momentum is zero. That means that after the explosion, the total momentum of both objects involved must also be zero, and the objects involved end up moving in opposite directions to achieve this, since mass is always positive. This is expressed as m1v1 + m2v2 = 0

Question 30

Define impulse, and give its equation.

Answer 30

Impulse is the product of a force applied to an object and the time over which said force acts. This is given by impulse = F delta T. This is equal to the change in momentum, so we can say that Ft=m delta v.

Question 31

How might we determine impulse from a force-time graph?

Answer 31

It is given by the area underneath a force-time graph.

Question 32

If momentum is conserved during a collision, what can say about the shape its vectors form when arranged tip-to-tail?

Answer 32

The vectors form a closed shape.

Question 33

How do we apply the principle of conservation of momentum to a two-dimensional collision?

Answer 33

Consider the horizontal and vertical components of the momenta before and after the collision separately. Remember that sum of momentum before = sum of momentum after.

Question 34

State Hooke’s Law.

Answer 34

The extension of an elastic body is proportional to the force causing it. This relationship only applies within the elastic limit of the spring.

Question 35

Give an equation for Hooke’s law.

Answer 35

F = kx where K is the spring constant in Nm-1

Question 36

Describe the transfers of energy when a spring is extended.

Answer 36

Work is done to stretch a spring, where we input elastic potential energy. This is then stored within the spring.

Question 37

How can we determine work done to a spring from a force-extension graph?

Answer 37

Work done is given by the area beneath the graph.

Question 38

Define elastic deformation, and state when it occurs.

Answer 38

Elastic definition is when a spring returns to its original shape after the force causing the extension is removed. This occurs prior to the elastic limit.

Question 39

What happens during inelastic deformation?

Answer 39

The spring does not return to its original length after the force causing the original extension has been removed, after the elastic limit has been exceeded.

Question 40

How is the ‘stiffness’ of a spring related to spring constant?

Answer 40

A stiffer spring has a higher spring constant.

Question 41

What is the effect on the spring constant for the following spring combinations, where the springs used are identical? - In parallel - In series

Answer 41

- In parallel, the spring constant is doubled. Twice the force is required to cause a similar extension. - In series, the spring constant is halved. The same applied force gives rise to a doubled extension.

Question 42

Define and give an equation for tensile stress.

Answer 42

Tensile stress is defined as force per unit area. It is given by the equation sigma (stress) = F/A, with units Nm-1 or Pascals. Note that this is the same as pressure….

Question 43

Define and give an equation for tensile strain.

Answer 43

Tensile strain is the extension per unit length. It is given by epsilon = x/L. Since both x and L have units m, the quantity of strain has no units - it is dimensionless.

Question 44

What is the Young modulus and how do we calculate it?

Answer 44

The Young modulus is the ratio of stress to strain for a given material. It does not take into account less useful factors like shape We calculate it by dividing stress by strain. It is presented with the letter E.

Question 45

How do we calculate the Young modulus graphically?

Answer 45

It is given by the gradient of an stress-strain graph. These graphs usually have a straight line within the elastic limit, since stress is proportional to strain.

Question 46

Describe the features of a stress-strain graph for a ductile material.

Answer 46

- Stress is proportional to strain until the limit of proportionality. - Elastic deformation occurs up to E, the elastic limit. - From Y1 to Y2 the material deforms plastically for a small increase in stress. This is the yield stress. - UTS is the ultimate tensile strength, the max. tension withstood before fracture point F.

Question 47

Describe the features of a stress-strain graph for a brittle material.

Answer 47

- Elastic behaviour occurs up until the ultimate tensile strength is reached. This point is equal to the fracture point. - Hooke’ s Law is therefore obeyed until the fracture point.

Question 48

How might the stress-strain characteristics of a polymeric material differ to what we would expect?

Answer 48

- These behave differently due to temperature and molecular structure. - They sometimes have different unloading and loading lines due to energy losses during these processes to heat.

Question 49

Define and give an example of a ductile material.

Answer 49

Ductile materials can withstand large plastic deformations before breaking. One example might be copper.

Question 50

Define and give an example of a brittle material.

Answer 50

These are materials that fracture before plastic deformations. An example might be glass.