C5-6. Mechanics II Flashcards
What is the definition of work done?
Work is done when an external force causes an object to move through a certain distance. It is measured in Nm.
What is the equation for work done?
W=Fx, where W is measured in Joules, F in Newtons, and X being distance in metres.
What can we say about the relationship between energy transferred and work done?
Work done = energy transferred. When an object is falling for example, its weight does work, transferring gravitational potential to kinetic energy.
How might we derive an equation for work done by a force applied at an angle?
work done = Fx cos(angle)
Define kinetic energy, and give an equation to calculate it.
Energy due to motion of an object with mass. E=1/2mv^2
Define GPE, and give an equation to calculate it.
Energy of an object due to location in a gravitational field. E=mgh
Define chemical energy.
Energy contained within chemical bonds of atoms.
Define elastic potential energy, and give an equation to calculate it.
Energy stored in an object due to a reversible change in shape. E=1/2ke^2
Define electrical potential energy.
Energy of electrical charges due to their position in an electric field.
Define nuclear energy.
Energy within the nuclei of atoms released when subatomic particles are rearranged.
Define radiant/electromagnetic energy.
Energy of any EM wave stored within the oscillating electric and magnetic fields.
Define sound energy.
Energy of mechanical waves due to the movement of atoms.
Define internal/thermal energy.
The sum of random potential and kinetic energies of atoms in a system.
What is the principle of conservation of energy?
The total energy contained within a closed system remains constant; energy can neither be created nor destroyed, only transferred.
How can we explain and derive the equation for gravitational potential energy?
E=W=Fs
W=(mg)s and S=h
Therefore E=mgh
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?
Work is done against the propulsive force causing the final kinetic energy to be lower than. the initial.
When an object is falling, what can we say about the transfer of energy through it?
- 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
Define power and give an equation for it.
Power is the rate of work done (the rate of energy transfer), measured in Js-1 or Watts. P=W/t
How could we derive the power equation for an object in motion?
P=w/t and W=Fx
P=Fx/t therefore P=Fv
What can we say about out the forces and work done on a car moving at a constant speed on a flat plane?
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.
What equation do we use to calculate the efficiency of a system?
efficiency = useful output/total input, where we can use energy in J or power in W.
State Newton’s First Law.
An object remains at rest or in its constant state of motion unless acted on by an overall resultant force.
State Newton’s 2nd Law.
The resultant force upon an object is directly proportional to the rate of change of its momentum, and acts in the same direction.
State Newton’s 3rd Law.
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).
What is the equation for momentum? State the units.
Momentum = mass * velocity
p=mv
The units are kgms-1.
What is the principle of conservation of momentum?
For a given direction, the total momentum before an event is equal to the total momentum after the event.
What is the difference between elastic and inelastic collisions?
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.
Give an algebraic expression for the conservation of momentum.
m1u1 + m2u2 = m1v1 + m2v2
How can we apply the conservation of momentum principle to explosions?
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
Define impulse, and give its equation.
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.
How might we determine impulse from a force-time graph?
It is given by the area underneath a force-time graph.
If momentum is conserved during a collision, what can say about the shape its vectors form when arranged tip-to-tail?
The vectors form a closed shape.
How do we apply the principle of conservation of momentum to a two-dimensional collision?
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.
State Hooke’s Law.
The extension of an elastic body is proportional to the force causing it. This relationship only applies within the elastic limit of the spring.
Give an equation for Hooke’s law.
F = kx where K is the spring constant in Nm-1
Describe the transfers of energy when a spring is extended.
Work is done to stretch a spring, where we input elastic potential energy. This is then stored within the spring.
How can we determine work done to a spring from a force-extension graph?
Work done is given by the area beneath the graph.
Define elastic deformation, and state when it occurs.
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.
What happens during inelastic deformation?
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.
How is the ‘stiffness’ of a spring related to spring constant?
A stiffer spring has a higher spring constant.
What is the effect on the spring constant for the following spring combinations, where the springs used are identical?
- In parallel
- In series
- 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.
Define and give an equation for tensile stress.
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….
Define and give an equation for tensile strain.
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.
What is the Young modulus and how do we calculate it?
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.
How do we calculate the Young modulus graphically?
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.
Describe the features of a stress-strain graph for a ductile material.
- 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.
Describe the features of a stress-strain graph for a brittle material.
- 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.
How might the stress-strain characteristics of a polymeric material differ to what we would expect?
- 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.
Define and give an example of a ductile material.
Ductile materials can withstand large plastic deformations before breaking. One example might be copper.
Define and give an example of a brittle material.
These are materials that fracture before plastic deformations. An example might be glass.
