Work and energy

Question 1

What is work? (W)

Answer 1

The work of a force F on an object is the product of the force by the distance travelled by the object where the force is in the direction of the displacement

Work and energy are measured in joules

Question 2

What is a ‘joule?’

Answer 2

Unit of energy/work

1 J = (1 N)(1 metre)

Question 3

Give the formula for work (W) for a linear and nonlinear displacement

Answer 3

Linear
W = Fd

Nonlinear
W = Fd(cosθ)

Question 4

What is the work-energy theorem?

What does this say about the work done by a particle if its speed is constant?

Answer 4

A net force is the sum of interior and exterior forces acting upon the system. The variation of the kinetic energy of a system is equal to the work of the net force applied to the system.

W (of the resultant force) = ΔEk

Consequently, if the speed of a particle is constant, ΔEk = 0, than the work done by the resultant force must be zero.

Eg. In uniform circular motion the speed of the particle remains constant, thus the centripetal force does no work on the particle. A force at right angles to the direction of motion merely changes the direction of the velocity but not its magnitude.

Question 5

What are the three rules of a conservative force?

Answer 5

1. After a round trip, the kinetic energy of a particle on which a force acts, must return to its initial value.
2. After a round trip, the work done on a particle by a force must be zero
3. The work done by the force on a particle depends on the initial and final positions of the particle and not on the path taken

Question 6

What is power?

Answer 6

The power (P) applied during the work (W) performed by a force (F) is equal to the work divided by the time necessary to do the work. In other words, power is the rate of doing work

P = ΔW/Δt

Power is in the watt (W) unit = 1 J/s

Question 7

What are the two types of friction?

Answer 7

Static friction - Relevant when surfaces are not slipping

Kinetic friction - Relevant when surfaces are slipping

If a force applied on an object on a surface increases, static friction applies only until it begins to move (at which point kinetic friction becomes relevant). The maximum static friction is the amount of force it will take to make an object move (overcome static friction)

Question 8

When a force is applied to on an object, but friction is preventing its movement, what is that type of friction and what is the magnitude of the frictional force?

Answer 8

Static friction

Static friction equal to the amount of force applied (only as long as the object doesn’t move, once it moves, kinetic friction takes over)

Question 9

Consider the following two scenarios:

A. A box is being pushed up a long distance/shallow incline to a height of 10 m.

B. A box is pushed a short distance/steep incline to a height of 10 m.

In which case is the magnitude of work the greatest?

Answer 9

Neither! The work done depends only on the height climb h from the beginning to the end and not at all on the path between the two.

Question 10

The formula for work is:

W = FΔxcosσ

What is cosσ when the force is in the same direction as the motion? Opposes the motion? Perpendicular to the motion?

Answer 10

Same direction: cosσ = 1
Opposite direction: cosσ = -1
Perpendicular: cosσ = 0

Question 11

A woman carries a crate up a 10 m ladder across a 10 m hallway and then down a 10 m ladder. What is the amount of work she has done on the crate?

Answer 11

Work = FΔxcosσ

The work going up the ladder: 100 J

Work going across hallway: 0 J (cosσ = 0 for perpendicular motion to gravity)

Work going down the ladder: -100 J

The net amount of work is zero joules!

Question 12

What is the amount of work done on the earth by the sun’s gravitational pull in a year?

Answer 12

zero joules

Neither the potential energy or kinetic energy of the earth changes and the speed of the earth is constant (net force = zero)

Question 13

A bullet of mass 10 g is fired (100 m/s) into a tree stump, where it embeds 2 metres inside. What is the average force exerted by the stump on the bullet?

Answer 13

This problem deals with work and kinetic energy.

Ek = 1/2mv^2

W = Fd(cosσ)

Ek = 1/2(.01 kg)(-100^2)
Ek = -50 J = W

-50 J = F(2)(-1)
F = 25 N

When a bullet embeds in a stump, kinetic energy is converted to heat.

Question 14

Bulk motion relies on what type of energy?

Answer 14

Kinetic energy

Question 15

An object’s position relies on what type of energy?

Answer 15

Potential energy

Question 16

An object’s position in gravity relies on what type of energy?

Answer 16

Gravitational potential (mgh)

Question 17

What does electrical energy refer to?

Answer 17

The movement of electrons

Question 18

What is nuclear energy?

Answer 18

Energy in the nucleus, radioactivity, fission reactor etc.

Question 19

What type of energy do pressure waves rely on?

Answer 19

Sound energy

Question 20

What type of energy does electric and magnetic field waves rely on?

Answer 20

Light energy

Question 21

What type of energy does random motion of particles rely on?

Answer 21

Heat

Question 22

A woman pushes a cart up a hill and then lets it go. Describe the flow of energy until the cart comes to a stop at bottom of hill.

Answer 22

1. Woman pushes cart (chemical energy to potential energy)
2. Cart rolls to bottom of hill (potential to kinetic energy)
3. Friction slows cart to stop (kinetic energy dissipated as heat)

Question 23

Give the equation for determining the efficiency of energy conversion

Answer 23

Efficiency = (energy in desired form)/(energy in original form) x 100

Question 24

What is the difference between an elastic and inelastic collision? What is a completely inelastic collision?

Answer 24

Elastic: kinetic energy does not change

Inelastic: Kinetic energy is converted to heat and energy (usually the case)

Completely inelastic: Everything is stuck together in the end

Question 25

What is power?

Answer 25

The ‘rate’ at which energy is produced, consumed or transformed.

P = ΔE/Δt

Question 26

Give the formula for determining the tension on a rope when a mass is connected to it AND another rope (or is hanging between two segments of the same rope)

Answer 26

T = (1/2)mg

This is true regardless of how many pulleys the rope goes around or how it is orientated, assuming the mass on the rope is pulled straight down by only gravity.

Question 27

What physical quantity would be the result of multiplying megawatts by an amount of time?

Answer 27

Any number of watts refers to Power (P = W/t = IV).

Taking P x t = W/t x t = W = energy (in units of Joules)

Question 28

A researcher tries to determine the ionization energy of iron (Fe) by irradiating the metal with X rays of known energy (E) and then measuring the kinetic energy (Ke) of the emitted electrons. How will she compute the ionization energy from the data obtained?

Answer 28

E - Ke

Ionization energy (or potential!) is the energy required to remove the least tightly bound electron from an atom. If at the end of the process, that electron has some additional energy (ie Ke), then that is clearly over and above just the energy required to remove the electron. Thus we can write:

E(total) = IE + Ke

IE = E - Ke

Question 29

A mass slides down a ramp and is acted on by friction. The work done by friction on the mass as it travels down the ramp is equal to W.

How will increasing the initial speed of the mass by double change the amount of work done on it?

Answer 29

It won’t!

This is because frictional force is due to gravity (which is a constant).

Kinetic energy does not directly play a part in work, only potential energy (which is not reliant on velocity, unless kinetic energy is being transformed into potential energy, in this case the opposite is happening.)

Question 30

A mass slides down a slope with friction. In which of the following two cases is work the greatest?

• Steep slope
• Shallow slope

Answer 30

First off, W = Fdcosσ

But that’s not really necessary to look at. You just have to realize that the steep slope has the mass basically in free fall, and so the force of friction due to the normal force will be very low compared to the shallow slope.

Therefore the shallow slope will perform the greatest work due to friction, as long as static friction is overcome and the mass is moving with kinetic friction.