2. Work and Energy

Question 1

What is energy?

What is the SI unit for energy?

Answer 1

Energy is the property of a system that enables it to do something or make something happen, including the capacity to do work.

The SI units for all forms of energy are Joules (j)

Question 2

What’s the difference between kinetic and potential energy?

Answer 2

Kinetic Energy: Kinetic Energy is the energy of motion. It is related to the mass of an object, as well as its speed squared.

Potential Energy: Potential energy is energy associated with a given position or intrinsic property of a system; it is stored in gravitational, electrical, elastic, or chemical forms.

Question 3

(Equation) What is the equation for kinetic energy?

Answer 3

K= Kinetic energy (in Joule)
Joule= (kg×m²)/s²)
m= mass (in kilograms!)
v= speed (m/s)

²

Question 4

True or false: kinetic energy is related to velocity.

Answer 4

False. It’s related to speed. Direction is not important.

Kinetic energy is related to speed, NOT velocity. An object has the same kinetic energy regardless of the direction of its velocity vector.

Question 5

(Equation) What is the equation for gravitational potential energy?

Answer 5

U=mgh

U= potential energy(in Joule)
Joule= (kg×m^2)/s^2 

    m= mass in kilograms
g= acceleration due to gravity (9.8 m/s)
h= height of the object above the datum.

Question 6

(Equation) What is the equation for elastic potential energy?

Answer 6

U= potential energy
k= spring constant (a measure of the stiffness of the spring)
x= the magnitude of displacement from equilibrium

Question 7

What are conservative forces?
What are non-conservative forces?

Answer 7

Conservative forces are path independent and do not dissipate the mechanical energy of a system. (gravity)

Non-conservative forces are path dependent and cause dissipation of mechanical energy from a system. (friction)

Question 8

True or false: Work can be considered energy.

Answer 8

False.

Work is not energy but a measure of energy transfer. The other form of energy transfer is heat.

Question 9

How do you define work?

Answer 9

Work is a process by which energy is transferred from one system to another.

Question 10

(Equation) What is the equation for work? (like pushing or pulling something)

Answer 10

Work is a function of force and displacement

W= F *d = Fd cos Ө

W= work
F= magnitude of the applied force
d= distance of displacement
Ө= the angle between the applied force vector and the displacement vector

Question 11

(Equation) What is the equation for work? Like a piston?

Answer 11

W= P ∆V

W= work
P= pressure
∆V= volume

Key Concept: When work is done by a system (the gas expands), the work is said to be positive. When the work is done on a system (the gas compresses), the work is said to be negative. The MCAT will not expect you to calculate the integral of a P-V graph using calculus, but you are expected to be able to calculate the area under a straight line graph if necessary.

Question 12

What is power?

What is the SI unit for power?

Answer 12

Power is the rate at which work is done or energy is transferred.

The SI unit for power is the watt (W).

Key Point: Power is always a measure of the rate of energy consumption, transfer, or transformation per unit time.

Question 13

(Equation) What is the equation for work?

Answer 13

P= power
SI unit for power is Watt, which is equal to J/s
W= work (which is equal to ∆E, the change in energy)
t= time

Question 14

(Equation) What is the work-energy theorem, what what does it mean?

Answer 14

The work-energy theorem states that when net work is done on or by a system, the system’s kinetic energy will change by the same amount. In more general applications, the work done on or by a system can be transferred to other forms of energy as well.

W_net= ∆K = K_f- K_i

W_net= total energy completed
∆K= change in kinetic energy
K_f= final kinetic energy
K_i= initial kinetic energy

Question 15

What are the units for work? How are work and energy different?

Answer 15

a. The unit of work is the joule, which is also the unit for energy. Work and energy are related concepts.
b. By performing work, the energy of a system is changed.
c. Work, along with heat, is a form of energy transfer.

Question 16

Provide three methods for calculating the work done on or by a system?

Answer 16

W =Fd= Fd cos θ (the dot product of the force and displacement vectors)
W = PΔV (the area under a pressure–volume curve)
W_net = ΔK(the work–energy theorem)

Question 17

While driving a vehicle at a constant velocity on a flat surface, the accelerator must be slightly depressed to overcome resistive forces. How does the amount of work done by the engine (via the accelerator) compare to the amount of work done by resistance?

Answer 17

according to the work–energy theorem, the net work must also be zero, and we can infer that the amount of positive work done by the engine must be equal to the amount of negative work done by resistance.

Long answer: Begin by thinking about how each form of work is affecting the vehicle. While we could try to work through what may be happening in terms of forces and displacements, this gets very tricky when considering moving engine parts. In this case, it is simpler to think about each work in terms of kinetic energy. The work done by the engine increases the kinetic energy of the car, so it’s positive. Conversely, the work done by resistance decreases the kinetic energy of the car, meaning the work done on the car is negative. If the engine does more work than friction, then there is a positive change in kinetic energy. If resistance does more work, then the change is negative. If they do equal amounts of work, then there is no change in kinetic energy. We are given that the vehicle maintains a constant velocity; thus, there is no change in kinetic energy. Therefore, according to the work–energy theorem, the net work must also be zero, and we can infer that the amount of positive work done by the engine must be equal to the amount of negative work done by resistance.

Question 18

What is the definition of mechanical advantage?

Why does it create an advantage?

Answer 18

Mechanical advantage is the factor by which a simple machine multiples the input force to accomplish work.

Any device that allows work to be accomplished through a smaller applied force

Mechanical advantage makes it easier to accomplish a given amount of work because the input force necessary to accomplish the work is reduced; the distance through which the reduced input force must be applied, however, is increased by the same factor (assuming 100% efficiency).

Question 19

(Equation): What is the equation for mechanical advantage?

Answer 19

Mechanical Advantage = F_out/F_in

F_out= force exerted on an object by a simple machine
F_in = force actually applied on the simple machine

Mechanical advantage is a ratio of the output force generated given a particular input force.
Efficiency is a ratio of the useful work performed by a system compared to the work performed on the system.

Question 20

How do pulleys perform mechanical advantage?

Answer 20

Pullies have to lift the object the same distance

However, pulleys allow heavy objects to be lifted using a much reduced force. The distance through which the displacement is achieved is greater than the displacement (an indirect path).

Question 21

(Equation) In mechanical advantage, what is the equation for efficiency?

Answer 21

Efficiency
W_out= load or load distance
W_in= effort or effort distance

Another way to think of this is efficiency= (Force x distance for the load being lifted or the object) / (Force x distance for the person pulling the object).

In this case, the distance is going to be less for the object, and more for the person pulling. However the force will be less for the person pulling, and more for the object.

Mechanical advantage is a ratio of the output force generated given a particular input force. Efficiency is a ratio of the useful work performed by a system compared to the work performed on the system.

Question 22

As the length of an incline plane increases, what happens to the force required to move an object the same displacement?

Answer 22

As the length of an inclined plane increases, the amount of force necessary to perform the same amount of work (moving the object the same displacement) decreases.

This is paradoxical

Remember, work = force x distance. So if you increase the length of the plane, the distance increases, so the force decreases.

Question 23

As the effort decreases in a pully system, what happens to the effort distance to maintain the same work output?

Answer 23

As the effort (required force) decreases in a pulley system, the effort distance increases to generate the same amount of work.

Question 24

What accounts for the difference between work input and work output in a system that operates at less than 100% efficiency?

Answer 24

The decrease in work output is due to non-conservative or external forces that generate or dissipate energy.

Question 25

What does it mean for a device to provide mechanical advantage?

Answer 25

When a device provides mechanical advantage, it decreases the input force required to generate a particular output force. This is accomplished at the expense of increased distance over which the force must act.

Question 26

Name a few simple machines that provide mechanical advantage.

Answer 26

inclined plane, wedge, wheel and axle, lever, pulley, and screw.

Question 27

What is the definition of isochoric?

Answer 27

Isochoric means that there is no change in volume.
Likewise, in an equation that is W = PΔV, volume would be 0, so there would be no work being done.

Similarly, in the equation U=Q-W, U would equal Q.