2 Work and energy

Question 1

Give the equation for calculating kinetic energy (K)

Kinetic energy (K) is in joules

Answer 1

K = ½mv²

^{K: kinetic energy}

^{m: mass (kg)}

v: speed (m/s)

K: kinetic energy (J)

Question 2

What is one joule equal to?

Answer 2

. It is equalto the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre (1 newton metre or N⋅m)

Question 3

What is the equation for potential gravitational energy?

Answer 3

U = mgh

U: potential energy (J)

m: mass (kg)
g: acceleration due to gravity (10 m/s²)
h: height (m)

Question 4

When a spring is stretched or compressed from its equilibrium (relaxed) length, the spring has elastic potential energy. Give the equation for this:

Answer 4

U = ½kx²

^{U: elastic potential energy (J)}

^{k: spring constant (stiffness of spring)}

^{x: magnitude of displacement}

Question 5

What is total mechanical energy and how do you calculate it?

Answer 5

E = U + K

E: total mechanical energy

U: potential energy

K: kinetic energy

Energy is never created or destroyed, therefore when potential energy is spent it becomes kinetic energy and vice versa. Of course, thermodynamics dicates that energy can be lost in other ways, such as heat by friction.

Question 6

When the work done by nonconservative forces is zero, or when there are no non-conservative forces acting on the system, the total mechanical energy of the system will be?

How can this be used to calculate work done by nonconservative forces when there IS work by nonconservative forces at play?

Answer 6

Constant

ΔE = ΔU + ΔK = 0

E: total mechanical energy (J)

U: potential energy (J)

K: kinetic energy (J)

W_{nonconservative} = ΔE = ΔU + ΔK

You can think about _{Wnonconservative} as the work of nonconservative forces equaling the energy lost from a system (e.g. as heat from friction)

Question 7

Give the equation to calculate work (J) when force and displacement are involved

Answer 7

Mechanical work is the dot product of force and displacement vectors. Cosine is used.

W = F*d = Fdcosθ

W: work (J)

F: force (N)

d: displacement (m)

θ: angle between force vector and displacement vector

Question 8

How can you find the work done on or by a system undergoing a thermodynamic process?

Answer 8

By finding the area enclosed by the corresponding pressure vs. volume curve

Question 9

What is Power and how is it calculated?

Answer 9

Power is the rate at which energy is transferred from one system to another.

P = W/t = ΔE/t

P: power (J/s = watt = W)

W: work (J)

t: time (s)

E: total mechanical energy (potential + kinetic energy)

Question 10

What is the work-energy theorem and how does it allow us to easily calculate work for systems where kinetic energy is being spent?

Answer 10

Direct relationship between work done by forces acting on a system and the change in kinetic energy of that object.

W_net = ΔK = K_f - K_i

Question 11

How can you calculate the mechanical advantage of a simple machine? Does this change the amount of work done on a system?

How can you calculate the efficiency of a simple machine?

Answer 11

mechanical advantage: F_out/F_in

It’s really just a ratio.

Simple machines work by spreading force over a greater distance. Considering the forumula W = FD, simple machines don’t change the amount of work done, just the force required.

Efficiency: Wout/Win = (load)(load distance) / (effort)(effort distance)

e.g. a pulley that uses six lengths of rope will be able to lift a load with 1/6th as much effort as a pulley with one length of rope