Work and Energy

Question 1

Work

Answer 1

W = Fdcosθ

F is force, d is the distance over which the force is applied, and θ is the angle between the force and distance.

Question 2

Units of Work

Answer 2

Joule = N·m = kg·m/s²·m = kg·m²/s²

Question 3

Sign Conventions of Work

Answer 3

If the force and the distance applied is in the same direction, work is positive.

If the force and the distance applied is in opposite directions, work is negative.

Question 4

When is no work done if a force is acting in one direction?

Answer 4

If the force is acting in one direction, but the object moves in a perpendicular direction, then no work is done.

Question 5

Work of Gravitational Force

Answer 5

Unlike friction, gravity always acts downwards. Thus, it does not matter what detour you take because sideward motion perpendicular to the gravitational force involves no work.

Question 6

Does the amount of work depend on the path?

Answer 6

No, work is path independent. Pushing an object at constant speed up a frictionless inclined plane involves the same amount of work as directly lifting the same object to the same height at constant speed.

Sliding down a frictionless inclined plane involves the same gravitational work as doing a free fall at the same height.

Question 7

Mechanical Advantage

Answer 7

Mechanical advantage = little input force (effort) -> large output force.

Question 8

Work-kinetic energy theorem

Answer 8

Work on an object can transform into kinetic energy and kinetic energy can do work.

Question 9

When you are pushing on an object, what is the expression for work?

Answer 9

Fd = ½mv²

Question 10

When gravity does work on an object, what is the expression for work?

Answer 10

F_weighth = mgh = ½mv²

Question 11

Power

Answer 11

Power is the rate of work, or work over time: P = W/t

The unit for power is the Watt, or W (don’t confuse this W with the shorthand of work).

Watt = Joule / second

Question 12

Kinetic Energy

Answer 12

½mv²

Question 13

Units of Kinetic Energy

Answer 13

Joule (kg m²/s²)

Question 14

Local Gravitational Potential Energy

Answer 14

mgh

Question 15

Spring Potential Energy

Answer 15

(1/2)kx²

Question 16

Is the k value larger or smaller for stiffer springs?

Answer 16

Stiff springs have a larger k because they are harder to stretch (it takes more energy to stretch them).

Question 17

General Gravitational Potential Energy

Question 18

Conservation of Energy

Answer 18

The total amount of energy before = the total amount of energy after.

Question 19

Conservative Forces

Answer 19

If a force doesn’t dissipate heat, sound or light, then it is a conservative force.

Question 20

Work done by conservative forces are path (dependent/independent)

Answer 20

Work done by conservative forces are path independent.

Question 21

Non-Conservative Forces

Answer 21

non-conservative include frictional forces and human exertion. When friction acts on an object, the heat and sound released cannot be recovered. When you flex your arm, you lose heat that cannot be recovered (you cannot re-absorb the heat you lost).

Question 22

Power Units

Answer 22

The unit for power is the Watt, or Joule per second.