Energy and Equilibrium

Question 1

Torque

Answer 1

a measure of a force’s ability to cause rotational acceleration.

torque = FrsinØ, where r is the position vector (distance from point of rotation to the point of application of force).

If the object is not rotating, any fixed point can be designated as the point of rotation.

Question 2

Lever arm

Answer 2

position vector that extends from the point of rotation to the point where the force acts at 90°.

torque = Fl

Force and lever arm are inversely proportional.

Question 3

Torque increases as

Answer 3

1. the component of the force acting perpendicular to the position vector increases.
2. the distance between the point of application of the force and the point of rotation increases.

Question 4

Equilibrium

Answer 4

a state in which there is no net force and no net torque.

equilibrium does NOT mean motionless. It means constant velocity.

Question 5

Static Equilibrium

Answer 5

Velocity is a constant zero.

Question 6

Dynamic Equilibrium

Answer 6

velocity is constant but not zero.

Question 7

Open System

Answer 7

allows exchange of energy and mass with the surroundings.

Question 8

Closed System

Answer 8

allows exchange of energy with the surroundings, but not mass.

Question 9

Isolated System

Answer 9

allows no exchange of energy or mass with the surroundings.

Question 10

Energy of a system

Answer 10

is never destroyed. It is either converted from one form to another or transferred as work or heat.

“balance the books”

Question 11

Joule (J)

Answer 11

unit of energy.

one joule is 1 kg m²/s², which is the same as 1 N m.

Question 12

Mechanical energy

Answer 12

is the energy of a macroscopic system.

mechanics is the study of bodies, the forces that act on them, and the motion that they experience.

divided into kinetic and potential energy.

Question 13

Kinetic Energy (K)

Answer 13

is the energy of motion. Any moving mass has a kinetic energy, K = 1/2 mv²

Question 14

Potential Energy (U)

Answer 14

is the energy of position. Potential energy of an object depends on where it is located.

Question 15

Gravitational Potential Energy (U_g)

Answer 15

is potential energy created by the force of gravity.

U_g = - G m₁m₂/r, energy decreases as the distance between objects decreases.

gravitational potential energy of an object near the earth’s surface, U_g = mgh

Question 16

Elastic potential energy (U_e)

Answer 16

restorative elastic force. Most objects follow Hooke’s law. A deformed object following Hooke’s law has an elastic potential energy, U_e = 1/2 k (change in)x².

constant k is an intrinsic property of the material, measures the extent to which the material resists deformation, and is expressed in N/m.

Question 17

Two types of energy transfer

Answer 17

Heat and Work

Question 18

Heat (q)

Answer 18

is energy that is transferred between a system and its surroundings due to a temperature difference between them.

Question 19

Work (W)

Answer 19

is energy transferred for any reason other than a temperature difference.

Question 20

First law of thermodynamics

Answer 20

any change in the total energy of a system is due to either work or heat.

W + q = change in E_total

Assuming change in E_internal is zero (unless otherwise explained in passage), W + q = change in kinetic energy + change in potential energy.

Question 21

energy transfer that occurs when a force acts over a distance.

Answer 21

W = Fd cos Ø = change in kinetic energy + change in potential energy.

Only a force or component of force in the direction parallel to the system’s direction of displacement can do work on the system.

Question 22

Sign Conventions for work

Answer 22

First identify the system of interest. If energy is going in, assign a positive value. If energy is going out, assign a negative value.

Energy goes into a system when work is done on the system.

Energy goes out of a system when the system does work.

If force acts in the direction of displacement, assign positive value.

If force acts in the opposite direction, assign negative value.

Question 23

Power (P)

Answer 23

the amount of work done by a force per unit time, P = W/t

more generally, the rate of energy transfer, P = change in energy/t

Unit of power is the watt (W), which is defined as J/s.

Instantaneous pwer due to a force, P = Fv cos Ø

Question 24

Law of conservation of mechanical energy

Answer 24

when only conservative forces are acting, the sum of mechanical energies remains constant.

Mechanical energy before equals mechanical energy after, K₁ + U₁ = K₂ + U₂

Gravitational forces and Hooke’s law forces are conservative forces.

Question 25

Non-conservative force

Answer 25

When a non-conservative force does work on a system, the mechanical energy of the system changes.

Question 26

Machines

Answer 26

reduce the force required to do a given amount of work.

ability to reduce applied force is referred to as mechanical advantage.

machines are able to reduce force but do NOT change work.

Question 27

Ramp

Answer 27

an inclined plane that reduces the force needed to do work by increasing the distance over which the force is applied.

in order to reduce the force by a certain fraction, we must increase the length of the ramp by the reciprocal of that fraction.

Question 28

Lever

Answer 28

is a beam attached to a fulcrum (pivot point).

lever is based on principle of torque

F = mg L₁/L₂, where L₁ is the length of the lever from the fulcrum to the mass and L₂ is the length of the lever from the fulcrum to the force.

Question 29

Pulley

Answer 29

uses rope to increase the distance over which the force acts.

the magnitude of the force acting throughout the length of a rope is called tension. assume tension throughout rope is constant.