MCAT Study Guide Physics Ch. 5 – Work, Power and Energy 2017-08-15T06:45:05+00:00

## I.          5.1:  WORK

The product of the force (only the appropriate component) and distance

### A.     W  = Fd → W = Fdcosθ

1.     θ is the angle between F and d

2.     If F and d are parallel, cosθ = 1

### D.    EX:

Box with mass m  (20 kg) is pushed 6 meters with a force F (100 N); μk = 0.4

1.     How much work is done by F?

a)     W = Fdcosθ = 100 N * 6 M * 1 = 600 J

2.     How much work is done by the normal force?

a)     FN = Fgcosθ = m*g*cos(90) = 20 kg * 10 m/s2 * 0 = 0 N

3.     How much work is done by gravity?

a)     Since the gravitational force is perpendicular to the floor, the θ = 90, and cosθ = 0. Therefore, work done by gravity is 0.

4.     How much work is done by the force of friction?

a)     FF = μk FN; W =  μk *mg*d*cosθ = 0.4*20kg*10m/s2*1 = 80 N

b)     W = Fdcosθ = 80N*6*cos180 = 80*6*(-1) = -480 J

5.     What is the total work done on the crate?

a)     Add all the work done by each of the forces

b)     Wtot = Wby F + Wby Fn + Wby Fg + Wby Ff = 600 J + 0 + 0 + (-480) = 120J

## II.          5.2:  POWER

Measures how fast work gets done(in J/s)

### A.     P = W/t

1.     Power is measured in Watts (J/s)

2.     Horsepower = 750 watts

## III.          5.3:  KINETIC ENERGY

Energy in objects that are moving and can exert a force; kinetic energy is the energy an object has after a force has been applied; the KE can perform work → KE units are the same as work!!

v2 = v02 + 2 ad

### E.     WORK-ENERGY THEOREM

1.     Above, we assumed that v0 = 0; what if it was not?

a)     v2 – v02 = 2(F/m)d → ½m(v2 – v02) = Fd → ½mv2 -½m v02 = Fd

b)     → W = ½mv2 – ½mv02 =  KEfinal – KEinitial

c)     ∴ Wtot = ΔKE

d)     (+) W will add to KE, (-)W will take away from KE

## IV.          5.4:  POTENTIAL ENERGY

The energy an object has by virtue of its position (gravitational, electrical, elastic)

### A.     Gravitational → if a brick is lifted and placed on a shelf, how much did its potential energy change?

1.     Gravity did work on the brick while the brick was lifted (negative work)

2.     Wby Fgrav = Fgrav(-h) = -mgh

3.     ΔPEgrav = -Wby Fgrav =mgh

OR mgh ### B.     Gravity Is a Conservative Force

1.     Compare a brick being lifted 2 m or being pushed up a ramp to the same height; the work done by gravity is the same

a)     Large force over small distance vs small force over large distance

b)     Work depends only on the initial and final positions, not the pathway!

### C.    Friction Is Not a Conservative Force

1.     Friction does depend on path taken

2.     There is no such thing as “frictional potential energy”

### D.    Springs – elastic potential energy

1.     Hooke’s law – the amount of energy required to stretch/compress something elastic (like a spring) is directly proportional to the distance it will stretch

2.     k = spring constant

3.     F = -kx → x = distance

4.     Wspring = ½kx2

## V.          5.5: TOTAL MECHANICAL ENERGY

### B.     Conservation of Total Mechanical Energy

If the only forces acting on an object are conservative (e.g. no friction), then the object’s total mechanical energy will remain constant

1.     Any 2 positions or times should have the same total mechanical energy

2.     Ei = Ef

3.     KEi + PEi = KEf + PEf

## VI.          5.6:  SIMPLE MACHINES AND MECHANICAL ADVANTAGE

### B.     Mechanical Advantage = (effort distance)/(resistance distance)

1.     MA = deffort/dresistance

2.     This quantifies precisely how much less force is required when using simple machines

### C.    EFFICIENCY

Measures the degree to which friction and other facts reduce work output from theoretical maximum

1.     Efficiency (%) = Woutput/Energyinput

## VII.          5.7:  THERMAL ENERGY AND MODES OF HEAT TRANSFER

### A.     Heat is thermal energy and can be transferred in 3 ways:

1.     CONDUCTION – direct transfer of heat from one object to another caused by temperature difference

2.     CONVECTION – transfer of energy due to large scale motion of fluid (or air)

## VIII.          5.8:  MOMENTUM

Product of mass and velocity (kg⋅m/s), is a vector

### B.     IMPULSE (J) – can be used to predict the effect of a force

1.     F = ma  → a = Δv/Δt  → F = mΔv/Δt  → FΔt = mΔv = Δmv = Δp

2.     FΔt = Δp

### C.    Impulse Momentum Theorem

1.     J = impulse = change in momentum (remember signs! if a baseball changes direction and speed, one of the speeds must be negative)

2.     J = FΔt =mΔv = Δp

3.     Δp = pf – pinitial (only use this if collision is elastic)

4.     If there is a graph of F (vertical axis) and ∆T (horizontal axis), the area under the curve is the impuse

### D.    Conservation of Momentum

1.     Consider action/reaction pair

a)     F1-on-2 is force object 1 exerts on object 2

(1)   Impulse = J1-on-2 = F1-on-2Δt

b)     F2-on-1 is force object 2 exerts on object 1

(1)   Impulse = J2-on-1 = F2-on-1Δt

c)     Since the forces are equal and opposite, so are the impulses

d)     if J1-on-2 = -J2-on-1 → Δp1 = – ∆p2 → ∆p1 + ∆p2 = 0

e)     Law of conservation of momentum:  ∆psystem = 0  → total pinitial = total pfinal

### E.     Collisions

1.     Conservation of momentum applies to collisions; total kinetic energy, not necessarily!

2.     Consider cue ball hitting 8 ball; initial momentum is cue ball, final momentum is 8 ball plus cue ball after collision

3.     Collision definitions:

a)     Elastic collision – total momentum and total KE are conserved

b)     Inelastic collision – total momentum is conserved but KE is not conserved

c)     Perfectly inelastic – an inelastic collision in which the objects stick together afterwards

4.     Remember, KE = ½mv2

## IX.          5.9:  A NOTE ON ANGULAR MOMENTUM

### C.    Angular momentum is the rotational version of linear momentum (think of a rotating frisbee)

1.     Angular momentum must be defined relative to some reference point (often axis of rotation)

### D.    L  = ℓmv = Iω

1.     L = angular momentum

2.     ℓ = lever arm (shortest distance perpendicular to rotating mass)

3.     I = moment of inertia

4.     ω = angular velocity (radians/sec) → analog to speed, v

### E.     τ = ∆L/∆t

1.     Torque is the rate of angular momentum

## CHAPTER 5 SUMMARY

• Work → W = Fdcosθ
• Power → P = W/t
• Kinetic Energy → KE = ½ mv2
• Wtot = ∆KE
• Gravitational potential energy → ∆PEgrav = -WbyF grav = mg∆h
• Gravity is a conservative force
• Friction is NOT a conservative force
• Total Mechanical Energy E = KE + PE
• Conservation of Total Mechanical Energy → KEi + PEi = KEf + PEf
• Simple Machines:
• Efficiency (%) = Woutput/Energyinput
• Momentum → p = mv
• Impulse-momentum theorem → J = ∆p = F∆t
• Conservation of Total Momentum → total pinitial = pfinal
• Collisions always conserve momentum
• Elastic collisions also conserve KE
• Inelastic collisions do NOT conserve KE
• Perfectly inelastic collisions lose most of KE (objects stick together)
• Angular Momentum → L  = ℓmv = Iω # 10.

#### Ch. 11 Reflection + Refraction

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