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Physics 2053C – Fall 2001. Review for Final Exam http://www.hep.fsu.edu/~tadams. Important Topics. Kinematics Forces/Newton’s Laws Energy/Momentum Conservation Ideal Gases/Heat. Variable/Quantity/Units. t time s x distance m v velocity m/s a acceleration m/s 2

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Physics 2053c fall 2001

Physics 2053C – Fall 2001

Review for Final Exam

http://www.hep.fsu.edu/~tadams

Prof. Todd Adams,

FSU Department of Physics


Important topics
Important Topics

  • Kinematics

  • Forces/Newton’s Laws

  • Energy/Momentum Conservation

  • Ideal Gases/Heat


Variable quantity units
Variable/Quantity/Units

t time s

x distance m

v velocity m/s

a acceleration m/s2

F force N = kg.m/s2

E energy J = N.m

P power W = J.s


Kinematics
Kinematics

  • Position

  • Velocity – rate of change of position

  • Acceleration – rate of change of velocity

    • Constant acceleration

    • Constant velocity

    • Constant position

a = 0

v = 0, a = 0


Equations of motion
Equations of Motion

x = x0 + v0t + ½at2

v = v0 + at

v2 = v02 + 2a(x – x0)

x = position

x0 = initial position

v = velocity

v0 = initial velocity

a = acceleration

t = time


Forces
Forces

  • Force due to gravity

  • Normal force

  • Force due to friction

  • Tension

  • Buoyancy

  • External force (e.g. a push)


Gravity
Gravity

  • acceleration due to gravity (g = 9.80 m/s2)

  • force due to gravity F = mg

  • Weight = force due to gravity

  • which direction???

  • Also, F = G.(m1m2)/r2

Newtons


Types of energy
Types of Energy

  • Kinetic

    • Linear K = ½mv2

    • Rotational

  • Potential

    • Gravitational U = mgh

    • Spring U = ½kx2

    • Internal Energy

  • Heat Q = mcT

  • Work W = Fdcos


Ideal gas law
Ideal Gas Law

PV = nRT

P = pressure (atm, bar, N/m2)

V = volume (m3)

n = # of moles

R = gas constant

T = temperature (K)


How to solve force problems
How to solve FORCE problems

  • Read the problem.

    (identify what you do and don’t know, look for “hidden” knowledge)

  • Draw a free-body diagram

    (identify all forces acting upon object)

  • Add all forces in one direction together (x?)

    F = F1 + F2 + F3 + …

    (determine sum of forces, maybe Fnet = 0 or Fnet = ma)

  • Add all forces in other direction together (y?)

    (determine sum of forces, maybe Fnet = 0 or Fnet = ma)

  • Solve for what you don’t know


Sample force problem

T1

T2

M1

M2

Sample Force Problem

The boxes are not moving.

  • What is the value of T1?

  • What is the value of T2?

M1 = 20.0 kg

M2 = 10.0 kg

 = 0.3


Sample force problem cont

T2

T1

M1

T1

M2

Fg

Sample Force Problem (cont)

M1 = 20.0 kg

M2 = 10.0 kg

 = 0.3

F = T1 – Fg = 0

T1 = Fg

T1 = M2g = (10.0 kg)(9.80 m/s2)

T1 = 98.0 N

M2


Sample force problem cont1

T2

T1

M1

FN

T2

T1

M2

Ffr

Fg

Sample Force Problem (cont)

M1 = 20.0 kg

M2 = 10.0 kg

 = 0.3

Fy = FN – Fg = 0

FN = Fg

FN = M1g = (20.0 kg)(9.80 m/s2)

FN = 196.0 N

M1


Sample force problem cont2

T2

T1

M1

M2

Sample Force Problem (cont)

M1 = 20.0 kg

M2 = 10.0 kg

 = 0.3

FN

Fx = T1 – T2 – Ffr = 0

T2 = T1 - Ffr

T2 = 98.0 N – (0.3)(196.0 N)

T2 = 39.2 N

T2

T1

M1

FN = 196.0 N

Ffr

Fg


Sample force problem cont3

T1

T2

M1

M2

Sample Force Problem (cont)

What if the boxes are moving with constant velocity?

What if the boxes are accelerating at a = 2.2 m/s2?

What if we remove T2?

M1 = 20.0 kg

M2 = 10.0 kg

 = 0.3

T1 = 98.0 N

T2 = 39.2 N


How to solve energy problems
How to Solve ENERGY Problems

  • Identify types of energy

    Kinetic?

    Gravitational Potential?

    Spring Potential?

    Heat?

    Internal Energy?

    Work?

  • Identify initial and final conditions

  • Find unknown quantities:

    W = K + U (if W  0)

    Ki + Ui = Kf + Uf (if W = 0)


Sample energy problem

5 m

Sample Energy Problem

A 25 kg block is released from rest 5.5 m up a frictionless plane inclined at 30o. The block slides down the incline and along a horizontal surface. The horizontal surface has a coefficient of static friction of 0.32.

What is the velocity of the block at the bottom of the incline?

How far along the horizontal surface will the block slide?


Sample energy problem cont

5 m

Sample Energy Problem (cont)

What kind of energies are present?

Kinetic energy

Gravitational potential energy

Work done by friction

What is the energy at A?

EA = KE + PE = 0 + mgh = mgdsin = (25 kg)(9.80 m/s2)(5 m)(sin 30o)

EA =612.5 J

A

B

C


Sample energy problem cont1

5 m

Sample Energy Problem (cont)

What is the energy at B?

EB = EA = 612.5 J

What happens to the energy as the box goes from A to B?

What is the velocity at B?

EB = KE + PE = ½ mvB2 + 0

vB =7.0 m/s

A

B

C


Sample energy problem cont2

5 m

Sample Energy Problem (cont)

What happens to the energy as the box goes from B to C?

What is the energy at C?

EC = 0.0 J

How far does the box slide?

W = KE + PE Wfr = Ffrd = FNd

W = (0.0 J – 612.5 J) + 0 J Wfr = mgd

W = Wfr .

. -612.5 J = (0.32)(25 kg)(9.8 m/s2)d = (78.4 N)d

. d = (612.5 J)/(78.4 N) = 7.81 m

A

B

C


How to solve ideal gas problems
How to Solve IDEAL GAS Problems

PV = nRT

  • Identify initial and final conditions

  • Take ratio

    P1V1 n1RT1

    P2V2 n2RT2

  • Cancel anything which is constant

  • Solve for what you don’t know

=


Sample problem
Sample Problem

V = 10 m/s

V = 18 m/s

  • What are the forces on the motorcycle as it accelerates (A)?

  • What are the forces on the motorcycle as it moves at constant speed (B,C)?

  • How far does it travel while accelerating from rest to 30 m/s?

  • What is the kinetic energy at points A, B, C?

  • How much work is done by motorcycle?

  • How much work is done by friction getting to A, B, C?

  • What are the forces on the object as it moves upward from A to B?

M = 250 kg

30 m

F = 2500 N

25 m

A

B

C

0 to 30 m/s in 20 s


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