34. Let F

o

be the buoyant force of air exerted on the object (of mass m and volume V ), and F

brass

be the

buoyant force on the brass weights (of total mass m

brass

and volume V

brass

). Then we have

F

o

= ρ

air

V g = ρ

air

mg

ρ



and

F

brass

= ρ

air

V

brass

g = ρ

air

m

brass

ρ

brass



.

For the two arms of the balance to be in mechanical equilibrium, we require mg

− F

o

= m

brass

g

− F

brass

,

or

mg

− mg

ρ

air

ρ



= m

brass

g

− m

brass

g

ρ

air

ρ

brass



,

which leads to

m

brass

=

1

− ρ

air

/ρ

1

− ρ

air

/ρ

brass



m .

Therefore, the percent error in the measurement of m is

∆m

m

=

m

− m

brass

m

= 1

−

1

− ρ

air

/ρ

1

− ρ

air

/ρ

brass

=

ρ

air

(1/ρ

− 1/ρ

brass

)

1

− ρ

air

/ρ

brass

=

0.0012(1/ρ

− 1/8.0)

1

− 0.0012/8.0

≈ 0.0012

1

ρ

−

1

8.0



,

where ρ is in g/cm

3

. Stating this as a percent error, our result is 0.12% multiplied by



1
ρ

−

1

8.0



.

Document Outline

• Main Menu
• Chapter 1 Measurement
• Chapter 2 Motion Along a Straight Line
• Chapter 3 Vectors
• Chapter 4 Motion in Two and Three Dimensions
• Chapter 5 Force and Motion I
• Chapter 6 Force and Motion II
• Chapter 7 Kinetic Energy and Work
• Chapter 8 Potential Energy and Conservation of Energy
• Chapter 9 Systems of Particles
• Chapter 10 Collisions
• Chapter 11 Rotation
• Chapter 12 Rolling, Torque, and Angular Momentum
• Chapter 13 Equilibrium and Elasticity
• Chapter 14 Gravitation
• Chapter 15 Fluids
  • 15.1 - 15.10
    • 15.1
    • 15.2
    • 15.3
    • 15.4
    • 15.5
    • 15.6
    • 15.7
    • 15.8
    • 15.9
    • 15.10
  • 15.11 - 15.20
    • 15.11
    • 15.12
    • 15.13
    • 15.14
    • 15.15
    • 15.16
    • 15.17
    • 15.18
    • 15.19
    • 15.20
  • 15.21 - 15.30
    • 15.21
    • 15.22
    • 15.23
    • 15.24
    • 15.25
    • 15.26
    • 15.27
    • 15.28
    • 15.29
    • 15.30
  • 15.31 - 15.40
    • 15.31
    • 15.32
    • 15.33
    • 15.34
    • 15.35
    • 15.36
    • 15.37
    • 15.38
    • 15.39
    • 15.40
  • 15.41 - 15.50
    • 15.41
    • 15.42
    • 15.43
    • 15.44
    • 15.45
    • 15.46
    • 15.47
    • 15.48
    • 15.49
    • 15.50
  • 15.51 - 15.60
    • 15.51
    • 15.52
    • 15.53
    • 15.54
    • 15.55
    • 15.56
    • 15.57
    • 15.58
    • 15.59
    • 15.60
  • 15.61 - 15.70
    • 15.61
    • 15.62
    • 15.63
    • 15.64
    • 15.65
    • 15.66
    • 16.67
    • 15.68
    • 15.69
    • 15.70
  • 15.71 - 15.80
    • 15.71
    • 15.72
    • 15.73
    • 15.74
    • 15.75
    • 15.76
    • 15.77
    • 15.78
    • 15.79
    • 15.80
  • 15.81 - 15.90
    • 15.81
    • 15.82
    • 15.83
    • 15.84
    • 15.85
    • 15.86
    • 15.87
    • 15.88
    • 15.89
    • 15.90
• Chapter 16 Oscillations
• Chapter 17 Waves—I
• Chapter 18 Waves—II
• Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
• Chapter 20 The Kinetic Theory of Gases
• Chapter 21 Entropy and the Second Law of Thermodynamics
• Chapter 22 Electric Charge
• Chapter 23 Electric Fields
• Chapter 24 Gauss’ Law
• Chapter 25 Electric Potential
• Chapter 26 Capacitance
• Chapter 27 Current and Resistance
• Chapter 28 Circuits
• Chapter 29 Magnetic Fields
• Chapter 30 Magnetic Fields Due to Currents
• Chapter 31 Induction and Inductance
• Chapter 32 Magnetism of Matter: Maxwell’s Equation
• Chapter 33 Electromagnetic Oscillations and Alternating Current
• Chapter 34 Electromagnetic Waves
• Chapter 35 Images
• Chapter 36 Interference
• Chapter 37 Diffraction
• Chapter 38 Special Theory of Relativity
• Chapter 39 Photons and Matter Waves
• Chapter 40 More About Matter Waves
• Chapter 41 All About Atoms
• Chapter 42 Conduction of Electricity in Solids
• Chapter 43 Nuclear Physics
• Chapter 44 Energy from the Nucleus
• Chapter 45 Quarks, Leptons, and the Big Bang