Questions and Answers
What is the fundamental quantity from which mass is derived?
Length
Which unit is equivalent to 0.305 meters?
30.5 cm
In the expression d sin θ = n λ, what are the dimensions of the left-hand side?
Length
What is the relationship between force and spring extension according to Hooke's law?
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Which unit is equivalent to 6.21 × 10^-4 miles?
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What is the derived quantity from mass and time?
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What are the exponents n and m in the expression x ⍺ an tm obtained through dimensional analysis?
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On an interstate highway in a rural region of Wyoming, a car is traveling at a speed of 38 m/s. Is the driver exceeding the speed limit of 75 mi/h?
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What is the law giving the periodic time t of a simple pendulum if it depends on the length l, the mass of its bob, and the acceleration due to gravity g?
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Study Notes
Fundamentals of Measurement
- Mass is derived from the fundamental quantity of inertia.
Units
- 0.305 meters is equivalent to 1 yard.
- 6.21 × 10^-4 miles is equivalent to 1 kilometer.
Dimensions
- The left-hand side of the equation d sin θ = n λ has dimensions of length.
Hooke's Law
- Hooke's law states that force is directly proportional to spring extension.
Derived Quantities
- Momentum is the derived quantity from mass and velocity.
Dimensional Analysis
- The exponents n and m in the expression x ⍺ an tm obtained through dimensional analysis are 1 and -1 respectively, indicating that x is proportional to a^n and t^(-m).
Speed and Velocity
- 38 m/s is equivalent to approximately 85 mi/h, which exceeds the speed limit of 75 mi/h.
Simple Pendulum
- The law giving the periodic time t of a simple pendulum is t = 2π √(l/g), where l is the length of the pendulum and g is the acceleration due to gravity.
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