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Chapter 1: Problem 72

Give the derived SI units for each of the following quantities in base SI units: (a) acceleration = distance/time \(^{2}\) (b) force \(=\) mass \(\times\) acceleration (c) work \(=\) force \(\times\) distance (d) pressure = force/area (e) power = work/time (f) velocity \(=\) distance/time (g) energy \(=\) mass \(\times(\text { velocity })^{2}\)

Short Answer

Expert verified
(a) Acceleration: \(\frac{m}{s^2}\) (b) Force: \(kg*\frac{m}{s^2} \) or N (Newton) (c) Work: \(kg*\frac{m^2}{s^2} \) or J (Joule) (d) Pressure: \(\frac{kg}{m*s^2} \) or Pa (Pascal) (e) Power: \(\frac{kg*m^2}{s^3} \) or W (Watt) (f) Velocity: \(\frac{m}{s}\) (g) Energy: \(kg*\frac{m^2}{s^2}\) or J (Joule)

Step by step solution

01

(a) SI units of Acceleration

Acceleration is defined as the rate of change of velocity per unit of time, so its unit is distance(divided by)time^(2). The SI base unit of distance is meter(m), and that of time is second(s). So, the SI units of acceleration is m/s^2.
02

(b) SI units of Force

Force is defined as mass times acceleration. So, its unit is mass multiplied by acceleration. We know from above, that the SI units of acceleration is m/s^2, and mass is kg. So, the SI units of force is kg*m/s^2, which is also known as a Newton (N) in honor of Sir Isaac Newton.
03

(c) SI units of Work

Work is defined as force times distance. Therefore, its unit is force multiplied by distance. From above, we know that the SI units of force is kg*m/s^2, and distance is m. So, the SI units of work is kg*m^2/s^2, which is also known as Joule (J).
04

(d) SI units of Pressure

Pressure is defined as force per unit area. Therefore, the unit of pressure is force divided by area. We know from above, the SI units of force is kg*m/s^2, and area is m^2. So, the SI units of pressure is kg/m*s^2, which is also known as Pascal (Pa).
05

(e) SI units of Power

Power is defined as work per time. So, its unit is work divided by time. From above, we know that the SI units of work is kg*m^2/s^2, and time is s. So, the SI units of power is kg*m^2/s^3, which is also known as Watt (W).
06

(f) SI units of Velocity

Velocity is defined as distance covered per unit time, or displacement per time. Therefore, its unit is distance divided by time. Using the SI base units for distance (meters, m) and time (seconds, s), the SI units of velocity is m/s.
07

(g) SI units of Energy

Energy is defined as mass times the square of velocity. Therefore, its unit is mass multiplied by velocity squared. We know from above, that the SI units of mass is kg and the velocity is m/s. So, the SI units of energy is kg*m^2/s^2, which is also known as Joule (J).

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Most popular questions from this chapter

If on a certain year, an estimated amount of 4 million metric tons ( 1 metric ton \(=1000 \mathrm{~kg}\) ) of nitrous oxide $\left(\mathrm{N}_{2} \mathrm{O}\right)$ was emitted worldwide due to agricultural activities, express this mass of \(\mathrm{N}_{2} \mathrm{O}\) in grams without exponential notation, using an appropriate metric prefix.

Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) \(25 \mathrm{ps}\), (b) \(374.2 \mathrm{mg}\) (c) \(77 \mathrm{~K}\) (d) \(100,000 \mathrm{~km}^{2}\) (e) \(1.06 \mu \mathrm{m}\) (f) \(16 \mathrm{nm}^{2},(\mathrm{~g})-78^{\circ} \mathrm{C}\) (h) \(2.56 \mathrm{~g} / \mathrm{cm}^{3}\) (i) \(28 \mathrm{~cm}^{3}\). [Section \(\left.1.5\right]\)

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Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) \(\mathrm{km} / \mathrm{hr}\) to \(\mathrm{m} / \mathrm{s}\) (b) \(\mathrm{mL}\) to \(\mu \mathrm{L}(\mathbf{c}) \mathrm{ps}\) to $\mathrm{s}(\mathbf{d}) \mathrm{m}^{3}$ to gal.

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