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Chapter 1: Problem 72

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

Short Answer

Expert verified
The derived SI units for each quantity are as follows: (a) Acceleration: \[\frac{m}{s^2}\] (b) Force: \[kg\cdot\frac{m}{s^2}\] (c) Work: \[kg\cdot\frac{m^2}{s^2}\] (d) Pressure: \[\frac{kg}{m\cdot s^2}\] (e) Power: \[\frac{kg\cdot m^2}{s^3}\] (f) Velocity: \[\frac{m}{s}\] (g) Energy: \[kg\cdot\frac{m^2}{s^2}\]

Step by step solution

01

(a) Acceleration

Acceleration is defined as the rate of change of velocity with time, i.e., distance per time squared. Therefore, the acceleration has SI units of meter for distance (m), which we'll divide by second squared for time (s^2). The derived SI units for acceleration is: \[\frac{m}{s^2}\]
02

(b) Force

Force comes from Newton's second law of motion, which states that force equals mass times acceleration, i.e., F = ma. Mass has the SI unit of kilogram (kg) and acceleration has the derived SI unit of \(\frac{m}{s^2}\). So, the derived SI units for force is: \[kg\cdot\frac{m}{s^2}\]
03

(c) Work

Work is done when a force acts on an object and causes it to move in the direction of the force, i.e., W = Fd. Force has the derived SI unit of \(kg\cdot\frac{m}{s^2}\), and distance has the SI unit of meter (m). Therefore, the derived SI units for work is: \[kg\cdot\frac{m^2}{s^2}\]
04

(d) Pressure

Pressure is defined as force applied per unit area, i.e., P = \(\frac{F}{A}\). Force has derived SI units of \(kg\cdot\frac{m}{s^2}\), and area, being length squared, has the SI units of \(m^2\). Hence, the derived SI units for pressure are: \[\frac{kg}{m\cdot s^2}\]
05

(e) Power

Power is the rate at which work is being done, i.e., P = \(\frac{W}{t}\). Work has the derived SI units of \(kg\cdot\frac{m^2}{s^2}\), and time has the SI unit of second (s). So, the derived SI units for power are: \[\frac{kg\cdot m^2}{s^3}\]
06

(f) Velocity

Velocity is the rate of change of position, i.e., v = \(\frac{d}{t}\). Distance has the SI unit of meter (m), and time has the SI unit of second (s). Therefore, the derived SI units for velocity are: \[\frac{m}{s}\]
07

(g) Energy

Energy can be defined as the kinetic energy of an object, i.e., E = \(\frac{1}{2}mv^2\). Mass has the SI base unit of kilogram (kg), and velocity has the derived SI unit of \(\frac{m}{s}\). So, the derived SI units for energy are: \[kg\cdot\frac{m^2}{s^2}\]

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Most popular questions from this chapter

Suppose you decide to define your own temperature scale with units of \(\mathrm{O},\) using the freezing point \(\left(13^{\circ} \mathrm{C}\right)\) and boiling point \(\left(360^{\circ} \mathrm{C}\right)\) of oleic acid, the main component of olive oil. If you set the freezing point of oleic acid as \(0^{\circ} \mathrm{O}\) and the boiling point as \(100^{\circ} \mathrm{O},\) what is the freezing point of water on this new scale?

Make the following conversions: (a) \(72^{\circ} \mathrm{F}\) to \(^{\circ} \mathrm{C},\) (b) \(216.7^{\circ} \mathrm{C}\) to \(^{\circ} \mathrm{F},(\mathbf{c}) 233^{\circ} \mathrm{C}\) to \(\mathrm{K},(\mathbf{d}) 315 \mathrm{K} \mathrm{to}^{\circ} \mathrm{F},(\mathbf{e}) 2500^{\circ} \mathrm{Fto} \mathrm{K},(\mathbf{f}) 0 \mathrm{K}\) to \(^{\circ} \mathrm{F}\)

In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly 1 ft. An acre is 4840 yd. An acre-foot is enough water to supply two typical households for 1.00 yr. (a) If desalinated water costs \(\$ 1950\) per acre-foot, how much does desalinated water cost per liter? (b) How much would it cost one household per day if it were the only source of water?

(a) The temperature on a warm summer day is \(87^{\circ} \mathrm{F}\) . What is the temperature in \(^{\circ} \mathrm{C} ?\) (b) Many scientific data are reported at \(25^{\circ} \mathrm{C}\) . What is this temperature in kelvins and in degrees Fahrenheit? (c) Suppose that a recipe calls for an oven temperature of \(400^{\circ} \mathrm{F}\) . Convert this temperature to degrees Celsius and to kelvins. (d) Liquid nitrogen boils at 77 \(\mathrm{K}\) . Convert this temperature to degrees Fahrenheit and to degrees Celsius.

A 32.65 -g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 \(\mathrm{mL} .\) The solid and toluene together weigh 58.58 \(\mathrm{g}\) . The density of toluene at the temperature of the experiment is 0.864 \(\mathrm{g} / \mathrm{mL}\) . What is the density of the solid?
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