Question

b) units (13 pts): for each quantity listed, give the units of measurement and/or for each unit of measurement, give the quantity it measures. place the answer in the box below the quantity or unit of measurement. 1. specific heat 2. spring force 3. m/s² 4. liter (l) 5. temperature change 6. resistance 7. amperes 8. newton (n) 9. frequency 10. wave speed 11. kinetic energy 12. kilogram (kg) 13. wavelength

Explanation:

Step1: Specific Heat

Specific heat is the amount of heat energy required to raise the temperature of a unit mass of a substance by one unit of temperature. Its unit is joule per kilogram per kelvin ($\frac{J}{kg \cdot K}$) or calorie per gram per degree Celsius ($\frac{cal}{g \cdot ^\circ C}$).

Step2: Spring Force

Spring force is given by Hooke's law $F = kx$, where $F$ is the force, $k$ is the spring constant, and $x$ is the displacement. The unit of spring force is newton (N) as it is a force.

Step3: $\boldsymbol{m/s^2}$

The unit $m/s^2$ is the unit of acceleration. Acceleration is the rate of change of velocity, and the formula for acceleration is $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is the change in velocity (in meters per second, $m/s$) and $\Delta t$ is the change in time (in seconds, $s$). So, the unit of acceleration is $\frac{m/s}{s}=m/s^2$.

Step4: Liter (L)

A liter is a unit of volume. It is commonly used to measure the volume of liquids. 1 liter is equal to 1 cubic decimeter ($1\ L = 1\ dm^3$) or 1000 cubic centimeters ($1\ L=1000\ cm^3$).

Step5: Temperature change

Temperature change is measured in degrees Celsius ($^\circ C$) or kelvin (K). The change in temperature $\Delta T=T_2 - T_1$, and the unit for the change in temperature is the same as the unit for temperature, i.e., $^\circ C$ or $K$.

Step6: Resistance

Resistance is a property of a material that opposes the flow of electric current. It is measured in ohms ($\Omega$). From Ohm's law $V = IR$, where $V$ is voltage (in volts, $V$), $I$ is current (in amperes, $A$), and $R$ is resistance. So, $R=\frac{V}{I}$, and the unit of resistance is $\frac{V}{A}=\Omega$.

Step7: Amperes

Ampere (A) is the unit of electric current. Electric current is the rate of flow of electric charge, and the formula is $I=\frac{Q}{t}$, where $Q$ is charge (in coulombs, $C$) and $t$ is time (in seconds, $s$). So, the unit of current is $\frac{C}{s}=A$.

Step8: Newton (N)

Newton is the unit of force. From Newton's second law $F = ma$, where $m$ is mass (in kilograms, $kg$) and $a$ is acceleration (in $m/s^2$). So, $1\ N=1\ kg\cdot m/s^2$.

Step9: Frequency

Frequency is the number of oscillations or cycles per unit time. Its unit is hertz (Hz), where $1\ Hz = 1\ cycle\ per\ second$.

Step10: Wave Speed

Wave speed ($v$) is given by the formula $v = f\lambda$, where $f$ is frequency (in Hz) and $\lambda$ is wavelength (in meters, $m$). So, the unit of wave speed is meters per second ($m/s$).

Step11: Kinetic Energy

Kinetic energy is given by the formula $KE=\frac{1}{2}mv^2$, where $m$ is mass (in $kg$) and $v$ is velocity (in $m/s$). So, the unit of kinetic energy is joule (J), and $1\ J = 1\ kg\cdot m^2/s^2$.

Step12: Kilogram (kg)

Kilogram is the unit of mass. Mass is a measure of the amount of matter in an object, and its SI unit is kilogram (kg).

Step13: Wavelength

Wavelength is the distance between two consecutive points in phase on a wave. Its unit is meter (m), or other units like centimeter (cm) or nanometer (nm) depending on the type of wave.

Answer:

1. Specific Heat: $\boldsymbol{\frac{J}{kg \cdot K}}$ (or $\boldsymbol{\frac{cal}{g \cdot ^\circ C}}$)
2. Spring Force: $\boldsymbol{N}$
3. $\boldsymbol{m/s^2}$: Acceleration
4. Liter (L): Volume
5. Temperature change: $\boldsymbol{^\circ C}$ (or $\boldsymbol{K}$)
6. Resistance: $\boldsymbol{\Omega}$
7. Amperes: Electric Current
8. Newton (N): Force
9. Frequency: $\boldsymbol{Hz}$
10. Wave Speed: $\boldsymbol{m/s}$
11. Kinetic Energy: $\boldsymbol{J}$
12. Kilogram (kg): Mass
13. Wavelength: $\boldsymbol{m}$ (or cm, nm etc.)