Exam 6: Fundamental Dimensions and Units

The force between two charged particles can be calculated using the following equation: $F = k \frac { q _ { 1 } q _ { 2 } } { r ^ { 2 } }$ where F= force in newtons G= electrostatic constant = charge of particle 1 in coulombs = charge of particle 2 in coulombs r= distance between particles in meters What is the appropriate unit for $k$ if the preceding equation is to be homogeneous in units?

A motorcyclist's final speed after 2 minutes is 165 miles per hour and the peak power generated was 115 horsepower.Convert all of the values given to U.S.Customary units.

$\text { A motorcyclist who weighs } 150 \mathrm { lbs } \text { accelerates his } 200 \mathrm {~kg} \text { motorcycle at a rate of } 20 \mathrm {~m} / \mathrm { s } ^ { 2 } \text { over }$ $\text { a distance of } 100 \text { yards in } 5 \text { seconds. Convert all of the values given to SI units. }$

What is the temperature difference between your body and the classroom in: a.kelvin b.degrees Celsius

One milliliter (ml) is the volume in one cubic centimeter (cc) .How many $c c {~ }^ { \prime } s$ of soda would it take to fill a 2literbottle?

The friction force between two surfaces is modeled using the following equation: $f = \mu N$ where f= friction force in newton \mu= coefficient of friction N= normal force in newton What is the appropriate unit for $\mu$ if the preceding equation is to be homogeneous in units?

Which of the following are U.S.Customary units:

Express the work done Work (Force)(dist) by a 200 N force exerted over a distance of 15 m using SI units.

Convert the information given in the table below from USCS to SI units: U.S. Customary Units SI Units 32./ / 35 120\nobreakspace

While driving down the highway you notice that your speedometer reads 22 m/s and 80km hr . Which is faster, one meter per second or one kilometer per hour?

A racquetball court is 12 m long by 6 m wide by 6 m high.Express the volume of the racquetball court in m $\mathrm { m } ^ { 3 }$ and liters.

Circle the fundamental dimensions and write the fundamental SI units adjacent to each fundamental dimension: Length Volume Power Permeability Force Temperature Energy Weight Speed Strength Electrical current Permittivity Elongation Direction Time Stress Acceleration Frequency Velocity Voltage Viscosity Momentum Strain Luminous intensity Work Torque Resistance Period Mass Inertia Area Inductance Loudness Amplitude Amount of a substance Refractivity Specific gravity Density Pressure Specific weight

A sheet of notebook paper is one-tenth of a centimeter thick.What is the thickness, in centimeters, of a 500-sheet stack of notebook paper?

The amount of heat needed to change the temperature of an object can be calculated using the following equation: $Q = m c _ { p } \Delta T$ where $Q =$ amount of heat in calories $m =$ mass of object in grams $c _ { p } =$ specific heat of object $\Delta T =$ change in temperature in ${ } ^ { \circ } \mathrm { C }$ What is the appropriate unit for $c _ { p }$ if the preceding equation is to be homogeneous in units?

$\text { An engineering professor weighs } 180 \mathrm { lbs } \text {. Express the mass and the weight of the professor }$ $\text { in SI and U.S. Customary units. }$

The amount of time it takes for a pendulum to swing "to-and-fro" through one complete cycle is called the "period" and is calculated using the following equation: $T = 2 \pi \sqrt { \frac { I } { m g h } }$ where T= period in seconds I= mass moment of inertia m= mass of pendulum in kilograms g= gravitational acceleration, 9.8/ h= effective length of pendulum in meters What is the appropriate unit for $I$ if the preceding equation is to be homogeneous in units?

Present the results of the following operations using the proper number of significant digits: Your Calculator Displays Should Be Recorded As 9.386.47= 1098.6= 10 97 = 6.672= 6.021.7\div4.83=

The speed of sound in a fluid can be calculated using the following equation: $v = \sqrt { \frac { B } { \rho } }$ where v= speed of sound in / B= bulk modulus \rho= fluid density in / What is the appropriate unit for $B$ if the preceding equation is to be homogeneous in units?

Convert the following: a. area $= 40$ hectares to $\mathrm { m } ^ { 2 }$ b. $10 \mathrm {~m} ^ { 3 }$ to liters c. power $= 75$ horsepower to watts d. length $= 100 \mathrm {~mm}$ to meters e. speed $= 30 \mathrm {~m} / \mathrm { s }$ to $\mathrm { km } / \mathrm { hr }$

A garden plot is 60 m long by 30 m wide.Express the area of the garden in $\mathrm { m } ^ { 2 }$ and hectares.