Formula Sheet (Practice Questions)

A person of 776-Newtons weight is standing up on a square scale with a side-length of 23- cm. What is the pressure in Pascals exerted by the person on the scale? Round to the nearest unit. ( 1cm = 0.01 m)

First start by converting the 23 cm into meters because Pascals is N/m^2.23cm x0.01m=0.23mNext the equation for pressure is P=F/A Where F stands for Force and A stands for Area. Then find area. The side length of the square is 23cm or 0.23m as we did before. A=LxWA=0.23mx0.23mA=0.0529m^2Finally, plug in the quantities for force and area to find the pressure P=F/AP=776N/0.0529m^2 P= 14669 Pascals

Calculate the wavelengths of sounds in mm, at the extremes of the audible range of 20,000 HZ, in conditions where sound travels at 315.7 m/s. Round to the nearest hundredth.

First, we know the formula v=fλ (velocity= frequency x wavelength) can be used to find wavelength by rewriting as: λ=v/f Plug in the given variables to get: λ = 315.7 / 20000 Solving this gives: 0.015785 m This is correct, but the questions asks for the wavelength in mm so multiply your answer by 1,000 0.015785 * 1000 = 15.785 and round to the nearest hundredth λ=15.79 mm

Calculate the mass in grams of 77 cubic centimeters of water at room temperature with a density of 1.0 g per cubic centimeter.

For this problem we must multiply the 77x1=77. therefore, the answer is 77.

At 192 k Ohms, how much current in micro Amperes flows through your body if you touch the terminals of a 3.9-V battery? (Give your answers with one numerical digit)How many Coulombs of charge travel through a light bulb rated 100 W, in 9 hours?

For this question we are finding the current and need to use the Ohm's Law equation: I=V/R Current = Voltage / Resistance We are given a voltage of 3.9V and resistance of 192,000Ω Plugin what we have: 3.9 / 192000 = 0.0000203125 A The question asks for the answer in rounded Micro amperes so we need to take the solution and multiply it by 10^ -6 0.0000203125 * 10^-6 = 20.3

The magnetic force acting on a wire carrying a current of 1.3 A, of length 1.0 M, in a region of the magnetic field of 0.004Tesla in Newtons is;

Formula: Force= magnetic field x current x length Solve: F= (0.004)(1.3)(1.0)= 0.005N Solution: 0.005N

An electronic device requires 3 volts to operate correctly. A transformer nicely allows the device to be powered from a 120-volt outlet. If the primary has 120 turns, how many should the secondary have?

Formula: primary voltage/primary # of turns= secondary voltage/ secondary # of turns Solve: Step 1- 120/120=3/? Step 2- 3/ (120/120)= 3 turns Solution: 3 turns

If the frequency of a particular wave is 7Hz, what is its period in seconds?

From the problem, we know that f=7Hz. And we know that t=1/f therefore when we divide 1 by f (1/7) we get 0.14285. then, we must round it the nearest hundredth the answer is 0.14 seconds.

Air pressure and air density inside an inflated tire are greater than the atmospheric pressure and density outside.Twice as many molecules in the same volume doubled the air density. If we add more air molecules into a tire, increasing the density by a factor of 1.26, the pressure in the tire changes by a factor of : (Round to the nearest hundredth.)

Step 1: In the problem we are told that if there is twice as many molecules in the same volume means that the air density will be doubled. We also know that Density is directly proportional to pressure and indirectly proportional to temperature. Step 2: In our problem we are told that the air density in the tire increased by a factor of 1.26 so the pressure inside has to change by a factor of 1.26 also since density is directly proportional to pressure. Answer: 1.26

An electric car requires 12 V for its devices. When connected to a 120-V household circuit, a transformer is needed. If the car used 15 Amperes of current, how much current does the transformers get from the household circuit?

Step 1: We know that P1 = P2 and so V1 / I1 = V2 / I2. We can then plug in our numbers and we get 120 / 15 = 12 / ?. Step 2: To solve for ?, we can use the same cross multiplication method as in #9. We take 12 / (120 / 15), again making sure to do the function in parenthesis first. Then we get 1.5 so our answer is 1.5 amperes.

What is the resistance of a person's body when the skin is moist, and a current of 0.002-A is measured when the person touches the terminal of a 8-V battery? (Round to one decimal place)

Step 1: We know that R = V / I and we are given V = 8 and I = 0.002. Step 2: When we plug these numbers into the equation, we get R = 8 / 0.002 = 4000. Since we have to round to one decimal place, our answer is 4000.0.

A red laser emits light with a wavelength of 739 nm. What is the frequency in 1014Hz? Round to the nearest tenth.

Step 1: We know that c = λf. So if we are solving for frequency, we can rearrange the equation to be f = c / λ. Step 2: The problem tells us that λ = 739 nm but we want this to be in meters. To do this, we have to divide 739 nm by 1.0E9 since there are a billion nm in a meter. This gives us 7.39E-7 m. Step 3: The speed of light in a vacuum is 3.0E8 m/s so we can plug this in for c and 7.39E-7 m in for λ. Now we have f = 3.0E8 / 7.39E-7. When we put this into our calculator and round to the nearest tenth, we get f = 4.1E14. Step 4: Because the question is asking us what the frequency is in 1014Hz, the answer is simply 4.1.

A beam of light enters a glass of water with sugar at an angle of 36 degrees with respect to the normal. What is the value of the speed of light in x10^8 m/s water if the the index of refraction of the water with sugar is n = 1.3. Round to the nearest hundredth.

Step 1: We know that n = c / v. We are looking for the value of v, so we can rearrange the equation to give us v = c / n. Step 2: The speed of light in a vacuum is 3.0E8 m/s so we can plug that in for c. We also know that n = 1.3 so we can plug that into our equation as well. Step 3: Now we have v = 3.0E8 / 1.3. When we put this into our calculator and round to the nearest hundredth, we get v = 2.31E8. Step 4: Because the question is asking for the speed of light in x108 m/s, the answer is just 2.31.

Pascal's principle states that a change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid. If we apply a force of 68-Newtons on the smaller area of a U-shape tube with a ratio of areas of 1-32, what is the force that can be supported by the liquid on the other end of the U-tube, of the larger area?

Step 1: We know that p1=p2 and that f1/a1=f2/a2 and that the ratio of areas for the problem is 1-32 Step 2: We were told the force on area 1 is 68 N we are trying to find the force on area 2 which is 32 times bigger. Step 3: To find the force that can be supported by the liquid on the other side we have to multiply F1 by 32 since the ratio of the areas is 1-32 which also means that F2 is 32 times bigger Step 4: 68 ? ---- = ----- = 68x32= 2176 N 1 32

What is the power rating in Watts of a lamp connected to a 6-V source when it carries 8 A?

Step 1: We know that power = current x voltage. In the problem, we are given the current, 8 A, and voltage, 6 V. Step 2: Now we can plug in these numbers to the equation and we get power = 8 x 6 = 48. So our answer is 48.

An electric car requires 12 V for its devices. When connected to a 120-V household circuit, a transformer is needed. If the primary coil of the transformer has 230 windings, how many turns should there be in the secondary coil?

Step 1: We know that primary voltage / primary # of turns = secondary voltage / secondary # of turns. So when we plug in our numbers, we have 120 / 230 = 12 / ?. Step 2: To solve for ?, we take 12 / (120 / 230), making sure to do the function in parenthesis first. Then we get 23 so our answer is 23 turns.

Calculate the mass in grams of 43 cubic centimeters of salted water at room temperature with a density of 1.1 g per cubic centimeter. (Round to the nearest tenth)

Step 1: You would use the formula M=v(d) to solve this equation to get the the answer in grams. Step 2: You would take 43 which is the cubic centimeters listed above and then multiply that by 1.1 which is the grams per cubic centimeter. You would do 43(1.1) = 47.3 g as you final answer when solved. Answer: 47.3 g

An electronic device requires 51 volts to operate correctly. A transformer nicely allows the device to be powered from a 120-volt outlet. If the primary has 120 turns, how many turns should the secondary have?

Steps: 1.) We know that primary voltage/primary number of turns = secondary voltage/secondary number of turns 2.) So when we plug into the equation what we are given it looks like 120 / 120 = 51 / unknown 3.) To solve for the unknown value we can do 51 / (120 /120) which equals 51. Answer : 51 turns

A person of 650-Newtons weight is standing up on a square scale with a side-length of 26- cm. What is the pressure in Pascals exerted by the person on the scale? Round to the nearest unit. ( 1cm = 0.01 m)

We need to use the equation: P= f / a (pressure = force / area) We know that the Force = 650 N and that the side length of the scale is 26 cm First, to find the area we need to take the side length and convert it into meters26 * 0.01 = 0.26 <- multiply this number by itself to get the area Area= 0.26 * 0.26 = 0.0676 Now, plug everything into the equation to get: P= 650 / 0.0676 = 9615.3846 Rounded to 9615

When 2 identical lamps are connected in series to a battery, the current going through the lamps decreased by a factor of

What We Know I = I -current decreases every lamp you have Solution So, if you have 2 lamps it will decrease by 2.

What is the resistance of a toaster that draws a current of 9.6 A when connected to a 120-V circuit?

What are we solving for? We are solving for resistance (R) Equation : R (resistance) = V (voltz) / I (amps) Steps : 1.) Plug in what we know. We know both the amp and voltz values. So we can plug those values into the equation. R= 120 / 9.6 2.) Solve for "R" (resistance) 120 / 9.6 =12.5 Answer : R = 12.5

How much energy in Joules gets transmitted from the outlet to a light bulb rated 20 in 20 hours?

What are we solving for? We are solving for the amount of energy in joules that is transferred from the outlet to the light bulb. Steps : 1.) We need to convert our time (20 hours) to seconds. To do so we will take 20 and multiply it by 60, this will give us minutes. But we need to get our answer in seconds so we need to multiply by 60 again. 20 x 60 x 60 = 72,000 2.) Now that we have our time in seconds we can multiply 72,000 by the rate of our light light bulb which is 20. 72,000 x 20 = 1,440,000 Answer : 1,440,000

What is the resistance of a person's body when the skin is moist, and a current of 0.014-A is measured when the person touches the terminal of a 7.5-V battery? (Round to one decimal place)

What we know: Formula is R = V/I V = 7.5 I = 0.014 To solve: 1. Since we know our V and our I, we'll plug our numbers in. 7.5/0.014 = 535.714286 2. The question asks us to round to one decimal place so we'd just leave the answer as 535.7 3. Resistance = 535.7

Calculate the mass in grams of 19 cubic centimeters of water at room temperature with a density of 1.0 g per cubic centimeter.

density=mass/volume we are finding the mass so the equation is mass=density x volume given: 19 cm^3 which is volume 1.0 g/cm^3 which is the density mass= 1.0 g/cm^3 X 19 cm^3 mass= 19 grams

According to Coulomb's law, if we change the distance between a pair of particles, by a factor of 0.4, so the new distance is 0.4 times the original one, force acting on them changes by a factor of: (Round your answer to two digit values)

f=kq1q2/r^2 Since the distance r is .4 it's original distance, then r squared is equal to .16. The original numerator is then divided by .16, which gives you a factor of 1/.16 = 6.25.

What is the current drawn by a light bulb rated 12-W? Give the answer with two decimal places.

power=current x voltage --------> current=power/voltage Given: 12-W=power 120-V= voltage 12/120= 0.1 The current is 0.1-A

A 4.3-kg object, when submerged under water has an apparent mass of 0.1-kg. What is the buoyant force in kg? Round to the nearest tenth.

Equation~ Fb=pgV Fb=buoyant force p=fluid density g=acceleration due to gravity V=fluid volume Given~ 4.3kg 0.1kg (the gravity is 9.8m/s, it does not say in the problem but I am assuming that this is taking place on earth) Fb=4.3x9.8x0.1 Units is in Newtons (N) Answer~ 4.2N You could also just subtract 4.3-0.1 because when something is submerged in water, it loses mass.

Mercury has a density of 13.6 grams per cubic centimeter. How many times heavier is one cubic centimeter of mercury than one of water? Round to the nearest tenth.

Equation~ V=m/d Given~ 13.6g/cm^3 1cm^3 V=13.6/1 Unit is cm^3 Answer~ 13.6cm^3

If the fundamental frequency of a cord is 215Hz what is the frequency of the 2th harmonics?

F= 215Hz x 2= 430Hz The frequency of the 2th harmonics is 430Hz

What is the wavelength in nm of a laser beam with a frequency of 4.3x10^14 Hz? Round to the nearest tenth.

wavelength = constant/volume constant is the constant speed of light which is 3x10^8 (3x10^8) / (4.3x10^14) = 6.977e^-7 next we need to convert meters to nanometers which we do by multiplying the meters by 1x10^9nm/1m (6.977e^-7) x (1x10^9) /1 = 697.67 when rounding to the nearest tenth we keep one digit after the decimal so our final answer is 697.7 nm

Two sound waves have frequencies of 203 Hz and 263 Hz. What is the beat frequency produced by their interference?

Beat frequency = |f2 - f1| = | 263 Hz - 203 Hz | = 60 Hz

A wire carrying current is in a region of magnetic field. If the magnetic field suddenly increases 8.4-times, how many times does the force in the wire increases?

The Force is directly proportional to the magnetic field (B), therefore if we multiply the magnetic field by 8.4, the resulting force is also multiplied by 8.4 as shown below: F=IL(8.4B)sin(theta)

A water wave with a wavelength of 5 meters, oscillates at 27 times per second. With what velocity did the wave travel in m/s? Round to the nearest tenth.

The equation that I used to solve this problem is Velocity= Wavelength*Frequency Now we can plug into the equation the parts that we know Velocity =5*27 Velocity = 135.0 m/s

How much current flows through a lamp with a resistance of 360 Ohms when the voltage across the lamp is 120 V? (Give the answer with two decimal places.)

To solve this problem you take 120 V and divide it by 360 Ohms which gives you the 0.33 when rounded. 120 V/ 360 Ohms= 0.33

If a 120-V line to a socket is limited to 15A by a safety fuse, will it operate a 1200-W hair dryer?

Using P=VI we can solve for the amount of current (I) a 1200W hair dryer draws from a 120V power source. I=P/V I=1200/120 I=10A

Sound travels at 340 m/s in air at 20ºC. The speed of sound increases by 0.6 m/s for each increase of 1ºC above the 0ºC. What is the speed of sound (in m/s) in air at 6 ºC? Give the answer with one decimal place.

We first need to figure out the difference in temperatures of the air 20ºC-6 ºC=14ºC Then since we were told that the speed of sound increases by 0.6 m/s for each increase of 1ºC we now do 14ºC x0.6 m/s=8.4 m/s This now gives us the change in speed so the final step is to do 340 m/s-8.4 m/s= 331.6 m/s.

An electronic device requires 36 volts to operate correctly. A transformer nicely allows the device to be powered from a 120-volt outlet. If the device draws 0.1 ampere of current from the outlet, how many amperes of current does it use? Round the answer to the nearest tenth.

We know that Power = Voltage*Current, and we know that the input power of an ideal transformer is equal to the output transformer. The input power is Pin=(120V)(.1A) = 12W So the output power is Pout=(36V)*I=12W, since Pin=Pout 36I=12 I=12/36 I=.33A

Mercury has a density of 13.6 grams per cubic centimeter. How much volume of oil of 0.93 grams per cubic centimeter has the same mass as 6.4 cm3 of mercury at room temperature? Round to the nearest tenth.

We know that d=m/v where d is density m is mass and v is volume. We are trying to find the volume of oil needed for the oil and the mercury to have the same mass at room temperature Find the mass of mercury Mercury has a density of 13.6 g/cm^3 (d=13.6) and it has a volume of 6.4 cm^3 (v=6.4) d=m/v m=dv m=13.6x6.4 m=87.04 g Now that we have the mass of mercury we can find the volume of oil. Since the mass of mercury and the mass of oil are the same (m=87.04) The density of the oil is given as 0.93 g/cm^3 (d=0.93) d=m/v v=m/d v=87.04/0.93 v=93.6cm^3 So the volume of oil needed for this oil to have the same mass as the mercury as room temperature is 93.6 cm^3.

If the period of a particular wave is 5 seconds, what is the frequency in Hz? Round to the nearest hundredth

We know that f=1/T so we can replace the variables with what is known f=1/5 (5 is our time (T)) 1/5= 0.2

Calculate the wavelengths of sounds in meters at the extremes of the audible range of 20 Hz, in conditions where sound travels at 335.7 m/s. Round to the nearest hundredth.

We know that the frequency is 20Hz and the speed of the wave is 335.7m/s and we are looking for wavelength. speed of wave = wavelength x frequency (335.7m/s) = wavelength x (20Hz) divide by 20 to find wavelength 335.7/20=wavelength wavelength= 16.785m round to nearest hundredth wavelength=16.79m