Unit & Dimensions Questions and Answers

RCP11 9 XP 003 A 61 0 kg man lies on his back on a bed of nails with 1 204 of the nails in contact with his body The end of each nail has area 1 15 x 10 6 m What average pressure is exerted by each nail on the man s 0 508160 10 6 X Pa MY NOTE

A soccer ball was kicked into the air at a speed of 35 miles per hour at an angle of 45 from the horizontal Express this velocity in vector form Round your answer to four decimals Answer 2 Points Keyboard St

Problem 1 Coulomb s law can be summarized as 1 Q 4 0 R F 1 where F is a force Qis a charge and R is a length Use the units or di mensions of this problem to write down dimensionally correct expressions for a an energy b a voltage energy per charge c an electric field voltage per meter You may only use the inputs co Q and R in your answers and all we care about are the units not the detailed form or 47 factors

4 Write each vector in component form 8 pts tof 15m R 10m 30 py 40 nu 8m f

Make sure to show all work in complete detail NO CREDIT will be given if NO work is shown 1 It is given that A B 50 4i m C 62 0 i m and A B C 14 2 i m Find the vectors A and B 8 pts

A piston A as shown at right has a diameter of 0 64 cm A second piston B has a diame ter of 3 8 cm Deter mine the force F necessary to support the 500 0 N weight in the absence of friction B 500 0 N F

1 Fill in the chart below with the missing pieces Measurement Work Acceleration Force Variable W t Ax V KE Unit Seconds s Kilograms Meters per second kg m s Newton seconds Ns

A student measured the acceleration of a car using two different methods The result from method one is 2 5 m s2 while the result from method two is 2 9 m s Find the percent difference between the two results 17 40 14 15 20

1 Show the correctness of the following units Resistance 52 kg m s A Electric field kg m s C Surface charge density As m Resistance 2 VIA Electric field V m Current density C s m Electrical Potential kg m As Electrical Potential J As Kapasitans Farad A s4 kg m

ZOOM Merrill was solving the equation 2 x 2 x elow Step 1 Step 2 Step 3 Stan 4 2 x 2 2 x 2 V 2 x 2 x 2x 4 x Y 4

The amount of water in reservoirs is often measured in acre-ft. One acre-ft is a volume that covers an area of one acre to a depth of one foot. An acre is 43,560 ft. Find the volume in SI units of a reservoir containing 66.0 acre-ft of water.

A house is 59.0 ft long and 38 ft wide, and has 8.0-ft-high ceilings. What is the volume of the interior of the house in cubic meters and cubic centimeters? m3 cm 3

A 2.2 kg mass vibrates according to the equation x = 0.71 cos8.5t where x is in meters and t in seconds. Calculate the frequency in Hz.

Learning Goal: To practice Tactics Box 13.2 Finding whether an object floats or sinks. you hold an object underwater and then release it, it can float to the surface, sink, or remain hanging" in the water, depending on whether the fluid density pr is larger than, smaller than, or equal to the object's average density - These conditions are summarized in this Tactics Box. TACTICS BOX 13.2 Finding whether an object floats or sinks Y Part A Pull = Submit Part B An object sinks if it weighs more than the fluid it displaces, that is, if its average density is greater than the density of the fluid Pars > Pt. Ice at 0.0°C has a density of 917 kg/m³. A 3.00 cm³ ice cube is gently released inside a small container filled with oil and is observed to be neutrally buoyant. What is the density of the oil, Pa? Express your answer in kilograms per meter cubed to three significant figures. VAE Submit Object sinks " d Part C Request Answer Once the ice cube melts, what happens to the liquid water that it produces? View Available Hint(s) C? The liquid water sinks to the bottom of the container. The liquid water rises to the surface and floats on top of the oil. The liquid water is in static equilibrium at the location where the ice cube was originally placed. Object floats 42 An object rises to the surface if it weighs less than the fluid it displaces, that An object hangs motionless if it weighs exactly the same as the fluid it displaces-that is, if its average density equals the density of the fluid is, if its average density is less than the density of the fluid: Pang Pt Parz Pr. What happens if some ethyl alcohol of density 790 kg/m³ is poured into the container after the ice cube has melted? Alayer of ethyl alcohol forms between the oil and the water. The layer of ethyl alcohol forms at the bottom of the container. The layer of ethyl alcohol forms on the surface. Object has neutral buoyancy A

If nºh division of main scale coincides with (n+1)th division of vernier scale and main scale division is equal to a mm, then Least count of Vernier calliper is 0.1 mm for a = 1 mm and n = 9 Least count of Vernier calliper 0.1 mm for a= 2 mm and n = 19 If value of n increases, then least count will also increase If value of n increases then least count will also decrease

(a) Assume the equation x = At³ + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (Use the following as necessary: L and T, where L is the unit of length and T is the unit of time.) [A] = [B] = (b) Determine the dimensions of the derivative dx/dt = 3At² + B. (Use the following as necessary: L and T, where L is the unit of length and T is the unit of time.) [dx/dt] =

While Newton's Second Law often deals with formulas and numerical calculations, there exist one very important nonnumerical convention that must be appreciated and adhered to. On September 23, 1999, Mars Climate Orbiter--a $125 M space mission-was lost when a small rocket was fired to adjust entry to the Mars atmosphere. Unfortunately, one operator assumed the thrust value was given in English units when actually NASA specifications gave it in metric units. This is an example of consequences if the MKS convention is not precisely honored. What does the MKS convention designates the following?

The bent rod is supported at A, B, and C by smooth journal bearings. Compute the x, y, z components of reaction at the bearing B. Enter the x, y, and z components of the reaction using three significant figures separated by commas.

Convert 1.2 x 10^-3 O 1.200 O 0.1200 O 0.0120 0.0012 10-3 to decimal notation. 0.00012

What is the difference between 103.5 and 102.24 written with the correct number of significant figures? 1 O 1.3 O 1.26 O 1.260 O 1.2600

If a tree is 15 m tall, its height expressed in feet is x ft, where x is less than 15. O greater than 15.

Consider the functions f(x) and g(x), for which f(0) = 7, g(0) = 8, f'(0) = -9, and g'(0) = -2. f(x) g(x) Find h'(0) for the function h(x) = h'(0) =

The unit millirem (1 rem = 1,000 mrem) is often used to measure the amount of radiation absorbed. (a) The average yearly dose of radiation from radon gas is 200 mrem. How many rem does this correspond to? (b) If a thyroid scan exposes a patient to 0.020 rem of radiation, how many mrem does this correspond to? (c) Which represents the larger dose?

A rectangular airstrip measures 30.40 m by 280 m, with the width measured more accurately than the length. Find the area (in m²), taking into account significant figures.

The average distance between the Sun and Neptune is 4450 x 106 km. Express this distance in AU with two significant figures. (Numerical answer only)

As of summer 2020, Voyager 1 is about 13.8 billion miles from Earth. Express this distance in AU, using scientific notation, with two significant figures. (For your work to be correctly graded by Canvas, please write your answer in the same format as 1.23 x 10^4, including spaces before and after the "x" but with the correct number of significant figures.)

Mercury, also known as quicksilver, is a metallic element and a liquid at room temperature. Calculate mercury's density if a sample of mercury is found to have a mass of 657.0 g and a volume of 49.29 mL. density: g/mL

The following conversions occur frequently in physics and are very useful. (a) Use 1 mi = 5280 ft and 1 h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling object is 32 ft/s². Use 1 ft = 30.48 cm to express this ac- celeration in units of m/s². (c) The density of water is 1.0 g/cm³. Convert this density to units of kg/m³.

An American Football field is 91.44 meters long from goal line to goal line. How many kilometers are in a football field from goal line to goal line?

The sides of a small rectangular box are measured to be 1.80 ±0.01 cm long, 2.02± 0.02cm long, and 3.10 ± 0.01cm long. Calculate the box's volume and approximate uncertainty in cubic centimeters. Hint: Volume of a box = Length x Width x Height. Remember that when performing multiplication with uncertainties, you must change the absolute uncertainty to a percent uncertainty to begin and then convert back to an absolute uncertainty. Also, remember significant numbers for your uncertainty answer.

A vector has an x-component of -25.5 units and a y-component of 43.0 units. Find the magnitude and direction of the vector.

An airplane is traveling through the sky. It is moving at a speed of 200 m/s, with a tailwind of 50 m/s, for 3600 seconds a) Draw a vector diagram representing the word problem.

(10%) Problem 8: Joan is setting up her new gaming PC, however she is worried about it overheating. She finds that the rate of heat loss (H), in W, that her cooling system can generate depends on the speed (V) and surface area (4) of her fans and the density of her coolant (p).

You are a sports agent's assistant. You are preparing a report on contracts you have obtained for the agent's clients. You recently negotiated the following annual contracts: $2.8 million, $18.9 million, $1.5 million, $1.2 million, $1.5 million, and $3.5 million per year. The standard deviation of the data is 6.3, and the range is 17.7.

A microbiologist measures the speed of a swimming bacterium. The 2bacterium covers a distance of 6.82 microns in 3.5 seconds. The biologist wished to compare the speed of the bacteria with other animals, but the speeds of other animals are listed in kilometers per hour. What is the speed of the bacterium in kilometers per hour? (1 micron = 1x 10^-6 m) Use scientific notation and express your answer to the correct number of significant figures. You must show your work for full credit.

7. If the displacement of an object, x, is related to velocity, v, according to the relation x Av, the constant, 4, has the dimension of which of the following? a. acceleration b. length c. time d. area

(b) A displacement is related to time as x = A sin(2xft), where A and fare constants. Find the dimensions of A. (Hint: A trigonometric function appearing in an equation must be dimensionless.) L L/T L X T T/L T

Find the uncertainty in kinetic energy. Kinetic energy depends on mass and velocity according to this function E(m,v) = 1/2 m v2. Your measured mass and velocity have the following uncertainties Sm= 0.45 kg and Sv 1.12 m/s. What is is the uncertainty in energy, SE, if the measured mass, m = 3.24 kg and the measured velocity, v = 11.88 m/s? Units are not needed in your answer.

Vector A has a magnitude of 25.5 units and it points in a direction 335° counterclockwise from the positive x-axis. What are the x and y-components of A?

A snowboarder starts from rest at the top of a double black diamond hill. As she rides down the slope, GPS coordinates are used to determine her displacement as a function of time: x = 0.5t³ + 2 + 2t, where x and t are expressed in feet and seconds, respectively. Determine the position, velocity, and acceleration of the boarder when t = 5 seconds.

A student performs an experiment to find the density of a block made up of some unknown substance. He measures mass (m) as 125.35 gram and volume (V) of the block as 20.0 cm³. He will report the density as (density= m /v) (A) 6.2675 g/cm³ (C) 6.26 g/cm³ (B) 6.268 g/cm³ (D) 6.27 g/cm³

Your car gets 34.7 mi/gal on a vacation trip in the U.S. If you were figuring your mileage in Europe, how many km/L (kilometers per litter) did it get? (3.79 L = 1.00 gal; 1.00 mi 1.61 km) 14.7 km/L 55.9 km/L 9.16 km/L 32.4 km/L

A new midsize car has tires with a diameter of 25.4 inches. The tires have a tread-life warranty of 55,000 miles. (a) How many radians will the tires rotate through within the full warranty length? (b) How many revolutions is this equivalent to?

The side length of a square is decreasing at a rate of 2 kilometers per hour. At a certain instant, the side length is 9 kilometers. What is the rate of change of the area of the square at that instant (in square kilometers per hour)? A. -81 B. -36 C. -4 D. -324