Unit & Dimensions Questions and Answers

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

The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. Two cells are measured using this method: Cell E: 4.5 x 10-³ centimeters Cell F: 7.4 × 10-4 centimeters How many times larger is the diameter of cell E than the diameter of cell F? Write your answer in standard notation, rounding to the nearest tenth.

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)