Calculating density, acceleration, mass, and distance

Please give an answer and explanation with steps if needed.

1) A block of material has dimensions 3.8cm by 6.1 cm by 3.8cm. Its mass is 594g. What is the density? Answer in units of g/cm^3

2) An acceleration of 4.2 mi/h/s is equal to: Answer in units of m/s^2.

3) Grains of fine beach sand are assumed to be spheres of radius 57.7 micro meters. These grains are made of silicon dioxide which has a density of 2600 kg/m^3.

a) What is the mass of each grain of sand? in units of kg?

Then for the same problem consider a cube whose sides are 0.903 m long.

b) How many kg of sand would it take for the total surface area of all the grains of sand to equal the surface area of the cube? in units of kg.

4) Water flows into a swimming pool at the rate of 8.79 gal/min. If the pool dimensions are 20.7 ft wide, 44.4 ft long and 16.6 ft deep, how long does it take to fill the pool? ( 1 gallon = 231 cubic inches and answer in units of min.

5) A car travels along a straight stretch of road. It goes for 13.4 mi at 50 mi/h, then 29.5 mi at 43 mi/h, and finally 32.3 mi at 30.8 mi/h. What is the car's average velocity during the entire trip and answer in units of mi/h.

Solution Preview

1.) Density = mass/volume = 594/(3.8*6.1*3.8) = 6.74 g/cm^3 --Answer

2.) Because 1 mile = 1609.3 m, and 1 hr = 3600 s
Therefore, acceleration
4.2 mi/h/s = 4.2*1609.3/3600 = 1.8775 m/s^2 --Answer

3.) a.) Radius of sand grain r = ...

Solution Summary

This solution provides brief calculations for each problem in order to calculate the necessary answers.

... (c) Calculate the average ... b) Density = Mass/Volume = 322 x 1016/(14100x109) = 228 x 103 ...Acceleration due to rotation (centrifugal acceleration) is given by : a ...

... b) Calculate the Period of oscillation ... The force on the particle inside the earth is calculated and the ... The second problem is to derive density as a function of ...

... to gravity at the surface of the earth is given by g = W/m = 10.78/1.1 = 9.8 m/s2 Now as the acceleration due to ... (b) Calculate the average density of Earth ...

... Using this information, calculate the mass and average density of Mars. ... This posting offers help with calculating mass and average density of Mars. ...

...Density of water = 1000 kg/m3. ... b) calculate the average speed of the Earth with respect to the Sun; c) calculate the radial acceleration of the Earth. ...

...density of iron = 7210 kg/m^3. ... Or you can use the known free fall acceleration on Earth's ... Identical PDF and Word documents show how to calculate the force of ...

... answering the problems, assume that the density of water ... it is not possible to calculate the distance... vehicle ie the car will experience greater acceleration. ...

... of moment of inertia; to be able to calculate the moments ...acceleration C. angular speed D. angular acceleration E. total mass F. shape and density of the ...

... depends on many things, such as the density of an ...distance is 5.6 x 1010 meters) b. Calculate the force of ... depend on the mass, but that the acceleration due to ...