Mechanics | Relativity Answers

A 900kg car is travelling at 30km/hour in the positive x-direction when the driver fails to notice that the vehicle in front of then has stopped - they drive into the back of the stopped car. Both cars are stationary after the collision. What was the change on momentum of the first car?

An ideal gas at 2 bar is contained in a cylinder behind a piston with the initial volume being 0.02 m3 . When it expands reversibly to a final volume of 0.025 m3 according to a law 𝑝𝑉 1.5 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, where 𝑝 is pressure and V is total volume, calculate the work done on the fluid by using 𝑊 = − ∫ 𝑝𝑑𝑉 .

0.25 kg of carbon dioxide (CO2) is compressed reversibly and isentropically from 2.0 bar 27 ˚C to 4.0 bar. Assume CO2 is a perfect gas and its relative molecular mass is 44. Calculate:

1) Specific gas constant of CO2 gas

2) work done

3) heat flow

A relatively small nozzle is horizontally placed and a working fluid is passing through steadily. At the nozzle’s inlet, the velocity of fluid is 5 m/s and the specific enthalpy is 2200 kJ/kg. At the exit from nozzle, its specific enthalpy is 2000 kJ/kg. Calculate: 

1)velocity at fluid exit

2) The mass flow rate of fluid when the inlet area is 0.01 m2 and specific volume at inlet is 0.5 m3 /kg

Consider the fully developed flow of glycerine at 40oC through a 157 m long, 5 cm diameter, horizontal, circular pipe . If the flow velocity at the centreline is measured to be 8 m/s, calculate the:

. The percent increase of the flow rate if the pipe is inclined 15 degree downward

The percent decrease if it is inclined 26 degree upward.

Properties: Density of glycerine = 1252 kg/m3 ; Dynamic viscosity of glycerine = 0.3073 kg/m s.

Assumptions: • The flow is steady, laminar and incompressible and fully developed • There are no pumps or turbines in the flow section

 substance has a mass M= 500 kg and a volume V=0.215 m3. Find 

 substance has a mass M= 100 kg and a volume V=0.415 m3. Find density

Examples of the key aspects of the assumptions of simple kinetic energy of gases

86 144 81 72 97 110 87 106 118 92

103 132 108 107 80 91 84 98 120 70

110 96 82 99 110 117 83 85 92 83

86 125 87 104 57 46 92 86 92 110

110 66 148 80 109 95 107 99 94 108

89 118 83 102 70 88 163 89 131 98

104 130 88 75 91 97 76 94 151 89

108 97 87 107 117 100 74 108 106 103

104 80 134 92 115 91 123 97 84 106

96 65 100 87 86 110 102 96 94 161

(a) Form a frequency table and plot a frequency distribution of this data.

(b) Calculate the mean value of the data.

(c) Find the equation for the normal distribution that would fit the data as closely as possible.

(d) Plot the normal distribution curve that is described by this equation

1.581 1.575 1.541 1.523 1.554 1.544 1.534

1.595 1.551 1.500 1.569 1.546 1.539 1.579

1.556 1.566 1.548 1.529 1.518 1.586 1.511

1.531 1.511 1.589 1.521 1.555 1.568 1.559

1.553 1.563 1.538 1.561 1.565 1.542 1.533

1.578 1.543 1.552 1.512 1.536 1.525 1.549

(a) Determine the frequency with which each value occurred and tabulate the data accordingly.

(b) Plot a histogram of the measurements.

(c) Calculate the mean value of the period and the standard deviation from the mean. (d) If the length of the pendulum is 60.0 cm, use the mean value of the period to calculate the gravitational acceleration g.

Calculate the standard deviation of these measurements and plot the frequency distribution.

Measurement no.(i) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. Diameter d (mm) 1.26 1.26 1.29 1.31 1.28 1.27 1.26 1.25 1.28 1.32 1.21 1.27 1.22 1.29 1.28

A substance has a mass M= 500 kg and a volume V=0.415 m3. Find