Answers to questions on Young's modulus

Questions on Young's modulus

Calculations on stress, strain and the Young modulus




Practice questions

These are provided so that you become more confident with the quantities involved, and with the large and small numbers.



Try these

A strip of rubber originally 75 mm long is stretched until it is 100 mm long.

1. What is the tensile strain?

2. Why has the answer no units?

3. The greatest tensile stress which steel of a particular sort can withstand without breaking is about 109 N m-2. A wire of cross-sectional area 0.01 mm2 is made of this steel. What is the greatest force that it can withstand?

4. Find the minimum diameter of an alloy cable, tensile strength 75 MPa, needed to support a load of 15 kN.

5. Calculate the tensile stress in a suspension bridge supporting cable, of diameter of 50 mm, which pulls up on the roadway with a force of 4 kN.

6. Calculate the tensile stress in a nylon fishing line of diameter 0.36 mm which a fish is pulling with a force of 20 N

7. A large crane has a steel lifting cable of diameter 36 mm. The steel used has a Young modulus of 200 GPa. When the crane is used to lift 20 kN, the unstretched cable length is 25.0 m. Calculate the extension of the cable.


Stress, strain and the Young modulus




1. A long strip of rubber whose cross section measures 12 mm by 0.25 mm is pulled with a force of 3.0 N. What is the tensile stress in the rubber?



2. Another strip of rubber originally 90 mm long is stretched until it is 120 mm long. What is the tensile strain?



3. The marble column in a temple has dimensions 140 mm by 180 mm.

I. What is its cross-sectional area in mm2?

II.

III. Now change each of the initial dimensions to metres – what is the cross-sectional area in m2?

IV. If the temple column supports a load of 10 kN, what is the compressive stress, in N m–2?



V. The column is 5.0 m tall, and is compressed by 0.1 mm. What is the compressive strain when this happens?



VI.

VII. Use your answers to parts 5 and 6 to calculate the Young modulus for marble.





4. A 3.0 m length of copper wire of diameter 0.4 mm is suspended from the ceiling. When a 0.5 kg mass is suspended from the bottom of the wire it extends by 0.9 mm.

I. Calculate the strain of the wire.







II. Calculate the stress in the wire.







III. Calculate the value of the Young modulus for copper.

Y12 Homework on Sankey Diagrams

Answers to calculations only.

Constructing Sankey Diagrams

1. An energy efficient light bulb is rated at 20W. It produces 5W of light. Calculate its efficiency and draw a Sankey Diagram to scale.

Efficiency = Useful power out/ power in x 100%

Eff= (5/20) x 100 = 25%

2. Paula transfers 40 000J of chemical energy during a race. She transfers 32 000J of heat energy to the surroundings during the race. Calculate her efficiency and draw a Sankey diagram to scale.

Efficiency = useful energy out/ energy in x 100%

Eff = 40 000 -32 000) /40000 = 8000/40000 = 0.2 =20%

3. Bradley does 1600J of work turning the pedals on his bike. 1577.6J is transferred to the rear sprockets. How much heat is lost and what is the efficiency of Bradley’s bike. Draw a Sankey diagram of Bradley’s chain

Efficiency = useful energy out/ energy in x 100%

Eff = 1577.6 / 1600 = 0.986 = 98.6%

4. The coal in Thomas’ boiler contains 40 kJ of energy. He loses 25.76kJ as heat as he puffs along a branch line. How efficient is Thomas and draw a Sankey diagram.

Efficiency = useful energy out/ energy in x 100%

Eff = (40 - 25.76)/40 = 0.356 = 35.6%

5. The fuel in Diesel’s tank contains 60kJ of chemical energy. He does 20.1kJ of work on the mainline. Calculate Diesel’s efficiency and draw a Sankey diagram.

Efficiency = useful energy out/ energy in x 100%

Eff = 20.1/60 = 0335 = 33.5%

6. The electric engine in Jeremy’s car can develop 3kW. If the car develops 2.658kW what is its efficiency.

 Efficiency = Useful power out/ power in x 100%

Eff = 2.658/3 = 0.886 = 88.6%

7. Jeremy dreams of a Ferrari Enzo which can develop a maximum of 700 bhp. (1 bhp = 750 Watts). Sadly for Jeremy cars are not very efficient. Typically, only about 30% of the energy that is available from the combustion of the petrol actually ends up overcoming friction to move the car forwards. Of the 70% of energy is that is not usefully converted, 55% may heat the cooling water that surrounds the engine block whilst  15% may be in the hot exhaust gases. To make car engines more efficient  the fuel has to burn at a higher temperature and the exhaust must be kept cooler. Draw a Sankey diagram of Jeremy’s dinosaur