## Saturday, 6 September 2014

### ELASTICITY MORE PROBLEMS

ELASTICITY

1. The Young modulus for steel is 2.00 x 1011 N m-2 calculate the work done in stretching a steel wire100 cm in length and of cross-sectional area 0.030 cm2 when a load of 100 N is slowly applied, the elastic limit not being exceeded.

2. A gymnast of mass 70kg hangs by one arm from a high bar. If the gymnast's whole weight is assumed to be taken by the humerus bone (in the upper arm) calculate the stress in the humerus if it has a radius of 1.5cm. (g = 9.8 Nkg-1)

3. (a) Find the maximum load that can be supported by a steel cable 1.5 cm in diameter in air.
(Breaking stress for steel = 500 MPa)
(b) would you expect this value to be greater or less if the load was immersed in water?

4. A hammer thrower swings a 7.25kg hammer in a horizontal circle at one revolution per second If the hammer wire is 1.20 m long. 1.5 mm in diameter and made of steel, calculate the extension produced in it. (The mass of the wire itself may be neglected)

5. A copper wire 200cm long and 1.22 mm in diameter is fixed horizontally between two supports 200 m apart. Find the mass in grams of the load which, when suspended at the midpoint of the wire, produces a sag of 2 cm at that point. The Young modulus for copper = 1.2 x 1011 N m-2.)

6. The gravitational field strength at the surface of a certain neutron star is 1.35 x 1012 N kg-1.
What would be the theoretical maximum height of a cylindrical granite column that could support its own weight without crushing when exposed to a field of this magnitude?
(Density of granite  2700 kg m-3, crushing strength  3.6 x 106 Pa.)

7. It has been calculated that during running the force on the hip joint is about five times the body weight. Estimate the compression of the femur during each running stride for a sprinter of mass 70 kg. (Young modulus for bone = 18x109 Pa).
You may assume that the femur is 0.40m long and has a mean diameter of 2.0 cm.

8. A steel tyre is heated and slipped on to a wheel of radius 40 cm, which it fits exactly at a temperature of  oC.
(a)    What is the maximum value of  if the tyre is not to be stretched beyond its elastic limit when it has cooled to air temperature (17 0C)? (Coefficient of linear expansion of steel = 0.000 012 oC-1)
(b)   What will then be the tension in the tyre, assu­ming it to be 4 cm wide and 3 mm thick?
The elastic limit for steel occurs at a tension of 2.75 x 108 Pa. The wheel may be assumed to be at air temperature throughout and to be incompressible.

9. A steel rod of mass 97.5 g and of length 50cm is heated to 200 0C and its ends securely clamped. Calculate the tension in the rod when its temperature is reduced to 00C, explaining how the calculation was made. Density of steel = 7560 kgm-3.

10.  The rubber cord of a catapult has a cross-sectional area of 1.0 mm2 and a total unstretched length of 10.0 cm. It is stretched to 15 cm and then released to project a missile of mass 5.0 g Calculate
(a) the energy stored in the rubber,
(b) the velocity of projection, and
(c) the maximum height that the missile could reach.
Take the Young modulus for rubber to be 5.0 x 108 Pa and state any assumptions made in your calculation.

11. A solid copper wire of cross-sectional area 8 mm2 and original length 110 m is set up as a telephone line with a uniform tension of 3.6 x 103 N. Assuming that the wire stretches elastically calculate
(a) the extension of the wire, and
(b) the elastic energy stored in the wire.
During cold weather the temperature falls by 15 K. Calculate
(c) the heat lost by the wire in this cooling and
(d) the change in elastic energy, assuming that the elastic properties of copper are unaffected by
the temperature change.
Young modulus for copper = 1.2x1011 Pa
Specific heat capacity for copper = 385 Jkg-1 oC-1
Density of copper = 8930 kgm-3
Linear expansivity of copper = 1.7x10-5 oC-1

12. A steel arrester wire mounted on the deck of an aircraft carrier is designed to stop a 20000 kg plane in a distance of 10 m. If the drum brakes jam and the plane is brought to rest by the forces set up in the wire and the landing speed of the plane is 50 ms-1 and the distance between the points of suspension of the wire is 20 m, calculate the minimum diameter of wire needed.
Young modulus for steel = 2x1011 Pa.

13.  A metal spring is compressed, clamped in a compressed position and then dissolved in acid. What has happened to the potential energy stored in the coils of the spring?

14. A fishing line will support a given load but will break when the same load is applied to it sharply. Why is this?