Advertisements
Advertisements
Question
A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has the cable stretched? (Young’s modulus for steel is 2 × 1011 Nm–2.)
Advertisements
Solution
According to the problem,
Length of steel cable l = 9.1 m
Radius r = 5 mm = 5 × 10–3 m
Tension in the cable F = 800 N
Young’s modulus for steel Y = 2 × 1011 N/m2
Change in length ∆L = ?
Young’s modulus If given by `Y = (F/A)/((∆L)/L)`
⇒ `∆L = (FL)/(Y(pir^2)`
`∆L = (800 xx 9.1)/((2 xx 10^11)(3.14 xx 25 xx 10^-6)) = 4.64 xx 10^-4 m`
⇒ ∆L = 5 × 10–4 m = 0.5 × 10–3 m
APPEARS IN
RELATED QUESTIONS
A steel wire of length 4.7 m and cross-sectional area 3.0 × 10–5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10–5 m2 under a given load. What is the ratio of Young’s modulus of steel to that of copper?
The figure shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?
Read the following statements below carefully and state, with reasons, if it is true or false
The Young’s modulus of rubber is greater than that of steel;
Two wires A and B are made of same material. The wire A has a length l and diameter rwhile the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is
The length of a metal wire is l1 when the tension in it T1 and is l2 when the tension is T2. The natural length of the wire is
A steel rod of cross-sectional area 4 cm2 and 2 m shrinks by 0.1 cm as the temperature decreases in night. If the rod is clamped at both ends during the day hours, find the tension developed in it during night hours. Young modulus of steel = 1.9 × 1011 N m−2.
A rigid bar of mass M is supported symmetrically by three wires each of length l. Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to ______.
The Young’s modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?
Identical springs of steel and copper are equally stretched. On which, more work will have to be done?
A steel rod (Y = 2.0 × 1011 Nm–2; and α = 10–50 C–1) of length 1 m and area of cross-section 1 cm2 is heated from 0°C to 200°C, without being allowed to extend or bend. What is the tension produced in the rod?
A steel wire of mass µ per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains << longitudinal strains, find the extension in the length of the wire. The density of steel is 7860 kg m–3 (Young’s modules Y = 2 × 1011 Nm–2).
In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by `(Ypir^4)/(4R) . Y` is the Young’s modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.
A boy's catapult is made of rubber cord which is 42 cm long, with a 6 mm diameter of cross-section and negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms-1. Neglect the change in the area of the cross-section of the cord while stretched. Young's modulus of rubber is closest to ______.
A uniform metal rod of 2 mm2 cross section is heated from 0°C to 20°C. The coefficient of linear expansion of the rod is 12 × 10-6/°C, it's Young's modulus is 1011 N/m2. The energy stored per unit volume of the rod is ______.
If the length of a wire is made double and the radius is halved of its respective values. Then, Young's modules of the material of the wire will ______.
What is longitudinal strain?
