Advertisements
Advertisements
Question
Identical springs of steel and copper are equally stretched. On which, more work will have to be done?
Advertisements
Solution
Work Done in stretching a Wire or Spring: In stretching a wire work is done against internal restoring forces. This work is stored in the wire as elastic potential energy or strain energy.
If a force F acts along the length L of the wire of cross-section A and stretches it by x, then work done in stretching a wire is given by W = 1/2F × Δl
As springs of steel and copper are equally stretched. Therefore, for the same force (F),
`W ∝ Δl` ......(i)
Young's modulus `(Y) = F/A xx l/(Δl)`
or `Δl = F/A xx l/Y`
As both springs are identical,
∴ `Δl ∝ 1/Y` ......(ii)
From equations (i) and (ii), we get `W ∝ 1/Y`
∴ `W_(steel)/W_(copper) = Y_(copper)/(Y_(steel)) > 1` ......(As `Y_(steel) > Y_(copper)`)
or `W_(steel) > W_(copper)`
Therefore, more work will be done for stretching copper spring.
APPEARS IN
RELATED QUESTIONS
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?
Two wires of diameter 0.25 cm, one made of steel and the other made of brass are loaded as shown in Fig. 9.13. The unloaded length of steel wire is 1.5 m and that of brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 cm and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.
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
A copper wire of cross-sectional area 0.01 cm2 is under a tension of 20N. Find the decrease in the cross-sectional area. Young modulus of copper = 1.1 × 1011 N m−2 and Poisson ratio = 0.32.
`["Hint" : (Delta"A")/"A"=2(Delta"r")/"r"]`
Young's modulus of a perfectly rigid body is ______.
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
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?
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 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.)
If Y, K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.
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 ______.
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 ______.
The force required to stretch a wire of cross section 1 cm2 to double its length will be ______.
(Given Young's modulus of the wire = 2 × 1011 N/m2)
Young's modulus is also known as ______.
What does the dimensional formula [L⁻¹M¹T⁻²] represent?
What is longitudinal strain?
