Question

Three blocks, each of same mass m, are connected with wires W1 and W2 of same cross-sectional area a and young's modulus Y. Neglecting friction find the strain developed in wire W2 .

Answer 1

Answer:

Find the square root of the following decimals using long division method...... ★ 50.41★610.09★0.0441★0.0036★0.1089

Answer 2

ANSWER:

The strain exhibited by the wire W2 is 2m/3aY.

EXPLANATION:

   As three blocks are connected by two wires and also as all the three blocks have same mass, so we can assume that any two blocks are connected to a single wire W1 in same side and another block is connected to wire W2 on another side. So the strain developed in wire W2 can be determined by the ratio of stress exerting on the wire W2 to the Young's modulus of the wire.  

  As we have assumed that two blocks are on side of the wire W1 connected via pulley to the wire W2 which is holding the other block, the stress exerting on the wire W2 will be the tension produced in the wire W2 due to the combined weights of all the three blocks per unit area.

According to standard pulley formula, the tension acting on a wire W2 will be  

As on one side, two blocks of mass m are attached in wire W1 sequentially or in series, the combined mass of the blocks in the wire W1 will be used as 2m. Similarly, the other side contains a single block of mass m, so the mass attached to wire W2 will be m. Thus,

$\text { Tension }=\frac{2 m * m}{2 m+m}=\frac{2 m^{2}}{3 m}=\frac{2 m}{3}$

Since ,stress can be calculated as tension acting per unit cross sectional area, the stress on wire W2 will be

$\text {Stress}=\frac{\text {Tension}}{\text {Cross sectional area}}=\frac{2 \mathrm{m}}{3 * a}$

Here, “a” is the cross sectional area of the wire W2.

So according to Hooke's law, stress acting on an object is directly proportional to the strain exerted by the object. The proportionality constant is the Young's modulus. So the strain of any body or the strain of wire W2 can be found as follows:  

$\text {Strain}=\frac{\text {Stress}}{\text {Young's modulus}}$

Let us consider Y being the Young's modulus of wire W2 and stress have been found earlier, substitute them in the formula for strain.

So the strain for the wire W2 will be

$\text {Strain}=\frac{\text {Stress}}{\text {Young's modulus}}=\frac{2 \mathrm{m}}{3 \mathrm{aY}}$

Thus the strain exhibited by the wire W2 is 2m/3aY.