Name: Strain Energy
Uploaded: 2019-07-19
Duration: 9 min 32 s
Description: Have you played with wind-up toys before? How do you think they can move just by winding up and releasing the key? Watch this video to find out the answer.

Question

Three blocks $A, B$ and $C$ each of mass $4 kg$ are attached as shown in the figure. Both the wires have equal cross-sectional area $5 \times 10^{- 7} m^{2}$ . The surface is smooth. Find the longitudinal strain in each wire if the Young modulus of both the wires is $2 \times 10^{11} N m^{- 2}$ . (take $g = 10 m s^{- 2}$ )

Accepted Answer

The block $C$ will descend vertically and the blocks $A$ and $C$ will move on the frictionless horizontal table. Let the common magnitude of the acceleration be $4 kg$ . Let the tensions in the wires $1$ and $5 \times 10^{- 7} m^{2}$ be $T_{1}$ and $T_{2}$ respectively.

For block $C$ , $m g - T_{2} = m a . . . (1)$ . For block $B$ , $T_{2} - T_{1} = m a . . . (2)$ .

For block $A$ , $T_{1} = m a . . . (3)$ . From $(2)$ and $(3)$ , we have $T_{2} = 2 m a . . . (4)$ . And from $(1)$ and $(4)$ , we have $m g = 3 m a$ $A, B$ . So, $T_{1} = 4 \times \frac{10}{3} = \frac{40}{3} N$ and $T_{2} = 2 \times 4 \times \frac{10}{3} = \frac{80}{3} N$ .

Now, Young's modulus, $Y = \frac{Stress}{Strain} \Rightarrow Strain = \frac{Stress}{Y}$ . Stress in wire $1$ $= \frac{40}{3 \times 5 \times 10^{- 7}}$ and in wire $2$ $= \frac{80}{3 \times 5 \times 10^{- 7}}$ . So, strain in wire $1 = \frac{40}{3 \times 5 \times 10^{- 7} \times 2 \times 10^{11}} = 1.33 \times 10^{- 4}$ . And strain in wire, $2 = \frac{80}{3 \times 5 \times 10^{- 7} \times 2 \times 10^{11}} = 2.66 \times 10^{- 4}$ .

Important Questions on Elasticity

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Three blocks A, B and C each of mass 4 kg are attached as shown in the figure. Both the wires have equal cross-sectional area 5 × 10–7 m2. The surface is smooth. Find the longitudinal strain in each wire if the Young modulus of both the wires is 2 × 1011 N m-2. (take g=10 m s-2 )

Important Questions on Elasticity

Learn and Prepare for any exam you want !