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Question: A spring of spring constant \(5 \times 10 ^ { 3 } \mathrm {~N} / \mathrm { m }\) is stretched initia...

A spring of spring constant 5×103 N/m5 \times 10 ^ { 3 } \mathrm {~N} / \mathrm { m } is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is

A

6.25 N-m

B

12.50 N-m

C

18.75 N-m

D

25.00 N-m

Answer

18.75 N-m

Explanation

Solution

Work done to stretch the spring from x1x _ { 1 } to x2x _ { 2 }

W=12k(x22−x12)W = \frac { 1 } { 2 } k \left( x _ { 2 } ^ { 2 } - x _ { 1 } ^ { 2 } \right)

=125×103[(10×10−2)2−(5×10−2)2]= \frac { 1 } { 2 } 5 \times 10 ^ { 3 } \left[ \left( 10 \times 10 ^ { - 2 } \right) ^ { 2 } - \left( 5 \times 10 ^ { - 2 } \right) ^ { 2 } \right] =12×5×103×75×10−4=18.75 N.m= \frac { 1 } { 2 } \times 5 \times 10 ^ { 3 } \times 75 \times 10 ^ { - 4 } = 18.75 \mathrm {~N} . \mathrm { m }