Question

A spring has natural length 20cm. a 40 n force is required to strecth to length of 30 cm. how much work done is required to stretch spring from 35cm to 38cm

Answer 1

Answer:

A spring has natural length 20cm. a 40 n force is required to strecth ... from its natural length. is called the spring constant. We want to know the work required to stretch the spring from 35cm to 38cm. Doing that gives us distances of 35-20 = 15cm = 0.15 m and 38-20 = 18 cm = 0.18m.

Answer 2

Answer:

Work done in stretching spring from 35 cm to 38 cm is 0.18 J.

Explanation:

• The amount of work done in moving a spring of spring constant, k by a distance x on applying a force F is
• W = ½kx².

Given that :

• Natural length of spring = 20 cm
• Force applied = 40 N
• Stretch in spring = 30 cm

To find :

• Work done to stretch spring from 35 cm to 38 cm

Solution :

• Let, the spring constant of given spring be k. A force, F of 40 N is applied to stretch the spring to length 30 cm.
• Since, F = kx

$F = kx \\ 40 = k(0.3 - 0.2) \\ k = \frac{40}{0.1} = 400 \: N/m$

• The spring constant of the given spring is 400 N/m.
• Now, work done in stretching spring from 35 cm to 38 cm is

$W = \frac{1}{2} k {x}^{2} \\ = \frac{1}{2} \times 400 \times {(0.38 - 0.35)}^{2} \\ = 200 \times {(0.03)}^{2} \\ = 0.18 \: J$

• Hence, work done in stretching spring from 35 cm to 38 cm is 0.18 J.