Question

A spring, having a spring constant of 400 kN/m, is initially compressed by 0.4 cm. The magnitude of work required to compress it
by another 0.44 cm is ________ J.

Answer 1

Explanation:

F = K∆x

F = 400 × (0.4÷100)

F = 1.6N

Workdone = Energy

Energy = ½F∆x

Energy = ½ × 1.6 × (0.44÷100)

Energy = 0.00352J

Answer 2

The work required to compress the spring is 0.00352 joule

Explanation:

Given Data

Spring constant (K) = 400 kN/m

Initial compression = 0.4 cm = 0.004 m

Final compression of the spring = 0.44 cm = 0.0044 m

To find the work required to compress the spring (0.44 cm) in joules

The formula for to find the force required by the spring is equal to Product of spring constant (K) and the distance traveled (x) by the spring.

Force (F) = K × x      (Newton)

Force = 400 × 0.004

Force = 1.6 kN

Workdone is defined as the product of force and displacement. Th eunit foe workdone is joules.

Work required to compress it by another 0.0044 m is,

Workdone = Force × Displacement

$workdone = \frac{1}{2} \times K \times x^{2}$

$Workdone = \frac{1}{2} \times 1.6 \times 0.004$

Workdone = 0.00352 kN-m

Where one kilo Newton meter is equal to one joule.

Workdone = 0.00352 joule

Therefore the work required to compress the spring one more time up to 0.44 cm is 0.00352 joule

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