Physics

Problem

A spring balance consists of a spring of length

20.0\text{ cm}

with a hook attached. When a fish of mass

3.0\text{ kg}

is suspended from the hook, the new length of the spring is

27.0\text{ cm}

. What is the spring constant of the spring? A)

4.2\text{ N m}^{-1}

43\text{ N m}^{-1}

110\text{ N m}^{-1}

420\text{ N m}^{-1}

Intuitive explanation

The key here is Hooke's Law: the force exerted by a spring is proportional to how much it stretches. When the fish hangs from the hook, its weight creates a downward force that the spring must balance. Find the extension (change in length), then use $F = kx$ where the force is the fish's weight ( $mg$ ) to solve for the spring constant $k$ .

Intuitive explanation

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