Question

A fisherman's scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant (b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5cm more and released so that it vibrates up and down.

I know the formula for spring stiffness is F= +kx. But Idk what k or x means and if this formula would help for part A. I'm just over all confused on how to answer both of the questions. Please help.

Answer 1

a) use relation \( F = -kx = mg \) to find the stiffness constant. Make sure all units are in SI.

b) since the displacement is 2.5 cm more than equilibrium, the amplitude of vibration will be 2.5 cm. The frequency of vibration is given by \( \frac{2 \pi}{T} \), where \( T = 2 \pi \sqrt{\frac{m}{k}}\)

Answer 2

k is called the spring force constant which tells you how stiff the spring is, with units of Newtons per meter, which literally means how much force it exerts per meter of extension. x represents the displacement of the spring, since the more it's pulled away, the greater the force exerted is. The negative sign in the equation shows that the spring is always going to force itself in the direction opposite of which it's pulled. So if you pull it to the left it goes right to return, or if you push a spring together it will spring back outwards again.

this is all how F=-kx and since this is a force, we can set it equal to F=ma, and help ourselves find what we don't know.

Answer 3

Thank you both so much! The answers really helped. Just for assurance. For part A) I multiply 2.7 kg times 9.8 m/s^2 to get Newtons which equals 26.46N and then I would convert 3.6cm to Meters and divide 26.46N over .036M? I did this and got 735 N/m :O

Answer 4

Also for part B would the formula for T= 2pi x square root of (k/m)?? Not "(m/k)"? Or am I wrong? :O

Answer 5

http://en.wikipedia.org/wiki/Simple_harmonic_motion#Mass_on_a_spring