The problem looks like this but its not 2M. I have a cart of mass(M) = 536.5 gra

Question

The problem looks like this but its not 2M.

I have a cart of mass(M) = 536.5 grams

On the cart track (frictionless) the spring is at rest or equilibrium at 159 cm.

The hanging mass (m (represented 2M in the picture) ) is 200 grams.

The hanging mass causes the spring to stretch to 161 cm on the track.

Thus the displacement is 2 cm.

I am supposed to find the spring constant (k), and I believe the formula is k = (2mgx)/Mg

where g is gravity (9.8 m/s) , x is displacement (.02 m), m is hanging mass (.2 kg), and M is the cart (.5365 kg).

Any help is appreciated, Thank You.

Explanation / Answer

g = 9.8 m/s, x = .02 m, m = .2 kg, M = .5365 kg find k if when x = 0.02 m, m is at rest with v = 0, a = 0, then kx = mg so k = mg/x = 98 N/m if when x = 0.02 m, m is only temporarily at rest with v = 0, a not = 0, then kx^2/2 = mgx so k = 2mg/x = 196 N/m

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