Physics homework question, gravitational energy and spring energy

A mass hanging from a vertical spring has gravitational potential energy and the spring has elastic potential energy. a) determine how far the spring (k=16N/m) stretches when a 100 g mass is hung from it and allowed to come to rest. b) If the mass is pulled down 3 cm further, determine the change in each type of energy.

For a)

gravitational energy=mgh

m=100
g=9.8
h=?

(100)(9.8)(?)

spring energy= 1/2kΔx^2

k=16N/m
Δx^2=?

1/2(16)(?)^2

would it be: mgh=1/2kΔx^2 If so it's: square root (2mgh/k)=Δx

what is h?

For b)

Is there a reverse energy due to tension on the spring? I have no idea how to do this one. Can you help?

Use Hooke's Law: F = -kx where x is distance so let x = h

F= -kh and so h = -(F)/k
where F = ma = (100x10^-3 kg)(9.81 m/s^2) = .981 N
h=(.981N)/-16N/m = -0.0613m or -6.13cm
(negative only means the direction here)

Im sure you can solve the rest just plug it in you're on the right track.

P.S.:
Always check units 100grams not 100 kg SI units is kg so convert.

For part b. I think you just get
E1= 1/2(kΔx^2) where Δx = xf-xi
I think you just assume xi = 0 and xf = x = h = -6.13cm
E2=1/2(kΔx^2) (f = final , i = initial)
Where Δx = xf-xi = hf - hi = (-6.13cm - 3cm)
Then:
ΔE = E2 - E1 = change in energy

Report Abuse