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Vegeance
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Homework Statement
3. A 0.5 kg mass is connected to the lower end of an ideal vertical coil spring suspended from a retort stand. The mass is held at rest with the spring completed unstretched and then allowed to fall. If the spring constant is 20 N/m, determine the maximum distance the mass drops before coming momentarily to rest and starting up again. Ignore frictional losses. (50 cm)
Egravity potential=Espring
[0.5][kx2]=mgx
[0.5][kx]=mg
[2mg/k]=[x]
[x] = 0.50m
4. In the problem above, the mass is now held initially at rest at a position where the spring is stretched 20 cm. Determine the maximum distance the mass will fall. (0.1 m)
Espring = Espring after - Egravity potential work done
[0.5][k(0.2)2] + [0.5kg][~10N/kg][x']=[0.5k][x+0.2m][2]
[0.4J]+[5x']=[10][x'2+0.4x'+0.04]
[0.4J]+[5x']=[10x'2-x'+0.4]
0=[10x2-x']
x = (1/10; 0)
5. In problem 3, determine how fast the mass was traveling on the way down when the spring was stretched 30 cm.
(1.5 m/s)
I am getting stuck at this question as how to conceptualize it, although I tried substituting to no avail.
Initial State : Potential Energy of Spring + Gravity Potential Energy Work Done
Final State : Potential Energy of Spring[x+0.3m] + Kinetic Energy
Homework Equations
Eg = mgh
Ek = 1/2mv^2
Es = 1/2kx^2