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lemon
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1. A mass of 100g is suspended from a light spring and extends the spring by 4cm when the mass in in equilibrium.
a) Find the spring constant k of the spring?
b) How much elastic energy is now stored in the spring?
c) What would be the extension of the spring if a mass of 170g were suspended?
d) How much extra energy would now be stored in the spring?
e) Why is more work needed to stretch a spring by 1cm from its unextended length, than is required to stretch it by an extra 1cm when the spring is already extended?
2. Let deltaX = e
F=ke
Ep=1/2Fe
Stress=F/A
Strain=e/L
E=stress/strain
F=ma
100g = 0.1kg
4cm = 0.04m
Let gravity = -10m/s
3. a) F=0.1 x 10 = 1N
k=10N/0.04m = 250N/m
b) E=1/2 x 10N x 0.04m = 0.2J
c) F=0.170 x 10 = 1.7N
e = 1.7N/250N/m = 0.006.8m
d) E = 1/2 x 10N x 0.170m = 0.85J
e) I know this holds true from my experience in reality, but when I consider the force extension graph and hook's law, it tells me that up until the elastic limit the same force is required to achieve the same extension. But considering E=1/2 x stretching force x extension, from this equation it is clear that an increase in extension will increase elastic potential energy.
Could someone kindly check and guide, please?
Thank you
a) Find the spring constant k of the spring?
b) How much elastic energy is now stored in the spring?
c) What would be the extension of the spring if a mass of 170g were suspended?
d) How much extra energy would now be stored in the spring?
e) Why is more work needed to stretch a spring by 1cm from its unextended length, than is required to stretch it by an extra 1cm when the spring is already extended?
2. Let deltaX = e
F=ke
Ep=1/2Fe
Stress=F/A
Strain=e/L
E=stress/strain
F=ma
100g = 0.1kg
4cm = 0.04m
Let gravity = -10m/s
3. a) F=0.1 x 10 = 1N
k=10N/0.04m = 250N/m
b) E=1/2 x 10N x 0.04m = 0.2J
c) F=0.170 x 10 = 1.7N
e = 1.7N/250N/m = 0.006.8m
d) E = 1/2 x 10N x 0.170m = 0.85J
e) I know this holds true from my experience in reality, but when I consider the force extension graph and hook's law, it tells me that up until the elastic limit the same force is required to achieve the same extension. But considering E=1/2 x stretching force x extension, from this equation it is clear that an increase in extension will increase elastic potential energy.
Could someone kindly check and guide, please?
Thank you
