Spring Weight
July 24th, 2009
Spring Weight
Check out this page if you are searching for Spring Weight
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A spring with a natural length of 15cm stretches to a length of 20cm when a 22kg weight is suspended from it.?
a)Use Hooke's Law to find and equation relating the amount of extension L with the suspended weight W.
b)Find the weight when the spring extension is 10cm.
c)Find the domain of the weight if the spring cannot be stretched to more than twice its natural length.
a) Hooke's Law:
W = -kL
(W = force in newtons, -k = restoring force exerted by the material in newtons/meter, L = distance spring is compressed in meters).
W = 22 kg.
1 kg. = 9.807 n.
W = 215.6n
L = 20 cm.
1 cm. = 0.01 m.
L = (20) (0.01)
L = 0.2 m.
k = - (W / L)
k = - (215.6 / 0.02)
k = - 1075 n./m.
b) L = 10 cm. = 0.1 m
k = - 1075 n./m.
W = -kL
W = - (-1075)(0.1)
W = 107.5 n
W = 10.96 kg.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
c) Since Hooke's Law is a linear expression, and has three variables, it is not a function. A linear equality has no limits, therefore, the domain would be (- ∞, ∞).
I think...