Answer:
<em>a) The spring constant is 50 lb/ft</em>
<em>b) The man is 26.3 ft close to the ground.</em>
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Explanation:
Height of tower is 130 ft
Specification calls for a cable of length 85 ft
the maximum this length stretches is 100 ft when subjected to a load of 750 lb
The extension of the cable is calculated from the formula from Hooke's law
F = kx
where F is the load or force on the cable
k is the spring constant of the cable
x is the extension on the cable
a) The extension on the cable is
x = 100 ft - 85 ft = 15 ft
substituting into the formula above, we'll have
750 = k*15
k = 750/15 = <em>50 lb/ft</em>
b) for a 185 lb man, jumping down will give an extension gotten as
F = kx
185 = 50*x
x = 185/50 = 3.7 ft
The total length of the cable will be extended to 100 ft + 3.7 ft = 103.7 ft
closeness to the ground = 130 ft - 103.7 ft =<em> 26.3 ft</em>
