1. Physicists have found that when a weight is attachedto a spring to stretch it

Question

1. Physicists have found that when a weight is attachedto a spring to stretch it, the relation beween the length / of thespring and the weight w applied to strentch it is linear. Consider a spring of original length 75 mm. a. If a weight of 500 grams stretches the spring to 115 mm,write a linear equation relating the extended length of the springand the weight applied to stretch it, / =f(w). Hint: whenw=0, f=75 b. What is the length of the spring after a weight of 1kilogram has been applied? 1. Physicists have found that when a weight is attachedto a spring to stretch it, the relation beween the length / of thespring and the weight w applied to strentch it is linear. Consider a spring of original length 75 mm. a. If a weight of 500 grams stretches the spring to 115 mm,write a linear equation relating the extended length of the springand the weight applied to stretch it, / =f(w). Hint: whenw=0, f=75 b. What is the length of the spring after a weight of 1kilogram has been applied?

Explanation / Answer

A)  Linear equation y = mx + b When x = 0mm we know y = 75mm, so b = 75mm y = mx + 75mm when x = 500g we know y = 115mm so 115mm = m*500g + 75mm subtract 75mm from both sides: 40mm = m * 500g m = 40mm/500g = .08mm/g
f(w) = (.08mm/g)x+75mm B) plug 1kg in for x x = 1kg = 1000g f(w) = (.08mm/g)*1000g + 75mm f(w) = 80mm + 75mm = 155mm

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