Please help with 41.3 I will rate According to Hooke\'s Law, the force (lb), F,

Question

Please help with 41.3 I will rate

According to Hooke's Law, the force (lb), F, required to hold a spring in place when its displacement from the natural length of the spring is x (ft), is given by the formula F = kx where k is called the spring constant. The value of k varies from spring to spring. Suppose that it requires 120 lb of force to hold a given spring 1.5 ft beyond its natural length. Find the spring constant for this spring. Include units when substituting the values for F and x into Hooke's Law so that you know the unit on k. What, including unit, is the constant value of dF/dx? Suppose that the spring is stretched at a constant rate of .032 ft/s. If we define t to be the amount of time (s) that passes since the stretching begins, what, including unit, is the constant value of dx/dt? Use the chain rule to find the constant value (including unit) of dF/dt. What is the contextual significance of this value?

Explanation / Answer

a) 120 / 1.5 = 80 lb/ ft b) k= 80 lb/ft C) .032 ft/s d)= k * dxdt = 80 * 0.032 = 24.16 lb/s

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