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Solved: CALC A certain spring found not to obey Hooke’s
Chapter 7, Problem 67P(choose chapter or problem)
Problem 67P
CALC A certain spring found not to obey Hooke’s law exerts a restoring force Fx(x) = -αx - βx2 if it is stretched or compressed, where α = 60.0 N/m and β = 18.0 Nm2. The mass of the spring is negligible. (a) Calculate the potential-energy function U(x) for this spring. Let U = 0 when x = 0. (b) An object with mass 0.900 kg on a frictionless, horizontal surface is attached to this spring, pulled a distance 1.00 m to the right (the +x-direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the x = 0 equilibrium position?
Questions & Answers
QUESTION:
Problem 67P
CALC A certain spring found not to obey Hooke’s law exerts a restoring force Fx(x) = -αx - βx2 if it is stretched or compressed, where α = 60.0 N/m and β = 18.0 Nm2. The mass of the spring is negligible. (a) Calculate the potential-energy function U(x) for this spring. Let U = 0 when x = 0. (b) An object with mass 0.900 kg on a frictionless, horizontal surface is attached to this spring, pulled a distance 1.00 m to the right (the +x-direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the x = 0 equilibrium position?
ANSWER:
Solution 67P
Problem (a)
Step 1:
Fx(x) = - -
-----(1)
= 60.0N/m
= 18.0N/m2
The spring does not obey Hooke’s Law
Mass of string is negligible