A mass (m = 3 kg) is connected to a spring of constant k (k = 50 N/m), where the

Question

A mass (m = 3 kg) is connected to a spring of constant k (k = 50 N/m), where the mass is connected at the top to a spring on a fixed incline. The coefficient of static friction between the mass and the incline is µ(subscript s) = 0.6 and the angle that the incline makes with the horizontal is ? = 20º. The mass is initially held in place so that the spring is at its natural length.

By what maximum amount can the mass be pulled up the incline and released and still have the mass in static equilibrium? Write your final answer as x(subscript s) = ___ centimeters.

Currently I have the equation set up for the force of gravity + force of the spring = force of friction. Is this correct and if not then why. Please work through problem I am very visual. Thank you.

Explanation / Answer

you want to use energy an equation setting 1/2kx^2 = frictional energy which is force of friction x distance

force of friction is N , where N is the normal force which is sin(20 degrees), and is .6

so the equation is 1/2 x 50 x x2 = .6 x sin(20) x x and then solve for x

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