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Open-Response Homework Problem 16.5 An object with mass m= 1 kg is connected to

ID: 1323528 • Letter: O

Question

Open-Response Homework Problem 16.5 An object with mass m= 1 kg is connected to a horizontal spring with spring constant k = 500N/m and equilibrium position at xo 10cm (for r > xo, the force is directed toward the origin). The object is initially held at rest at position x = 15cm. You grab the object and move it slowly to position r = 30cm. For the questions below, assume the object begins at rest at 15cm, and finishes at rest at 30 cm. (a)[6 pt(s) How much work did you do on the object? (b)[3 pt(s) How much work does the spring do on the object. if the spring is not in the system? (c)[2 pt(s) What is the total work done on the block, if the person and spring are not in the system?

Explanation / Answer

Given that,

mass of the object = m =1kg

Spring constant = 500 N/m

x' = 30-15 = 15cm =0.15m (At equi. at x0 = 10, at rest at x = 15, you move it to x = 30)

(a) Work done in moving object from x = 15 to x = 30 will be

W = 1/2k(x')2 = 1/2x500x (0.15)2 = 5.625 J

(b) Work done by the spring, if the spring is not in the system, the object would be at equil. postion only

W = 1/2k(0.1)2 = 2.5 J

(c)Total workdone on the block if the person and spring were not in the system, then only the grav. potential enegy will be there. So,

Workdone = mg* x= 1x9.8x0.1 = 0.98 J