A child\'s toy consists of a m = 39 g monkey suspended from a spring of negligib

Question

A child's toy consists of a m = 39 g monkey suspended from a spring of negligible mass and spring constant k. When the toy monkey is first hung on the spring and the system reaches equilibrium, the spring has stretched a distance of x = 13.8 cm, as shown in the diagram. This toy is so adorable you pull the Position monkey down an additional d = 6.5 cm from equilibrium and release it from rest, and smile with delight as it bounces playfully up and down. Using the given information, determine the spring constant, k, in Newtons per meter, of the spring. k = _____________ Select the free-body diagram that best represents the forces acting on the monkey as you are pulling it down, immediately

Explanation / Answer

Part (a)

mass of the toy is m = 39g = 0.039kg

when it is hung from the spring the spring is stretched by x = 13.8cm = 0.138m, in the equilibrium position.

Let the spring constant be k. The spring exerts a force kx upwards on the toy

in the equilibrium position, the acceleration of the toy is zero,so equation of motion of the toy says;

mg = kx

or k = mg/x = (0.039kg)(9.8m/s2)/(0.138m) = 2.769N/m

So the spring constant is k = 2.769N/m

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P.S. - Question in Part (b) is not completely visible in the picture. So I have not solved it. If you make the whole question available I will solve it.....

This concludes the answers. Check the answer and let me know if it's correct. If you need anymore clarification or correction I will be happy to oblige....

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