(33%) Problem 3: A child\'s toy consists of a m-25 g monkey suspended from a spr

Question

(33%) Problem 3: A child's toy consists of a m-25 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 IIcm, as shown in the diagram. This toy is so adorable you pull the monkey down an additional d-4.1 cm from equilibrium and release it from rest, and smile with delight as it bounces playfully up and down down to here Randomized Variables m-25 g x-1I cm d- 4.1 cm 14% Part (a) Using the given information, determine the spring constant, k, in Newtons per meter, of the spring. Potential sin) coso sin acoso acotan) sinho cosho tanh) ODegrees Radians Feedback:eduction per Sonhck 14% Part (c) Calculate the potential energy, Ebottom, in Joules, stored in the st retched spring immediately before you release it. 14% Part (d) Assume that the system has zero gravitational potential energy at the lowest point of the motion. Derive an expression for the total mechanical energy Eequilibriums of the system as the monkey passes through the equilibrium position in terms of m, x, d, g, k, and the speed of the monkey,- 14% Part (e) Calculate the speed of the monkey, we, in meters per second, as it passes through equilibrium. 14% Part (f) Derive an expression for the total mechanical energy of the system as the monkey reaches the top of the motion, Etop in terms of m, x, d, k, the maximum height above the bottom of the motion, hmax, and the variables available in the palette 14% Part (g) Calculate the maximum displacement, h, in centimeters, above the equilibrium position, that the monkey reaches.

Explanation / Answer

when the body is suspended by the spring it will be stretched by some amount x0

then upward restoring force =down ward weight at equilibrium

kx0=mg so k=mg/x0=25(980)/11=2227.27dynes/cm=2227.27(10)-3=2.227N/m

here the potential energy just after monkey hangs W1=1/2(kx2)=0.5(2.227)(.11)2=0.01345J

when you pull the monkey by 4.1cm then the potential energy W2=1/2(k)(x+d)2=0.5(2.227)(15.1)2(10)-4=253.88(10)-4=0.0254J

hence work done by pulling force =0.0254-0.0135=0.119J

if the

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