(a) Find the speed of the mass at points B and C . v B = 1m/s v C = 2m/s (b) Fin

Question

(a) Find the speed of the mass at pointsB and C.
vB = 1m/s
vC = 2m/s

(b) Find b.
b = 3 N/m A 0.33 kg point mass moving on africtionless horizontal surface is attached to a rubber band whoseother end is fixed at point P. The rubber band exerts aforce F = bx toward P, where xis the length of the rubber band and b is an unknownconstant. The mass moves along the dotted line. When it passespoint A, its velocity is 4.2 m/sdirected as shown. The distance AP is 0.6 m andBP is 1.0 m (a) Find the speed of the mass at pointsB and C. vB = 1m/s vC = 2m/s (b) Find b. b = 3 N/m Comment

Explanation / Answer

the rubber is like a spring with constant k=b conservation of energy, speed at B is v1 m*v2/2+ +b*0.62/2=m*v12/2+b*12/2   (1) the force from the rubber is through the center of pivot => conservation of momentum v*0.6=v1*1 =>v1=2.52m/s=vB C and A are symmetric => vc=v=4.2 m/s (b) from (1) => b=5.82 N/m (b) from (1) => b=5.82 N/m

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