A small block on a frictionless horizontal surface has a mass of 2.30 A small bl

Question

A small block on a frictionless horizontal surface has a mass of 2.30

A small block on a frictionless horizontal surface has a mass of 2.30 times 10?2kg . It is attached to a massless cord passing through a hole in the surface. (See the figure below (Figure 1) .) The block is originally revolving at a distance of 0.350m from the hole with an angular speed of 2.00rad/s . The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.105m . You may treat the block as a particle. What is the new angular speed? Find the change in kinetic energy of the block. How much work was done in pulling the cord?

Explanation / Answer

angular momentum will be conserved

initial angular momentum= mvR=mR^2w=2.3E-2*0.35^2*2

final angular momentum= mvR=mRw^2=2.3E-2*0.105^2*w

B) ==> 2.3E-2*0.35^2*2= 2.3E-2*0.105^2*w

==> w=0.35^2*2/0.105^2=22.22 rad/s

C) K.E=0.5*mv^2=0.5*2.3E-2(0.105*22.22)^2=0.06259 J

D) initial K.E= 0.5*mv^2=0.5*2.3E-2(0.35*2)^2=5.635 E-3 J

==> work done= 0.06259 J- 1.689 E-3 J= 0.0609 J

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