A small block on a frictionless horizontal surface has a mass of 3.00?10?2 kg. I
ID: 2114187 • Letter: A
Question
A small block on a frictionless horizontal surface has a mass of 3.00?10?2 kg. It is attached to a massless cord passing through a hole in the surface. (See the figure above .) The block is originally revolving at a distance of 0.310 m from the hole with an angular speed of 1.70 rad/s. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.185 m. You may treat the block as a particle. A) What is the new angular speed? B) Find the change in kinetic energy of the block. C) How much work was done in pulling the cord?
A small block on a frictionless horizontal surface has a mass of 3.00?10?2 kg. It is attached to a massless cord passing through a hole in the surface. (See the figure above .) The block is originally revolving at a distance of 0.310 m from the hole with an angular speed of 1.70 rad/s. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.185 m. You may treat the block as a particle. A) What is the new angular speed? B) Find the change in kinetic energy of the block. C) How much work was done in pulling the cord?Explanation / Answer
a) angular momentum = mr^2* = constant
0.03*0.31^2*1.7 = 0.03*0.185^2*
= 4.77 rad/s
b) initial KE = 1/2*(mr^2)*^2 = 1/2*(0.03*0.31^2)*1.7^2 = 0.004166 J
Final KE = 1/2*(mr^2)*^2 = 1/2*(0.03*0.185^2)*4.77^2 = 0.0117 J
Change in KE = 0.0117 - 0.004166 = 0.007534 J
c) Work done = change in KE = 0.007534 J
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