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A small block on a frictionless, horizontal surface has a mass of 2.50 A small b

ID: 2240559 • Letter: A

Question

A small block on a frictionless, horizontal surface has a mass of 2.50

A small block on a frictionless, horizontal surface has a mass of 2.50 Times 10?2kg . It is attached to a massless cord passing through a hole in the surface (the figure (Figure 1) ). The block is originally revolving at a distance of 0.300 m from the hole with an angular speed of 1.85rad/s . The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.150 m. Model the block as a particle.

Explanation / Answer

As the net external torque is zero, the angular momentum is conserved.


I*w = I* w


mr^2*w = mr^2*w


mr^2/w/(mr^2) = w2


(2.5*10^-2) (.3)^2*1.85/((2.5*10^-2) (.150)^2) = 7.4 rad/sec


v = wr, KE = (1/2)(m)(v)^2 = (1/2)(m)(w)^2(r)^2 = (1/2) (2.5*10^-2) (7.4)^2*.15^2 - (1/2) (2.5*10^-2) (1.85)^2*(.3)^2 = 0.0115 J increase in kinetic energy, the work is equal to this value because no change in gravititonal energy.