Three children are trying to balance on a seesaw, which consists of a fulcrum ro

Question

Three children are trying to balance on a seesaw, which consists of a fulcrum rock, acting as a pivot at the center, and a very light board 3.6 m long (See Figure). Two playmates are already on either end. Boy A has a mass of 50 kg, and girl B a mass of 35 kg. Where (x=?) should girl C, whose mass is 25 kg. place herself so as to balance the seesaw? The pulley in the figure has mass M = 10 kg and radius R = 0.5 m. It is a uniform solid disk with moment of inertia I = MR2/2. A massless cord is wrapped around it and a tension force Ft is applied. It starts from rest. After FT is applied for 10 s, the angular speed is to omega = 50 rad/s. What is the pulley's angular acceleration? What is the net torque acting on the pulley? If FT is the only force producing a torque, calculate FT. After FT is applied for 10 s, what are the pulley's kinetic energy ?

Explanation / Answer

I= .5 * 10 * .52 = 1.25

a. v = t

50 rad/s = * 10s

= 10 rad/s2

b. = I

= 1.25 * 10 rad/s2 = 12.5 N m

c.   Ft * r =

Ft = 12.5 Nm/.5m = 25 Nm

d. ke = 1/2 I 2

ke = .5 * 1.25 * (50 rad/s)2 = 1.56 kJ

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