13. A playground merry-go-round consists of a áat disc with a radius of 1:5 m an

Question

13. A playground merry-go-round consists of a áat disc with a radius of 1:5 m and moment of inertia of 40 kg m2 . It is rotating freely at 15 rev= min when a 30 kg child jumps on its edge. What is the new angular velocity of the merry-go-round plus child? a. 2:0 rpm b. 12 rpm c. 5:6 rpm d. 19 rpm e. 8:8 rpm

14. A torque of 3:1 N m is applied to a wheel that is initially at rest. If the moment of inertia of the wheel is 0:85 kg m2 , what is its angular velocity after 11 s? a. 22 rad=s b. 34 rad=s c. 45 rad=s d. 51 rad=s e. 40 rad=s

15. A railroad car with a mass of 40; 000 kg is going east at 3:0 m=s when it collides with a second car whose mass is 25; 000 kg and is going east at 1:0 m=s on the same track. If the two cars couple together, how much kinetic energy was lost at the collision? a. 5:0 105 J b. 7:3 104 J c. 1:8 105 J d. 3:1 104 J 2 e. 940 J

16. A thin, circular hoop is released at the top of an incline that is 8:0 m long and makes an angle of 370 above the horizontal. What is its speed at the bottom of the incline? Assume it rolls without slipping. a. 5:5 m=s b. 9:3 m=s c. 6:9 m=s d. 4:1 m=s e. 11:6 m=s

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Explanation / Answer

as force applied by the child will not generate any torque so angular momentum of the system will remain conserved-

I1*w1 = I2*w2 [w = 2pi f so 2pi will cancel out from each side]

40*15 = [40 + 30*1.52]*w2

w2 =5.58 rpm

2> torue = I*alpha

alpha = T/I

A = 3.1/0.85

A = 3.64 rad/sec2

w = w0 + At

w = 0 + 3.64*11

w = 40.11 rad/sec

15> linear momentum will remain conserved in the collision -

40,000*3 + 25,000*1 = 65,000*v

v = 2.23 m/sec

final kinetic energy = 0.5[40000+25000]*2.23*2.23

= 161619.25 joule

initial kinetic energy = 0.5 [40000*9 + 25000*1]

= 192500 joule

loss in kinetic energy = 30880.75 joule

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