Suppose a 0.250 kg ball is thrown at 17.0 m/s to a motionless person standing on

Question

Suppose a 0.250 kg ball is thrown at 17.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in Figure 9.31.

(a) Calculate the final linear velocity of the person, given his mass is 60.0 kg.
.0708  m/s
(b) What is his angular velocity if each arm has a 5.00 kg mass? You may treat his arms as uniform rods of length 0.9 m and the rest of his body as a uniform cylinder of radius 0.200 m. Neglect the effect of the ball on his rotational inertia and on his center of mass, so that it remains in his geometrical center.
_____________  rad/s
(c) Compare the initial and final total kinetic energy.
____________ (initial energy / final energy)

Explanation / Answer

a) Apply conservation of linear momentum

m*u = (m+M)*v

v = m*u/(m+M)

= 0.25*17/(0.25+60)

= 0.705 m/s

b) Initail angular momentum,L1 = m*v*L

= 0.25*17*0.9

= 3.825 kg.m^2/s

final angular momentum, L2 = I*w

= (0.5*50*0.2^2 + 2*5*0.9^2/3 + 0.25*0.9^2)*w

= 3.9*w

we know, L1 = L2

3.825 = 3.9*w

w = 3.825/3.9

= 0.98 rad/s

c) Ki = 0.5*m*u^2 = 0.5*0.25*17^2 = 36.125 J

Kf = 0.5*I*w^2 = 0.5*3.9*0.98^2 = 1.87 J

ki/kf = 36.12/1.87

= 19.3

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