You toss a .4 kg ball at 9.0 m/s to a 14 kg dog standing on an iced-over pond. T

Question

You toss a .4 kg ball at 9.0 m/s to a 14 kg dog standing on an iced-over pond. The dog catches the ball and begins to slide on the ice. a. Measured from the Earth reference frame, what is the velocity of the dog immediately after he catches the ball? b. Measured from the Earth reference frame, what is the velocity of an inertial reference frame in which the ball's kinetic energy does not change? c. Measured from the Earth reference frame, how much of the original kinetic energy is convertible? d. Measured from the reference frame described in part b, how much of the original kinetic energy is convertible?

Explanation / Answer

a)

Let use inelastic collision,

m1v1i+m2v2i=(m1+m2)vf

4.0*9.0+14.0*0=(4.0+14.0)*vf

vf=2.0m/s

b)

Velocity of CM

(m1v1i+m2v2i)/(m1+m2) = (4.0*9.0+14.0*0)/(4.0+14.0) = 2.0 m/s

c)

KE=1/2*(m1+m2)*vf^2 – [1/2*m1*v1i^2+1/2*m2*v2i^2) = ½*(4.0+14.0)*20^2 – [1/2*4.0*9.0^2+1/2*14.0*0^2] = -126.0 J

d)

KE=1/2*(m1+m2)*vf^2 – [1/2*m1*v1i^2+1/2*m2*v2i^2) = ½*(4.0+14.0)*7.0^2 – [1/2*4.0*2.0.0^2+1/2*14.0*2.0^2] = -90.0 J

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