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  3. 2. a 10 kg ball moving to the right with a speed o

2. A 10 kg ball moving to the right with a speed of 6.0 m/s collides...

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Physics

2. A 10 kg ball moving to the right with a speed of 6.0 m/scollides with a 20 kg ball moving to the left at a speed of 4.0m/s.

(a) If this is a head-on, perfectly inelastic collision, what isthe velocity of the balls after the collision. Give magnitude anddirection. (5 pts.)

(b) If this is a head-on collision and the the 10 kg ball movesto the left with a speed of 7.0 m/s after the
collision, what is the velocity of the 20 kg ball after thecollision? Give magnitude and direction.

(c) Is the collision in part b perfectly elastic? (You must showa calculation here.) (5 pts.)

(d) If the balls are in contact for 0.03 seconds during thecollision in part (b), what is the magnitude of
the average force that each ball exerts on the other? (5 pts.)

(e) Write an equation for conservation of momentum in the xdirection and determine the x component of the
velocity of the 20 kg mass. (5 pts.)

(f) Write an equation forconservation of momentum in the y direction and determine the ycomponent of the

velocity of the 20 kg mass. (5 pts.)

Answer & Explanation Solved by verified expert
4.3 Ratings (830 Votes)

m1=10kg, m2=20kg, v1i=6m/s , v2i=-4m/s

a) By law of conservation of momentum,

m1v1i+m2v2i=m1v1f+m2v2f ------------(1)

since inelastic collision,

m1v1i+m2v2i=(m1+m2)vf

10*6+20*-4 = (10+20)vf      => vf = -0.67m/s

b) By eqn (1),

10*6+20*-4 =10*-7+20*v2f       => v2f = 2.5m/s ………………directed to right

c) For perfectly elastic collision KE must be conserved.

1/2m1v1i^2 +1/2m2v2i^2 =1/2m1v1f^2+1/2m2v2f^2

1/2*10*6^2+1/2*20*-4^2 =1/2*10*7^2+1/2*20*2.5^2

340 ¹ 307.5

Thus this is not perfectly elastic collision

d) F1 = m1(v1f-v1i)/Δt = 10(-7-6)/0.03 = -4333.3 N ……………..directed to left

F2= m2(v2f-v2i)/Δt = 20(2.5-(-4))/0.03 = 4333.3 N ……………..directed to right

e) By law of conservation of momentum,

m1v1ix+m2v2ix=m1v1fx+m2v2fx

10*6+20*-4 =10*-7+20*v2fx      => v2fx = 2.5m/s ………………directed to right

f) By law of conservation of momentum,

m1v1iy+m2v2iy=m1v1fy+m2v2fy

10*0+20*0 =10*0+20*v2fx      => v2fx = 0m/s
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