A 10.0-g marble slides to the left with a velocity of magnitude 0.400 m/s on the

Question

A 10.0-g marble slides to the left with a velocity of magnitude 0.400 m/s on the frictionless, horizontal surface of an icy New York sidewalk and has a head-on, elastic collision with a larger 30.0-g marble sliding to the right with a velocity of magnitude 0.200 m/s. Let +x be to the right. (Since the collision is head-on, all the motion is along a line.)

a)Find the magnitude of the velocity of 30.0-g marble after the collision.

b)Find the magnitude of the velocity of 10.0-g marble after the collision.

c)Find the direction of the velocity of each marble after the collision.

given options :

Both marbles are moving to the left.

d)Calculate the change in momentum (that is, the momentum after the collision minus the momentum before the collision) for 30.0-g marble.

e)Calculate the change in momentum for 10.0-g marble.

1- The 10.0 g marble is moving to the left and the 30.0 g marble is moving to the right. 2- The 30.0 g marble is moving to the left and the 10.0 g marble is moving to the right. 3- Both marbles are moving to the right. 4-

Both marbles are moving to the left.

Explanation / Answer

A) let m1 = 30 g and u1 = 0.2 m/s

m2 = 10 g and u2 = -0.4 m/s

then

velocity of 30g marble is v1 = (m1-m2)*u1/(m1+m2) - 2*m2*u2/(m1+m2)

v1 = (30-10)*0.2/(10+30) - 2*10*0.4/(30+10) = -0.1 m/s

B) velocity of 10g marble is v2 = 2*m1*u1/(m1+m2) -(m2-m1)*u2/(m1+m2)

v2 = 2*30*0.2/(10+30) - (10-30)*0.4/(10+30) = 0.5 m/s

C) 10 gmarble moving to the right and 30g marble moving to the left

So the correct option is 2- The 30.0 g marble is moving to the left and the 10.0 g marble is moving to the right.

D) change in momentum of 30 g ball is pf-pi

pf = m*v1 = -0.030*0.1 = -0.0030 kgm/s

pi = m*u1 = 0.030*0.2 = 0.0060 kg m/s

then change in momentum of 30 g ball is pf-pi = -0.003 - 0.006= -0.009 kg m/s

E) the change in momentum for 10.0-g marble is m*(v2-u2) = 0.010*(0.5+0.4) = 0.009 kg m/s

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