Question

Sphere A of mass 0.600 kg is initially moving to the right at 4.00 m/s. sphere B, of mass 1.80 kg is initially to the right of sphere A and moving to the right at 2.00 m/s. After the two sphere collide, sphere is moving at 3.00 m/s in the same direction as before.

(c) Sphere B then has an off-center collision with sphere C,
which has mass 1.20 kg and is initially at rest. After this collision,
sphere B is moving at 19.0° to its initial direction at
What is the velocity (magnitude and direction) of sphere C after
this collision?

(d) What is the impulse (magnitude and direction)
imparted to sphere B by sphere C when they collide?

(e) Is this second collision elastic or inelastic?

(f) What is the velocity (magnitude and direction) of the center of mass of the system of three
spheres (A, B, and C) after the second collision? No external forces
act on any of the spheres in this problem.

Answer 1

mass Mb = 1.8 kg

mass Mc = 1.2 kg

Velocity Vbi = 3 m/

Momentum before collision = 3*1.8 - 5.4 kg-m/s

Let Vb and Vc be the velocitis of B and C after collision

The we have

1.8*Vb*Cos19 + 1.2*Vc*Cos = 5.4   - monetum along x-axis

1.7Vb +1.2*Vc*Cos = 5.4 ------------(1)

1.8*Vb*Sin19 =1.2*Vc*Sin       - momentum along y-axis

0.59 Vb = 1.2 Vc Sin ----------------(2)

0.5*(1.8)*(3)^2 = 0.5*(1.8)*(Vb^2) +0.5*(1.2)*(Vc^2) - conserving KE

9Vb^2 + 6Vc^2 = 81 ----------------(3)

1.7Vb +1.2*Vc*Cos = 5.4 ------------(1)

0.59 Vb = 1.2 Vc Sin ----------------(2)

Solving (1), (2), (3) we get Vb,Vc and

Vb = 0.65 m/sec, Vc = 3.59 m/sec, = 5.09⁰,

Sphere C makes an angle of 5.09⁰ with the horizontal in the forward direction know

d) To calculate the impulse we need to the time elapsed for the collision, without knowing the time elapsed you cannot calculate the acceleration or the force of impact.

e) The collision is elastic the spheres are seperated after collision. and there is loss of energy anywhere.

at the start we have

Ma = 0.6 Va = 4, Mb = 1.8, Vb = 2, Mc = 1.2 Vc = 0

Vcm = (Ma*Va +Mb*Vb +Mc*Vc)/(Ma+Mb+Mc)

         = (0.6*4+1.8*2+1.2*0) / (0.6+1.8+1.2) = 1.67 m/sec

direction towards right