Calculate the velocity of both pool balls after impact condi

Calculate the velocity of both pool balls after impact conditions before impact are shown above. E = 0.92 Calculate the velocity of this roller coaster at the bottom of the hill, A, And at the crest of the next hill, B.

Solution

1.

conservation of momentum :

momentum before collision = momentum after collision

i.e. m1*v1 + m2*v2 = m1*v1f +m2*v2f

here m2 = 5*m1

hence 9*m1 + 0*(5*m1) = v1f*m1 + v2f*(5*m1)

v1f + 5*v2f = 9 ...............(1)

Now from coefficient of restitution

0.92 = (v2f - v1f)/(v2 - v1)

0.92 =(v2f - v1f)/(0 - 9) ....................(2)

Solving both equations

velocities after collision

v1f = 8.4 ft/s

v2f = 0.12 ft/s

2.

Total energy of system is constant = Kinetic energy + potential energy

For point A

Total energy at start = Total energy at A

1/2* m * v² + m* g* h = 1/2* m * v_A² + m* g* h_A

1/2 * 9 + 9.8 * 90 = 1/2 * v_A² + 9.8 * 0

v_A   = 42.107 m/s

For point B

Total energy at start = Total energy at B

1/2* m * v² + m* g* h = 1/2* m * v_B² + m* g* h_B

1/2 * 9 + 9.8 * 90 = 1/2 * v_B² + 9.8 * 35

v_B = 32.969 m/s