Please help me to solve the following physics problem. On a snooker table (L2 =

Question

Please help me to solve the following physics problem.

On a snooker table (L2 = 3.7 times L1 = 1.8 m), the black ball is on its spot, 1 / 11 from the near cushion, and midway between the two side-cushions. The white cue ball is 011 the blue belli spot, in the exact centre of the table. The effective coefficient of friction (the ball is rolling, not sliding, but think of it as sliding) between ball and surface is mu s = 0.05, collisions between the balls and between belli and cushions is taken to be elastic. The balls have the same mass of m = 0.16 kg, and we take the y-coordinate to be along the short side of the table, the x-coordinate along the long side. The speed of the cue ball as it hits the black ball is 3 m/s and it is rolling along the middle of the table, in the x-direction. Assuming that the black ball is putted into the near right-side corner pocket, what are the velocities of the cue ball and black ball immediately after the collision? How many complete lengths of the table does the cue ball traverse after the collision, before it come to rest due to friction?

Explanation / Answer

Its an elastic collision,so the energy is conserved.

so,mu2^2+0=mv1^2+mv2^2, u2,v2=velocity of the cue ball before and after collision,v1=velocity of the black ball after collision.

m=mass of the balls,

u2^2=v1^2+v2^2,so the balls travel perpendicularly to each other.

now,momentum conservation: u2=v1*cos(theta)+v2*sin(theta); v1*sin(theta)=v2*cos(theta)

cos(theta)=0.6/sqrt(.6^2 +.9^2)=0.554,theta=angle of the black ball with x axis.

so,sin(theta)=0.832.

so,v1=0.666*v2.

so,3=v2*0.666*0.554+v2*0.832; v2=2.498 m/s.

v1=1.661 m/s.

b) w^2=2.498^2-2*0.312*0.728; w=2.405 m/s=velocity when it hits the near cushion,0.312=deceleration due to friction.

so it travels 0.728 m and hits the near cushion (upper one on the pic).

again,x^2=2.405^2-2*0.312*0.9; x=2.285 m/s.

so it travels 0.9 m before colliding at the left cushion.you can calculate 0.9 m from the geometry.

hence you can calculate the rest of destances until it comes to zero.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---