Two shuffleboard disks of equal mass, one orange and the other yellow, are invol

Question

Two shuffleboard disks of equal mass, one orange and the other yellow, are involved in an elastic, glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving with a speed of 4.00 m/s. After the collision, the orange disk moves along a direction that makes an angle of 38.0 degree with its initial direction of motion. The velocities of the two disks are perpendicular after the collision. Determine the final speed of each disk. (orange disk) (yellow disk) An unstable atom is nucleus of mass 1.92 times 10^-26 kg initially a rest disintegrates into three particles. One of the particles, of mass 5.19 times 10^-27 kg, moves along the y axis with a speed of 6.00 times 10^6 m/s. Another particle, of mass 8.49 times 10&-27 kg, moves along the x axis with a speed of 4.00 times 10^6 m/s. Find the velocity of the third particle. Find the total kinetic energy increase in the process.

Explanation / Answer

(i) the mass of 3rd particle = (19.2 - 5.19 - 8.49) x 10^(-27) = 5.52 x 10^(-27)

The total momentum along the X axis was 0. So, after the disintegration it must be 0.

Let v1 be the velocity of the 3rd particle along X axis.

The particle going y direction has no component along x.

So, (8.49 x 10^(-27) x 4 x 10^(6) ) + (5.52 x 10^(-27) x v1) = 0

=> v1 = - 12.37 x 10^(-3) m/s =- 6152173.91

= -6.15 Mm/s

The minus(-) sign indicates that 3rd particle's X component is in the opposite direction of 1st Particle.



(ii) Same way, if the y component of 3rd particle is v2, then,

(5.19 x 10^(-27) x 6 x 10^(6) ) + (5.52 x 10^(-27) x v2) = 0
=> v2 = -5.833 x 10^(-3) m/s

= - 5641304.34

= -5.641 Mm/s

The minus(-) sign indicates that 3rd particle's Y component is in the opposite direction of 2nd particle.


(iii) 3rd particles actual speed = sqrt((6.15^2) + (5.641^2)) = 8.61 Mm/s = 13.67 x 10^(-3) m/s

So, the total kinetic energy released in the process

= 1/2m1v1^2 + 1/2m2v2^2 + 1/2m3v3^2
= .5 x (8.49 x 10^(-27) x (6.15 x 10^(-3))^2 ) +
.5 x (5.19 x 10^(-27) x (6 x 10^(-3))^2 ) +
.5 x (5.52 x 10^(-27) x (13.67 x 10^(-3))^2)
= 4.984 x 10^(-31) Joule

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