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number 9 please The nucleus of a particular atom has a mass of 1.7 Times 10^-26

ID: 1361331 • Letter: N

Question

number 9 please

The nucleus of a particular atom has a mass of 1.7 Times 10^-26 kg and may be assumed to be at rest/ It decays into three particles, with the first having a mass of 5.0 Times^-27 kg and a velocity of 6.0 Times 10^6 m/s in the direction of the positive y-axis, and the second having a mass of 8.4 Times 10^-27 kg and a velocity of 4.0 Times 10^6 m/s in the direction of the positive x-axis. Find the magnitude and direction of the velocity of the third particle (which has a mass of 3.6 Times 10^-27 kg, found by requiring that the total mass is conserved). Gordon Summer is playing billiards^8 and hits the cue ball with a velocity of 3.50 It strikes the 8-ball and is deflected at an angle of 40.0 degree relative to its initial and with a final speed of 2.68 m/s. If the collision is elastic, find the angel of the after the collision and the speed of 8-ball. If you require it, the mass of each 0.165 kg. A diagram is provided.

Explanation / Answer

let,

mass m1=5*10^-27 kg and velocity v1=6*10^6 m/sec

mass m2=8.4*10^-27 kg and velocity v2=4*10^6 m/sec

mass m3=3.6*10^-27 kg and velocity v3=(v3x)i+(v3y)j

total mass M=(m1+m2+m3) =1.7*10^-26 kg


by using conservation momentum,


first particle is moving along +ve y axis,

momentum along y-axis,


m1*v1+m3*v3y=0

(5*10^-27)*(6*10^6)+3.6*10^-27*v3y=0

==> v3y=-8.3*10^6 m/sec

velocity y-component of third particle is,

v3y=-8.3*10^6 m/sec


and


second particle is moving along +ve x axis,

momentum along x-axis,


m2*v2+m3*v3x=0

(8.4*10^-27)*(4*10^6)+3.6*10^-27*v3x=0

==> v3x=-9.3*10^6 m/sec

velocity x-component of third particle is

v3x=-9.3*10^6 m/sec


magnitude of velocity of third particle is,

V3=sqrt((-9.3*10^6)^2+(-8.3*10^6)^2)

v3=12.46*10^6 m/sec

and

tan(theta)=v3y/v3x

tan(theta)=(-9.3*10^6)/(-8.3*10^6)

===>

theta=48.25 degrees,