Introductory Physics I Group Problem 1) A Uranium-234 nucleus is initially stati

Question

Introductory Physics I Group Problem 1) A Uranium-234 nucleus is initially stationary, but it is hit with a neutron with an initially velocity of 2.5 X 10* m/s, and breaks up into a Thorium nucleus, with a mass of 231 I amu, and an alpha particle (4 amu). If the Thorium nucleus is detected with a velocity of 9.2 X 1 velocity should the alpha particle be found? os m/s at an angle of 30 from the x-axis, at what angle, and with what kg soccer player is running due North with a speed of 7.4 m/s, and becomes tangled up with a 72-kg soccer player who is running due East with a speed of 6.9 m/s. How much kinetic energy is lost when they get tangled?

Explanation / Answer

1) Applying momentum conservation,

(234 x 0) + (1 x 2.5 x 10^8)i = (231 x 9.2 x 10^5)(cos(30)i + sin30)j) + (4 v)(cos(theta)i + sin(theta)j)

along j,

(231 x 9.2 x 10^5)sin30 + (4 v sin(theta)) = 90

4 v sin(theta) = - 1.063 x 10^8 ... (i)

along i,

2.5 x 10^8 = 1.841x 10^8 + 4 v cos(theta)

4 v cos(theta) = 0.659 x 10^8 .... (ii)

(i)/(ii) = tan(theta) = -1.613

theta = - 58 deg .....Ans

v = 0.312 x 10^8 m/s

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