Question

Solutions must be worked out symbolically first (that is, in terms of variables and constants) with numbers plugged in as the very last step. Make sure to double check the answer!

Vesta is an asteroid that has a mass of 259.0 x 10¹⁸ kg and is traveling at a speed of 13.34 x 10³ m/s. A crazy engineer sends another asteroid to collide with Vesta, at a 90° angle. The crazy engineer’s asteroid has a mass of 100.0 x 10¹⁸ kg and is traveling at a speed of 20.0 x 10³ m/s. Say that Vesta is traveling in the +x direction at the time of impact. However improbable, the two asteroids somehow stick together when they collide.What is the final velocity of the two asteroids? Explain (in words) how you would prove if this collision is elastic or inelastic.

A “lazy Susan,” invented by Elizabeth Howell in 1891, is a large, round platter that is free to spin; they are often placed in the center of a table to allow people to easily share dishes of food. Your lazy Susan has a mass of 150g and radius R, and is rotating freely at 3.5 rad/s. You set the salt shaker on it ¾ of the way from the center to the outer edge. After you do so, the lazy Susan is rotating at 2.5 rad/s. What is the mass of the salt shaker?

Answer 1

Applying momentum conservation for the collision,

(259 x 10^18)(13.34 x 10^3)i + (100 x 10^18)(20 x 10^3)j = (259 x 10^18 + 100 x 10^18) vf

vf = 9.62 x 10^3 i + 5.57 x 10^3 j

Speed = sqrt(9.62^2 + 5.57^2) x 10^3 = 11.12 x 10^3 m/s .......Ans

Direction = tan^-1(5.57 / 9.62) = 30 deg with x axis

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I1 = MR^2 / 2 = 0.150 R^2 /2 = 0.075 R^2

I2 = m x (3 R / 4)^2 = 0.5625m R^2

Applying angular momentum conservation,

I1 wi = (I1 + I2) wf

(0.075 R^2 ) ( 3.5) = (0.075 + 0.5625 m) R^2 (2.5)

0.075 = 1.406 m

m = 0.0533 kg Or 53.3 grams