Part A A predecessor of the pin-ball machine in the pin-cube table, in which a m

Question

Part A A predecessor of the pin-ball machine in the pin-cube table, in which a metal cube is launched onto the play surface instead of a rolling metal ball. (The launcher mechanism and game board are pictured below). A) (20 pts) magine that the play surface is a frictionless air table. If the table is angled upward by 200, the pin cube has a mass of 420 grams, and it must travel 1.10 m after it leaves the spring to and enter the game board, what is the minimum distance a player must compress the k= 4,000 N/m spring for a successful launch? xo 0 0

Explanation / Answer

(A) APplying energy conservation,

initial gravt. PE + spring PE + KE = final gravt. PE + spring PE + KE

- m g d sin20 + k d^2 /2 + 0 = m g 1.10 sin20 + 0 + 0

2000 d^2 - 1.41d - 1.55 = 0

d = 0.0282 m

(B) Work- energy theorem.

work done by gravity + work done by spring + work done by friction = change in KE

- 0.420 x 9.8 x (d + 1.10 )sin20 + 4000 d^2 /2 - 0.45 x 0.420 x 9.8 x (d + 1.10) cos20 = 0 - 0

2000 d^2 - 3.15 d - 3.46 = 0

d = 0.0424 m

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