You are playing with a toy in which a marble launched by a spring rolls along a

Question

You are playing with a toy in which a marble launched by a spring rolls along a track full of loop-the-loops and curves with almost no energy dissipated. You want the marble to have a speed of 0.70 m/s when it arrives at the top of a loop that is 0.20 m higher than the marble's position when you launch it.

a) What initial speed must the marble have?

b) If the marble has an inertia of 5.0 g and the spring has a spring constant of 17 N/m, how far back do you need to pull the spring on the level launching chute to get the marble to have this initial speed?

Explanation / Answer

speed, v=0.7 m/sec

height, h=0.2 m

a)

use,

u^2-v^2=2*g*h

u^2-0.7^2=2*9.8*0.2

===> initial speed, u=2.1 m/sec

b)

use,

1/2*k*x^2=m*g*h

1/2*17*x^2=5*10^-3*9.8*0.2

===> x=3.4 cm

compression, x=3.4 cm

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