# Spring and two balls

1. Dec 7, 2014

### Peethassandwich

1. You have one platform (1.2m high and 0.12m wide) and a few small balls of a different mass (0.09, 0.14, 0.25, 0.38, 0.57, 0.9 kg) that slide across the platform without friction and you have 4 springs with various stiffness (556, 918, 1110, 1546 N/m, ignore the mass of the spring). You can lay 2 balls on a platform (the heavier one on the left and the easier one on the right) and lay arbitrary spring on the platform squeezed by 0.02 m (the legth in its natural state is 0.1m). You have to (by using the spring) to make the balls fall from the platform onto the two buttons that are 2 metres apart from each other. If you want the ball to press the button it has to land max. 0,007m away from its centre. What is the value of Sm1, m1, m2 and k?
https://imageshack.com/i/eyledVFlp

I am really confused by this task so forgive me if you find some blunder in my solution
The first thing I am not sure about is whether the ball was still accelerating when it fell off the platform.
And since the force exerted on this ball behaved in a kind of "dirac delta" way I was wondering whether I could get this involved in calculating initial velocity of the ball. That is really the only thing I can't really figure out. I projected this motion into x-y plane and set up the following equations (let's say for the ball on the left):

X-axis sm1 = ? v(initial) = ? t = ?
Y-axis g = 9.81 m/s^2 d = 1.2 m v(initial) = 0 m/s
Then I used this equation : d = v(initial)*t + 1/2*g*t^2
so : 1.2 = 0.5*9.81*t^2
t = 0.494619 s
So according to this the ball was falling for 0.494619 s.
Then I tried to apply formula kX=ma but in this particular case I couldn't somehow get this thing involved since k,m,a are unknown.
X = 0.02m
F = k*X
F = 1/50*k

Edit : I posted an image as a reply since I couldn't display it in the problem.

Last edited: Dec 7, 2014
2. Dec 7, 2014

3. Dec 7, 2014

### haruspex

The first problem you need to solve is how the energy of the spring will be shared out between the two balls. What conservation laws can you think of that might apply? Remember that the spring is not fixed to the platform, and you are to ignore its mass.