Finding how high a ball will bounce with Hooke's Law?

Question

Ok, ill type it out how it is with the information I got from it. It's obsurd how teachers can give such a complex question at the Physics 11 level!

Tim tries to crush a 0.58kg basketball but is only able to compress it by 1.5cm when a force of 50N is applied.

a) Spring constant?
b) When he throws it against the floor it is compressed 3.4cm. How high will it bounce?

I got Force.. which is F=kx F = (3333.33N/m)(0.034m) thus F=113.33322N
I got accel.. which is F=ma A = 113.33322N / 0.58Kg thus A = 195.402m/s2

Now without using anything that has to deal with energy and simple harmonic motion.. I have to somehow get how high the ball bounces with Kinematics.. but I know Vf = 0 of the ball but not Vo.. hmmm help me out people around the world! Thankyou

Love, Michael.

Ok, ill type it out how it is with the information I got from it. It's obsurd how teachers can give such a complex question at the Physics 11 level!

Tim tries to crush a 0.58kg basketball but is only able to compress it by 1.5cm when a force of 50N is applied.

a) Spring constant?
b) When he throws it against the floor it is compressed 3.4cm. How high will it bounce?

I got Force.. which is F=kx F = (3333.33N/m)(0.034m) thus F=113.33322N
I got accel.. which is F=ma A = 113.33322N / 0.58Kg thus A = 195.402m/s2

Now without using anything that has to deal with energy and simple harmonic motion.. I have to somehow get how high the ball bounces with Kinematics.. but I know Vf = 0 of the ball but not Vo.. hmmm help me out people around the world! Thankyou

Love, Michael.

FIND IT WITHOUT USING KINETIC ENERGY and the like! Just simple KINEMATICS! thankyou

Sorry about double post.. didnt know how the extra details thing worked.. i thought i had to completely retype everything in again.. once again sorry

I dont under this part h = v^2/(2*g) = 0.68 m
..
The teacher never taught us that yet.

Answer 1

The acceleration you are getting is the ball's deaccleration as it compresses, not as it moves in the vertical direction.

When he bounces it on the floor, he compresses it and stores energy and it is then transfered into kinetic energy which supplies it with a vertical velocity.

E = KE
1/2*k*x^2 = 1/2*m*v^2

v = sqrt(k/m) * x

Then use this as vi and with vf^2 = vi^2 - 2*g*h find h, with vf = 0.

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I got h = .34 m


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There's no way to solve the problem without using energy to find the initial velocity. Perhaps your teacher did not want you to use energy to figure out how high it goes. You cannot use kinematics only.

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I got to thinking about it. If you can use kinematics. You have the acceleration and the displacement. Use
vf^2 = vi^2 + 2*a*d
After it's compression stage, the vi = 0 and the acceleration will be opposite the original deacceleration as long as energy is conservered since the force will be flipped around and used to propel the ball up.

vf = sqrt(2*a*d) = sqrt(2*195.4*.034) = 3.64 m/s

Then use
h = v^2/(2*g) = 0.68 m

It is different then the previous one I got.