If i have a ball and I drop it on the floor, knowing the mass (3g) and velocity it bounces up at, how do i calculate the height it bounces to. Assume 0 wind resistance and gravity is 10

radio
Dec 11, 2014

#6**+5 **

Apply Newton's 2nd law of motion (Force = mass*acceleration):

Vertical

Net force = -mg

-mg = m*d^{2}y/dt^{2}

so the mass cancels out and we are left with:

d^{2}y/dt^{2} = -g which is the same as your equation Melody.

Horizontal

Net force = 0

0 = m*d^{2}x/dt^{2}

so dividing by the mass we are left with

d^{2}x/dt^{2 }= 0

Mass is not relevant here.

.

Alan
Dec 13, 2014

#1**+5 **

According to your question, we are finding the height of second bounce.

If I say it's** s,**** **

the u(initial velocity) of first bounce should be 0, because you said you are dropping, not adding force.

the v(final velocity) of first bounce should be u(initial velocity) of second bounce.

and the ball at peak of second bounce, the speed should be 0.

if we work out the acceleration by F=ma, (or if time or acceleration is given and you didn't mention) then we can work out s. By formula $${{\mathtt{v}}}^{{\mathtt{2}}} = {{\mathtt{u}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{as}}$$

$$0=(u_1) ^2+2as$$ (I'm setting peak of second bounce as end)

flflvm97
Dec 11, 2014

#2**+5 **

Hi radio,

That is a good question.

I am not sure if the mass comes into this problem or not. I don't think that it does.

This is my guess. I will ask someone more knowledgable to take a look at this question though.

I usually do these with calculus.

Initially. When the ball first leaves the ground

$$\\t=0, \\ \quad accel= \ddot y = -10m/s^2, \\ \quad vel=\dot y=u\;\;m/s,\\ \quad displacement=y=0\;metres\\\\

Ongoing\\

\ddot y = -10\qquad $Any stat point will be a maximum$\\

\dot y=-10t+u\\

y=-5t^2+ut\\\\$$

Maximum height will be attained when velocity =0

$$\\-10t+u=0\\

10t=u\\

t=\frac{u}{10}\;\;seconds\\\\

$Now find y when $ t=\frac{u}{10}\\\\

y=-5\times \frac{u^2}{100}+u\times \frac{u}{10}\\\\

y=\frac{-u^2}{20}+ \frac{2u^2}{20}\\\\

y= \frac{u^2}{20}\\$$

-------------------------------------------------------------------------

LET me see if I can do the same thing using physics formulas.

Initial velocity =u

final velocity = v =0

accel =a = -10

find displacement s

the only formula with u,v,a and s is [4]

$$\\v^2=u^2+2as\\

0=u^2+2*-10s\\

-u^2=-20s\\\\

s=\frac{u^2}{20}$$

I got the same answer both ways. That is good anyway

The ball will reach a height of $${\frac{{{\mathtt{u}}}^{{\mathtt{2}}}}{{\mathtt{20}}}}$$ metres on the first bounce

Melody
Dec 13, 2014

#3**0 **

I'd really like a physics person to discuss the relevance of the mass of the ball. Please.

Melody
Dec 13, 2014

#5**+5 **

I was hoping you would discuss it a little more than that Alan.

Is there anything more that you can say - I mean, why is mass irrelevant?

Melody
Dec 13, 2014

#6**+5 **

Best Answer

Apply Newton's 2nd law of motion (Force = mass*acceleration):

Vertical

Net force = -mg

-mg = m*d^{2}y/dt^{2}

so the mass cancels out and we are left with:

d^{2}y/dt^{2} = -g which is the same as your equation Melody.

Horizontal

Net force = 0

0 = m*d^{2}x/dt^{2}

so dividing by the mass we are left with

d^{2}x/dt^{2 }= 0

Mass is not relevant here.

.

Alan
Dec 13, 2014