Calculating Ball Height from Horizontal Force: Newton's Second Law Explained

[ippo90]

Exams tomorow! please help

Homework Statement

A billiard ball is hit with a horizontal force F. The force hits the ball with the height h over the ball's center. the initial velocity is v₀ and the the velocity afterward is (9/7)v₀. Show that the height h is (4/5)R, where R is the radii of the ball.

Homework Equations

Newtons second law: Fdt=mdv

momentum: t=r x F=Iw

The Attempt at a Solution

I don't really understand this. please help. Thank you very much

 

[tiny-tim]

hi ippo90!

initially, the ball will slide (at velocity v₀) while spinning, but after a short time, friction will reduce the spin, and the ball will start rolling (at velocity (9/7)v₀)

 

[ippo90]

Thank you for the reply. The problem is I don't know where to start. Can you help me?

 

[ippo90]

just ignore my last post. I thought about what you said in you post, and it came out=) Thank you for your kind help.

one thing I not sure of is that when I integrated the torque i got something like

hFt=Iw

where h is height, t is time and w is the angul. velocity. here I chose the center as the point of momentum. but afterward I have to use that the angular momentum (L) is conserved. but this means that I have to choose the contact point as the poiint of momentum. why can I do this (why not)?

 

[gneill]

just ignore my last post. I thought about what you said in you post, and it came out=) Thank you for your kind help.

one thing I not sure of is that when I integrated the torque i got something like

hFt=Iw

where h is height, t is time and w is the angul. velocity. here I chose the center as the point of momentum. but afterward I have to use that the angular momentum (L) is conserved. but this means that I have to choose the contact point as the poiint of momentum. why can I do this (why not)?

It would be nice to see the problem worked out in detail.

 

[tiny-tim]

hi ippo90!

for L to be constant, you need zero https://www.physicsforums.com/library.php?do=view_item&itemid=175" …

if you take https://www.physicsforums.com/library.php?do=view_item&itemid=313" force will be an unknown non-zero torque, so you take it about the point of contact instead!