- #1
roadrunner1994
- 11
- 2
- Homework Statement
- A homogeneous ball with mass M and radius R is set in
motion on a horizontal floor in such a way that the ball initially (i.e., at
time t = 0) has the translational velocity Vo. We assume that the ball begins
its motion as pure sliding. The coefficient of friction between the ball and
the floor is μ. The motion of the ball between the time t = 0 and t = tr is
a combination of sliding and rolling. At time t = tr the ball begins to roll
without sliding. In the time between t = 0 and t = tr the ball has moved a
distance D along the floor.
(1) Determine tr.
- Relevant Equations
- -
Hi,
I solved this prolem in the following way.
I have started with the angular momentum theorem:
Iα=fR
As the force of friction vector is attached on point of contact of the ball and the supporting surface, the moment of inetria is:
Ic= MR^2 + Icm = MR^2 + (2/5)MR^2
Ic*a/R=μMgR
tr=7/5(v0/μg)
It seems that I've made a mistake during calculations of moment of inertia, because the right anwer is tr=2/7(v0/μg), but I can't find that mistake.
Thanks for your help!
I solved this prolem in the following way.
I have started with the angular momentum theorem:
Iα=fR
As the force of friction vector is attached on point of contact of the ball and the supporting surface, the moment of inetria is:
Ic= MR^2 + Icm = MR^2 + (2/5)MR^2
Ic*a/R=μMgR
tr=7/5(v0/μg)
It seems that I've made a mistake during calculations of moment of inertia, because the right anwer is tr=2/7(v0/μg), but I can't find that mistake.
Thanks for your help!