Recent content by Milo Martian

OK

But won't mechanical energy change due to friction? just curious

yes, that can also work for solving the question. But my main confusion was regarding finding the acm. But thanks for your help.

Okay, i got it . Fext= mgsinA - f= macm ...(1) fXR= torque = I X angular acc. = I X acm/R => f= Iacm/R2 ...(2) From (1) and (2) : macm = mgsinA - Iacm/R2 => acm= mgsinA/(m + I/R2) So, since Isolid sphere< Ihollow sphere Therefore, acm for solid sphere> acm for hollow sphere. i hope i am...

can u look at my calculations and tell me where i am going wrong?

ok, so rest of my calculation is right? let the two fs be f1 and f2. acm for solid sphere=5f1/2m acm for hollow sphere= 3f2/2m so how do i figure out which acm is more , since i don't know which among f1 and f2 is greater, and thus solve the initial question of which sphere reaches the bottom first?

ok, so Fext= mgsinA - f = macm => acm= (mgsinA-f)/m ...(1) Torque= fXR ( taken about cm)= I X angular acceleration angular acc. for solid sphere= fXR/ Isolid sphere = 5fXR/ 2mR2=5f/2mR linear acc. of cm for solid sphere= (5f/2mR) X R= 5f/2m ...(2) angular acc. for hollow sphere= fXR/ Ihollow...

Fext= net force external to the system of incline+ sphere. isn't friction internal to the system?if yes then the only external force is mgsinA, isn't it?

Ok so f not equal to mgsinA. But Fext= mgsinA, right? so acm = gsinA for both the spheres?

OK so,m being mass of the body, here normal force, N = mgcosA and since there is no slipping ( so there is only static friction) the static friction, f should be equal to mgsinA i think. There will be a torque due to the combination of friction, f and component of gravitational force mgsinA. Am...

Ok.. so to find out acm , need to find out angular acceleration and multiply it by R? and regarding the equation acm= Fext/M , can't we predict the motion of centre of mass from the knowledge of external forces and the mass? but the forces due to different parts of the sphere are internal...

Yes, i thought i said that only. The linear downslope acceleration comes from the component of gravitational force in that direction ( doesn't it) and the tangential acceleration comes from friction (doesn't it?) Since force= mass X acceleration and the mass and acceleration being equal , the...

But as the body does not slip , shouldn't the magnitude of static friction be equal to the magnitude of the external force trying to make it move?

Well... there's a force mgsin(theta) acting parallel to the incline along the centre of mass and friction acting at the bottom of the sphere in the opposite direction. Since there's no slipping, the forces should be equal.So, the net external force for both is 0? so, acm is 0? that can't be...