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This is the specific question w/o information on mass given, I think here is not enough info.

A block and a sphere are each released from rest at the top of an incline from the same height. The block slides with negligible friction while the sphere rolls without slipping. Compare the speed of the block at the bottom of the incline to the speed of the sphere at the bottom of the incline and explain the reasoning for that comparison.

Doesn’t mass matter so there is not enough information? Normally, you would use conservation of energy, but the problem is that they start out with different potential energies, depending on the mass (which we are not given).

Also, on the side of semantics, is it even possible to compare “speed” without specifying translational or rotational? You could do both, but not a general “speed” in my understanding.

Without more information, I am stuck. I think you can’t answer this without more info

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  • $\begingroup$ If you work through the problem you will find mass doesn't matter. Here "speed" refers to translational motion. $\endgroup$
    – BioPhysicist
    Commented Apr 1, 2020 at 0:09
  • $\begingroup$ @AaronStevens OK I think I got it then; so....: The block starts out with U=mgh. It turns into all KE by the end so mgh=1/2(m)(v)^2, v= sqrt(2gh). But this calculation doesn’t include the horizontal loss of speed (which I guess there is not). Next, the sphere starts out with its own U=mgh and turns into both rotational and translational KE, so mgh=1/2(m)(v)^2+ 1/2(I)(omega)^2, which is equivalent to mgh=1/2(m)(v)^2+1/2(mr^2)(v/r)^2=, so 2gh=2v^2, so v=sqrt(gh). Therefore the final speed of the block is greater than the final speed of the sphere (by a factor of sqrt(2)). Is that right? $\endgroup$
    – Alexander Ye
    Commented Apr 1, 2020 at 0:24
  • $\begingroup$ @AaronStevens Does my block velocity make sense though, because it has the same velocity whether or not it is on an incline, which intuitively seems false. Even if you remove friction. $\endgroup$
    – Alexander Ye
    Commented Apr 1, 2020 at 0:35
  • $\begingroup$ it has the same velocity whether or not it is on an incline, which intuitively seems false. Hint: The normal force doesn't do any work in this case $\endgroup$
    – BioPhysicist
    Commented Apr 1, 2020 at 1:11

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For each object for energy conservation you will have $\Delta\text{KE}=-\Delta\text{PE}$. Since both of these terms are directly proportional to the mass, the mass variables on each side of the equation will cancel out. Therefore, you do not need to know the mass of each object to solve this problem.

Also, in this case speed means the translational speed of the center of mass of the object.

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