How does weight of an object affect its rolling distance?

Answer 1

I'll presume that you want to know how far down a slope something rolls in a given time. ***(But see below.) Also, that the surface is an idealized one characterized by a coefficient of friction sufficiently large that the object rolls without slipping. ***(But see below, also.)

In that case, the weight of an object per se doesn't affect its progress of rolling distance with time, because the component of the weight parallel to the slope is proportional to the mass of the body itself. That means that in any equations involving acceleration under gravity, the specific mass of the body cancels out.

Of more importance is the so-called Moment of Inertia of the body. This is the sum of all quantities like mass x (distance from some axis)^2 or mass x (distance squared). This helps to determine what FRACTION of the gravitational energy released by rolling down a slope a certain distance goes into "linear" kinetic energy [(1/2) m v^2 DOWN THE SLOPE], and how much into ROLLING ENERGY, (1/2) [Moment of Inertia] x (angular speed)^2.

Consider a solid cylinder, a hollow cylinder, a solid sphere, or a hollow sphere. All of of these have DIFFERENT Moments of Inertia (k M R^2) for a given total mass M and radius R. (As far as sharing out the available K.E. --- rotational versus "linear" --- is concerned, what really matters is only that last ratio, the Moment of Inertia divided by M R^2, that is, just : k.) For THAT reason, each DIFFERENT KIND OF MASS DISTRIBUTION accelerates and rolls down a slope with DIFFERENT rates of acceleration. I emphasize once again: this is in the end QUITE INDEPENDENT of their individual total masses. It is ONLY a function of their "dynamical shape," or mass-distribution, from this dynamical point of view.

I hope that this answers your question. (If not, see *** below.)

Live long and prosper.

*** POSTSCRIPT. But perhaps you weren't thinking of an inclined plane and acceleration, but rather of rolling horizontally, in a more real world context, with friction? It then depends upon what you consider the relevant law of friction to be, and how realistically you want to treat it.

In an ideal situation in which no slipping were to occur (which means no dissipation of energy), the object would simply roll on forever, whatever its weight. Even with slipping, if the dynamical friction law still resmbled "Newton's law of Friction,", F = mu N, the rolling distances to stand still from a start with the same initial v should still be the same, since N is Mg and therefore the frictional force as well as the initial linear monentum would both be proprtional to m and therefore cancel out.

It would seem to require something in the effective friction law that would CHANGE the dynamical friction coefficient (as a function of weight or mass) to make the rolling distances different. I'm sure we all FEEL that a "heavy object" is likely to roll on further than a "light object" because it's got more momentum --- but, for the reasons already given, the some frictional law wouldn't do that.

Perhaps it's the case that an object with much larger weight tends to "iron out" microscopic surface disturbances as it rolls and, in so doing, creates a smaller frictional resistance for itself than that experienced by the lighter weight? Interesting --- I hadn't thought of that before.

Good question; thank you for keeping my aged brain active.

Answer 2

If there is no friction, the weight has no effect. In the presence of friction, it takes more energy to stop a heavier weight so it will travel further. However, if friction is increased by weight, that will tend to shorten the rolling distance. On a hard surface, rolling friction is small, but on a rubber-like surface, rolling friction will increase with weight. Then you would have to know the values of friction vs weight to get an answer for a particular situation.

Answer 3

Not at all. The weight of an object doesn't effect its speed or its distance. Gallileo used rolling objects to demonstrate that gravity doesn't affect an objects accelleration or the distance it travels. One possible answer, however, is very heavy rolling objects will obliterate anything in front of them whereas light objects will not.

Answer 4

think there replaced into no friction in any respect. Then the only forces appearing on an merchandise may be gravity and the reaction tension from the ramp. For a uniform ball or cylinder, the two those will act for the duration of the centreline and for this reason exert no torque, so the object will slide without rotating. it relatively is why we could differentiate between rolling without slippage and sliding with slippage. (no remember if there's a value for coefficient of friction which will enable an intermediate between the two extremes - some slippage, yet nevertheless some rotation - i don't understand.)

Answer 5

Doesn't momentum have an effect with this ?