# Different mass, different speed?

1. May 27, 2005

### TSN79

So once and for all I would like an answer to this; if two people with different mass sit on two bikes and roll down a hill, which one will reach the bottom first? Let's ignore the difference in air resistance for this one. Is it really an advantage for alpine skiers to have more mass? I know that two object dropped from a height reaches the ground at the same time, but will it work the same way here?

2. May 27, 2005

### Chi Meson

When you ignore air resistance, no there will be no difference.

The resistance of friction will be proportial to the mass of the object, but so will the accelerating force of gravity. In an ideal condition, it's a wash.

The reason massive alpine skiers ahve an advantage, is that more weight means more accelerating force, but the increase in surface area is not as significant. A 90 kg alpine skier will not have significantly more frontal surface area than a 60 kg alpine skier, especially when in an aerodynamic "tuck" position.

So you can't ignore air resistance for this question.

3. May 27, 2005

### Jameson

Well put, and to the OP, note ideal conditions are needed for the tie to occur.

4. May 27, 2005

### Staff: Mentor

As Chi Meson explained, if you are willing to ignore friction, two objects will slide down a hill at the same rate regardless of mass. But rolling is different than sliding. Something that rolls down the hill (which requires friction, by the way) has to transform its gravitational energy into both rotational and translational energy, thus its translational energy (and speed) will be less than if it could slide down a frictionless hill.

Of course, with a bike only the wheels are rotating. The rest of the mass only translates. Nonetheless, the bike will roll with a bit slower speed than it would if it just slid down. And I would imagine that a heavier person would make the rotation of the wheels even less significant, and thus would roll a tad faster.

Of course, just like in the skiing case, air resistance plays a major role and cannot be ignored. Chi Meson's arguments also apply to the bikers.

5. May 27, 2005

### SGT

I suspect that the heavier person would deform the tires more than the lighter person, making the rolling more difficult.

6. May 28, 2005

### Mk

The effect is negligable.

7. May 28, 2005

### SGT

In the conditions proposed by the OP (no air resistance) I think that tire deformation would be a major effect.