Rank the required forces

Three identical cars take the same flat circular curve. One holds a steady 10 m/s, one a steady 20 m/s, one a steady 30 m/s.

Which car needs the largest centripetal force, and which the smallest?

Three identical cars, one turn, three numbers: 10 m/s, 20 m/s, and 30 m/s. Exactly one quantity differs.

You have seen the relationship: F = mv²/r.

Same curve, same cars. Only the speed differs.

When exactly one quantity differs between scenarios, the relationship's direction puts them in order. No calculation is needed.

Mass differs alone: more mass needs more force, so the heaviest case needs the most.

Speed differs alone: more speed needs more force, so the fastest case needs the most.

Radius runs the other way: a tighter circle needs more force, so the smallest radius needs the most.

One quantity at a time, the relationship's direction sets the order.

So the 30 m/s car needs the largest centripetal force, the 20 m/s car the next largest, and the 10 m/s car the smallest.

The taught example, ordered: fastest needs most.

Check first that only one quantity differs. If two differ, the order needs the numbers, and that is not this lesson's job.

Three identical vans round the same flat curve at steady speeds of 12 m/s, 16 m/s, and 24 m/s. Which van needs the greatest centripetal force?

Three carts of mass 20 kg, 35 kg, and 50 kg follow the same circular path at the same steady speed. Which cart needs the least centripetal force?

The same bike is ridden at the same steady speed around three circular loops, of radius 10 m, 20 m, and 40 m. Rank the centripetal forces required, greatest first.

Only the radius differs among the three loops.

A tighter circle at the same mass and speed needs a larger centripetal force.

So the 10 m loop demands the greatest force, then the 20 m loop, then the 40 m loop.

Greatest first: the 10 m loop, the 20 m loop, the 40 m loop.

Luca says: three identical cars round the same curve at different steady speeds, so the fastest car needs the biggest centripetal force. Is he correct?

Your turn

Three sleds of mass 40 kg, 60 kg, and 80 kg are towed around the same circular course at the same steady speed. Rank the centripetal forces required, greatest first.

The same car at the same steady speed can take a curve of radius 30 m, a curve of radius 60 m, or a curve of radius 90 m. Rank the centripetal forces required, greatest first.

Three identical motorcycles round the same flat curve at steady speeds of 4 m/s, 7 m/s, and 10 m/s. Rank the centripetal forces required, greatest first.