The same car rounds the same circular bend twice, at a steady 11 m/s and then a steady 16 m/s. Same bend, same car, one thing changed: the speed.
Which run needs the larger centripetal force?
You have seen that a greater speed on the same circle means a greater centripetal acceleration.
Giving the same mass a greater acceleration takes a larger net force.
So the 16 m/s run needs a larger centripetal force than the 11 m/s run.
A later lesson gives the exact relationship. Here, the direction of the change is the point.
A subway train takes the same curved section of track at a steady 12 m/s, then at a steady 17 m/s. Compare the centripetal force needed on the faster run.
A go-kart laps a circular loop at a steady speed, then repeats the loop at a lower steady speed. Compare the centripetal force needed on the slower lap.
A motorcycle rounds the same flat curve at a steady 9 m/s, then at a steady 14 m/s. Compare the centripetal forces needed on the two runs.
The curve and the mass are the same on both runs. Only the speed differs.
A greater speed on the same circle needs a greater centripetal acceleration, and the same mass at a greater acceleration takes a larger force.
The 14 m/s run needs the larger centripetal force.
Luca says: the same sports car rounding the same curve needs a larger centripetal force at 25 m/s than at 20 m/s. Is he correct?
A city bus takes the same traffic circle at a steady 7 m/s on a quiet day and at a steady 10 m/s when running late. Which statement is correct?
Four identical vans round the same flat curve at steady speeds of 8 m/s, 10 m/s, 13 m/s, and 15 m/s. Which van needs the greatest centripetal force?
Two identical trucks round the same curve at steady speeds. The red truck needs a larger centripetal force than the white truck. Which statement follows?