A car holds a steady 13 m/s through a gentle circular bend of radius 80 m. Up the road, the same car holds the same steady 13 m/s through a tight circular bend of radius 20 m. Same car, same speed, one thing changed: the radius.
Which bend demands the larger centripetal force?
You have seen that a tighter circle at the same speed means a greater centripetal acceleration.
Giving the same mass a greater acceleration takes a larger net force.
So the tight 20 m bend demands a larger centripetal force than the gentle 80 m bend.
That completes the trio: the needed force grows with mass, grows with speed, and shrinks as the circle widens.
A later lesson ties the three together in one equation.
A taxi holds the same steady speed on a tight circular ramp of radius 25 m and on a gentle one of radius 75 m. Compare the centripetal force needed on the tight ramp.
A runner rounds a small circular loop, then a loop twice as wide, at the same steady pace. Compare the centripetal force needed on the wider loop.
A van at a steady speed can follow a wide circular loop or a tight one. Compare the centripetal forces the two loops demand.
The van's mass and speed are the same on both loops. Only the radius differs.
A tighter circle at the same speed needs a greater centripetal acceleration, and the same mass at a greater acceleration takes a larger force.
The tight loop demands the larger centripetal force.
Kaia says: a car leaving the highway at a steady speed needs a larger centripetal force on a tight circular exit ramp than on a gentle one. Is she correct?
A tour bus at a steady speed can take a bend of radius 40 m or a bend of radius 120 m. Which statement is correct?
The same car laps four flat circular test tracks at the same steady speed. The tracks' radii are 15 m, 30 m, 45 m, and 60 m. On which track does the car need the greatest centripetal force?
Two identical delivery vans hold the same steady speed, each on its own circular loop. The blue van needs a smaller centripetal force than the green van. Which statement follows?