An empty moving truck rounds a circular highway ramp at a steady 15 m/s. Later, loaded with furniture, the same truck rounds the same ramp at the same steady 15 m/s. Same circle, same speed, one thing changed: the mass.
Which run needs the larger centripetal force?
You have seen, in the dynamics topic, that a given net force accelerates a large mass less than a small one.
Read that relation the other way: to give a large mass the same acceleration, you need a larger net force.
On the same ramp at the same speed, the truck needs the same centripetal acceleration either way, because speed and radius set it.
So the loaded truck, with more mass, needs a larger centripetal force to hold the same circle.
The relation is direct, straight from the second law: double the mass, and the needed force doubles.
A pickup rounds the same flat curve at the same steady speed, first empty, then with its bed full of gravel. Compare the centripetal force needed on the loaded run.
A wagon carries two sandbags around a circular path at a steady speed. One sandbag is removed, and the wagon repeats the path at the same speed. Compare the centripetal force now needed.
A delivery van rounds a circular ramp at a steady speed, first empty, then carrying a full load of boxes. Compare the centripetal forces needed on the two runs.
The ramp and the speed are the same on both runs, so the needed centripetal acceleration is the same.
Giving a larger mass the same acceleration takes a larger net force.
The loaded run needs the larger centripetal force.
Ines says: a full school bus needs a larger centripetal force than the same bus empty, to round the same curve at the same steady speed. Is she correct?
A canoe follows the same circular turn at the same steady speed, first with one paddler aboard, then with two. Which statement is correct?
Four go-karts round the same flat circular track at the same steady speed. With their drivers, their total masses are 120 kg, 150 kg, 180 kg, and 210 kg. Which go-kart needs the greatest centripetal force?
A trailer is towed around a circular test loop at a steady speed, and the centripetal force needed is 800 N. The trailer is loaded so its mass doubles, and it repeats the loop at the same steady speed. Enter the centripetal force now needed in N.