Question

8 mark for review
in a demonstration, a physics teacher swings a bucket of water in a vertical circle, and the water does not spill out of the bucket. which statement correctly explains why the water does not fall out of the bucket at the top of the circle?
a the water is accelerated outward by the circular motion.
b the water is moving fast enough to have a downward centripetal acceleration greater than g.
c the centripetal force balances the force of gravity exerted on the water.
d the force of the bucket on the water and the weight of the water balance the centripetal force on the water.

Explanation:

At the top of the vertical circle, the net force acting on the water is the sum of the gravitational force (\(mg\)) and the normal force (\(N\)) from the bucket. The net force provides the centripetal force (\(F_c = ma_c\)). Using Newton's second law \(F_{net}=ma_c\), we have \(mg + N=ma_c\). For the water not to spill (\(N\geq0\)), \(a_c\geq g\). Centripetal acceleration \(a_c=\frac{v^{2}}{r}\). When \(a_c > g\), the water has enough speed so that the required centripetal acceleration (downward) is greater than \(g\). Option A is wrong because there is no "outward acceleration" in circular motion (centripetal acceleration is inward). Option C is wrong because if \(F_c = mg\) (\(a_c = g\)), it's the minimum condition (\(N = 0\)), but the correct explanation is about \(a_c>g\). Option D is wrong because the centripetal force is the net force (\(mg + N\)), not balanced by \(mg + N\).

Answer:

B. The water is moving fast enough to have a downward centripetal acceleration greater than \(g\).