- #1
Joshua A
- 10
- 0
Homework Statement
You hold a small ice cube near the top edge of a hemispherical bowl of radius 100 mm. You release the cube from rest. What is the magnitude of its acceleration at the instant it reaches the bottom of the bowl? Ignore friction.
Homework Equations
ΣF = ma
Fg = mg
The Attempt at a Solution
I know that when the ice cube is held at the top of the bowl (horizontal), there is a downward force due to gravity and no centripetal force. This downward force causes the ice cube to accelerate downwards. The instant the ice cube begins to slide down, there is an increasing centripetal force (equal to the force of gravity that is perpendicular to the bowl) in order to change the direction of the ice cube.
At the bottom of the bowl, the entire force of gravity is perpendicular to the bowl. I know that the ice cube will continue in circular motion so it's direction cannot change and there must be some acceleration at the bottom pointing upwards. This acceleration is due to the normal contact force the bowl exerts on the ice cube.
ΣF = ma
ΣF = Fnormal - Fg = Fnormal - mg = ma
a = Fnormal/m - g
The magnitude of the acceleration given from that equation will give me the answer to the question. However, I do not know how to find out what the normal force is.
Could someone help me figure out how to finish my answer? If there is a better/easier way to approach this problem, let me know.