# A Penny Falling Off a Non-moving Sphere

• Juan42
In summary, the problem involves a penny being released from a smooth sphere and sliding down to a certain point. The objective is to find the distance the penny falls from the point of contact between the sphere and the platform. Relevant equations include (1) V=Vo+at, (2) a=(V^2)/9.8, and (3) V^2=Vo^2+2a(x-xo). The attempt at a solution involves using conservation of energy to find the speed at which the penny leaves the sphere, then considering the forces at that point to find the distance it falls.
Juan42

## Homework Statement

A penny is released from the top of a very smooth sphere of radius 1 m. The sphere is fixed to a platform and doesn't move. The penny slides down from rest and leaves the sphere at a certain point. How far will the penny fall away from the point of contact of the sphere and the platform?

## Homework Equations

(1) V = Vo + at
(2) a = (V^2)/9.8
(3) V^2 = Vo^2 + 2a(x - xo)

## The Attempt at a Solution

Vo = 0 m/s
r = 1 m
a = g = 9.8 m/(s^2)
x = ? => The distance the penny fell from the top of the sphere to ground.

I used (1) in order to rearrange into

t = V/g

After doing that, I was thinking that maybe I could use (2) or (3) to rearrange the equation a little more to find the solution, but I'm sure that's not right, and I'm doing too much work. I've attached a pdf of the problem.

#### Attachments

• Challenging_3_PHY131.pdf
15.3 KB · Views: 287
Juan42 said:
(1) V = Vo + at
That's only valid for constant acceleration, which this is not. You need to find the point at which the penny leaves the sphere. Suppose the radius to that point makes an angle theta to the vertical. Use conservation of energy to find its speed there, then consider the forces on the penny at that point.

## 1. How does gravity affect a penny falling off a non-moving sphere?

Gravity is the force that pulls objects towards the center of the Earth. Since the sphere is not moving, the penny will fall straight down towards the ground due to the force of gravity.

## 2. Will the penny fall off the sphere at the same rate as it would if it were dropped from a stationary object?

Yes, the penny will still fall at a constant rate of 9.8 meters per second squared, regardless of whether it is falling off a sphere or being dropped from a stationary object.

## 3. Will the size or weight of the sphere affect the penny's fall?

No, as long as the sphere is not moving, the size or weight of the sphere will not affect the penny's fall. The force of gravity will act on the penny in the same way regardless of the sphere's characteristics.

## 4. What will happen if the sphere is spinning while the penny falls off?

If the sphere is spinning, the penny will still fall towards the ground due to gravity, but its trajectory may be affected by the spinning motion. The penny may fall off at an angle or be deflected by the spinning sphere.

## 5. Can the penny fall off the sphere in any direction?

Yes, the penny can fall off the sphere in any direction as long as it is not being held or guided by external forces. The direction of the penny's fall will depend on the sphere's position and any additional forces acting on the penny.

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