# Another bucket of water, centripedal force problem

• PhysicsDaoist
In summary: The bucket is easier because it is held down by the string.In summary, the conversation discusses a problem involving a bucket of water being whirled in a circular motion with a rope. It includes calculations for the acceleration, net force, and tension of the rope at different speeds. The question of whether the tension can be negative and the implication of this on circular motion is also raised. The conversation also considers the scenario of a roller coaster cart on a frictionless track and the concept of normal force.
PhysicsDaoist

## Homework Statement

This is a classic problem with a slight twist on followon questions -
A 1.50-kg bucket of water is tied by a rope and whirled in a circle with a radius of 1.00 m. At the top of the circular loop, the speed of the bucket is 4.00 m/s. a) Determine the acceleration, the net force and the individual force values when the bucket is at the top of the circular loop.
b) What if the velocity becomes 2 m/s? What is the tension (Ft) of the rope?
c) Can the tension be negative? Will cirular motion still hold when Ft is negative?

Ft = F_net - mg
F_net = m v^2/r

## The Attempt at a Solution

I can solve (a) easily -> a_c = v^2/r = 16 m/s^2; F_net = 24 N (down); Ft = 9.29 N.
and plugging in eqt. I also get (b)
a_c = 4 m/s^2; F_net = 6 N (down); Ft = -8.72 ! negative tension??
c) I have problem with this? In fact, I ran this in excel with velocity all the way down to 0.1 m/s and of course F_tens are negative, what does this mean? Does it mean that the bucket is not traveling in circular motion?
What if this is NOT a rope but roller coaster cart in frictionless track? does that mean the normal force acting on the cart change direction when velocity drops below certain threshold? Can someone help me with the free-body-diagram here?

Tricky business. For (a) it takes an Fc downward of 24 N to hold the bucket in circular motion. Gravity provides 14.7 N of this; the tension must provide the remaining 9.3 N.
For (b) it only takes 6 N to maintain circular motion and gravity still pulls with 14.7 N - too much - so the bucket will fall out of circular motion and spill the water. The string can't push upward to reduce the downward force to the required 6 N.

A roller coaster rides on top of the track, doesn't it? If so, it is in no danger of falling because the track holds it up. But in the (a) case it would be launched into the air unless the track can also hold it down.

## 1. What is the "another bucket of water, centripedal force problem"?

The "another bucket of water, centripedal force problem" is a physics problem that involves a bucket of water being swung in a circular motion on a string. It is used to demonstrate the concept of centripetal force and its relationship with the mass, velocity, and radius of an object in circular motion.

## 2. What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is necessary to maintain circular motion.

## 3. How does the mass of the bucket affect the centripetal force?

The mass of the bucket affects the centripetal force in a direct relationship. This means that as the mass of the bucket increases, the centripetal force required to keep it moving in a circular path also increases.

## 4. How does the velocity of the bucket affect the centripetal force?

The velocity of the bucket affects the centripetal force in a direct relationship. This means that as the velocity of the bucket increases, the centripetal force required to keep it moving in a circular path also increases.

## 5. How does the radius of the circular motion affect the centripetal force?

The radius of the circular motion affects the centripetal force in an inverse relationship. This means that as the radius of the circular motion increases, the centripetal force required to keep the bucket in circular motion decreases. In other words, the larger the radius, the less centripetal force is needed to keep the bucket moving in a circular path.

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