- #1

PhysicsDaoist

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## 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?

## Homework Equations

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?