Timmy twirls a dead rat (mass = 2 kg) attached to a rusty chain (length = 1m) in a vertical circle. With what

velocity should Timmy rotate the rodent so that the chain just goes slack (no force in the chain) at the top?

pls answer :(

You find velocity from acceleration formula: a=v^2/r

Your acceleration is 9.81 m/s^2 but for this problem round it to 10 m/s^2.
Plug in acceleration and radius on your formula:
a=v^2/r ==> 10=v^2/1 (Multiply both sides by 1 to get rid of the fraction you end up with:) 10=v^2 (to get rid of the square you square root both, the 10 and v^2) The square root of 10 is 3.16 which is also your answer: 3.16 m/s^2

3.16m/s

ignoring chain weight?

at the top, mg=mv^2/r
v=sqrt (rg)

3.16m/s

To find the velocity at which the chain goes slack at the top of the vertical circle, we need to determine the tension in the chain when it is at its lowest point and at the top point. At both points, the net force acting on the rat should be equal to zero.

Let's start by finding the tension at the lowest point of the circle. At the lowest point, the rat's weight is acting downwards, and the tension in the chain is acting upwards. So we have:

Tension - Weight = Centripetal Force

The weight of the rat can be calculated using the formula: weight = mass * gravitational acceleration. Assuming the gravitational acceleration to be 9.8 m/s², the weight of the rat is:

Weight = 2 kg * 9.8 m/s² = 19.6 N

At the lowest point, the centripetal force is just the tension, so we can rewrite the equation as:

Tension = Weight

Therefore, the tension at the lowest point of the circle is 19.6 N.

Now, let's move on to finding the tension at the top of the circle when the chain goes slack. At this point, the tension is zero, and the only force acting on the rat is its weight. So we have:

Weight = Centripetal Force

Again, the weight is 19.6 N, but now it is the centripetal force. We can use the centripetal force formula: centripetal force = (mass * velocity²) / radius, where the radius is the length of the chain.

19.6 N = (2 kg * velocity²) / 1 m

Rearranging the equation, we find:

velocity² = (19.6 N * 1 m) / 2 kg
velocity² = 9.8 m²/s²
velocity ≈ 3.13 m/s

Therefore, Timmy needs to rotate the rat with a velocity of approximately 3.13 m/s in order for the chain to go slack at the top of the vertical circle.

Timmy the angry teen twirls a dead rat (mass = 2 kg) attached to a rusty chain (length = 1m) in a vertical circle. With what

velocity should Timmy rotate the rodent so that the chain just goes slack (no force in the chain) at the top?

Yeh