Timmy the angry teen twirls dead rat mass is 2kg attached to the rusty chain length 1m in a vertical circle with what velocity should timmy rotates so that the chain just goes slack no force in the chain at the top?
at the top>
forcegravaity=centripetal force
mg=mv^2/r
v=sqrt(rg)
To find the velocity at which the chain will go slack when Timmy twirls the dead rat in a vertical circle, we need to consider the forces acting on the rat and the chain. At the top of the circle, when the chain is about to go slack, there will be no force acting on the chain.
To begin, let's consider the forces acting on the rat at the top of the loop. There are two forces to consider: the gravitational force (mg) pulling the rat downward and the tension force (T) in the chain pulling the rat inward towards the center of the circle.
At the top of the loop, the net force acting on the rat must be equal to zero for the chain to go slack. This means that the tension force in the chain must exactly balance out the weight of the rat.
Hence, we can set up the following equation:
Tension force (T) - Weight of the rat (mg) = 0
The weight of the rat can be calculated using the formula:
Weight (mg) = mass (m) × gravitational acceleration (g)
Given that the mass of the rat is 2 kg and the gravitational acceleration (g) is approximately 9.8 m/s², we can substitute these values into the equation:
T - 2 kg × 9.8 m/s² = 0
Simplifying the equation further, we get:
T - 19.6 N = 0
Now, to find the velocity at which the chain will go slack, we need to consider the centripetal force acting on the rat at the top of the loop. The centripetal force (Fc) is given by the formula:
Centripetal force (Fc) = mass (m) × velocity² (v²) / radius (r)
In this case, the radius (r) of the circle is given as 1 m.
Setting the centripetal force equal to the tension force, we can write:
T = m × v² / r
Substituting the value of tension (T) from the earlier equation, we get:
19.6 N = 2 kg × v² / 1 m
Simplifying the equation, we find:
19.6 N = 2 kg × v²
Next, we rearrange the equation to solve for the velocity (v):
v² = 19.6 N / 2 kg
v² = 9.8 m²/s²
Taking the square root of both sides, we get:
v = √(9.8 m²/s²)
Calculating the square root, the velocity (v) at which the chain will go slack is approximately 3.13 m/s.
Therefore, Timmy needs to rotate the dead rat with a velocity of approximately 3.13 m/s to make the chain go slack at the top of the vertical circle.
To find the velocity at which the chain just goes slack at the top, we can use the concept of centripetal force.
Step 1: Determine the force required to keep the chain taut at the top.
At the top of the circle, the tension in the chain is equal to the weight of the rat. The tension can be calculated using the formula:
Tension = Mass * gravitational acceleration
Given that the mass of the rat is 2 kg and the gravitational acceleration is approximately 9.8 m/s^2, the tension in the chain at the top is:
Tension = 2 kg * 9.8 m/s^2 = 19.6 N
Step 2: Determine the velocity at which the chain just goes slack.
Since the chain goes slack at the top of the circle, at that point, the tension in the chain is zero. The centripetal force necessary to keep circular motion can be calculated using the formula:
Centripetal force = Mass * Velocity^2 / Radius
In this case, the centripetal force is 19.6 N, the mass is 2 kg, and the radius is 1 m (as given in the question). The equation can be rearranged to solve for velocity:
Velocity^2 = (Centripetal force * Radius) / Mass
Substituting the given values:
Velocity^2 = (19.6 N * 1 m) / 2 kg
Velocity^2 = 9.8 N*m/kg
Velocity ≈ √9.8 m^2/s^2
Velocity ≈ 3.13 m/s
Therefore, Timmy should rotate with a velocity of approximately 3.13 m/s in order for the chain to go slack at the top with no force in the chain.