a 5.0 kg mass attached to the end of a string swings in a vertical circle (radius 2m) when the mass is at its lowest point on the circle the speed of the mass is 12 m/s. What is the tension of the string at this point?

ma=T-mg

mv²/R=T - mg
T = mv²/R + mg

To calculate the tension of the string at the lowest point of the swing, we can use the concept of centripetal force.

The centripetal force is the force that keeps an object moving in a circular path and is always directed towards the center of the circle. In this case, the tension in the string provides the centripetal force necessary to maintain the circular motion.

At the lowest point of the circle, the tension force can be represented as the sum of two forces: the tension force (

T

) and the weight of the object (

mg

). The weight is given by the mass of the object (

m

) multiplied by the acceleration due to gravity (

g

).

Since the object is moving in a vertical circle, we can express the centripetal force in terms of the speed of the object (

v

) and the radius of the circle (

r

). The centripetal force (

F

c

) is equal to the mass of the object (

m

) multiplied by the square of the velocity (

v

) divided by the radius of the circle (

r

).

Setting up the equation:

F

c

= T + mg

F

c

= m

v^2

r

Because the speed was given as 12 m/s and the radius of the circle is 2 m, we can substitute these values into the equation:

m

v^2

r

= T + mg

(5.0 kg) * (12 m/s)^2 / (2 m) = T + (5.0 kg) * (9.8 m/s^2)

Solving this equation will give us the tension of the string at the lowest point.

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