Calculating Tension in a Rope: A 2kg Stone and 1m Radius

[Atilla1982]

A stone with mass 2,0kg is tied to a rope with radius 1 meter to the circle center, and has the velocity 4 m/s.

a) What's the tension on the rope on the top point of the circle?

b) What's the tension on the rope on the bottom point of the circle?


Here's my attempt to solve these.

a) Fc = mv^2/r Fg= mg Ft= the force applied on the rope

Fc=Ft + Fg
Ft=Fc - Fg
Ft=mv^2/r - mg
Ft=2*4^2/1 - 2*9,8
Ft=12,4 N

b)
Fc=Ft - Fg
Ft=Fc + Fg
Ft=mv^2/r + mg
Ft=2*4^2/1 + 2*9,8
Ft=51,6 N

Can anyone please verify that this is correct?

 

[Doc Al]

Both of your solutions are correct.

 

[quicknote]

Yes, your calculations appear to be correct. To verify, we can use the equation for centripetal force, Fc = mv^2/r, where m is the mass of the stone, v is the velocity, and r is the radius of the circle. Plugging in the given values, we get Fc = 2*4^2/1 = 32 N. This is the force that is acting on the rope at all points along the circle.

At the top point of the circle, the only other force acting on the rope is the weight of the stone, Fg = mg = 2*9.8 = 19.6 N. Therefore, the tension on the rope at the top point is Fc - Fg = 32 - 19.6 = 12.4 N.

At the bottom point of the circle, the tension on the rope is the sum of the centripetal force and the weight of the stone, Fc + Fg = 32 + 19.6 = 51.6 N. This is because at the bottom point, the force of gravity is acting in the same direction as the centripetal force, so they add together.

Overall, your calculations and reasoning are correct. Keep up the good work!