Tension in string of pendulum

[carney]

The mass of the ball is m, as given below in kg. It is released from rest. What is the tension in the string (in N) when the ball has fallen through 45o as shown.

Hint: First find the velocity in terms of L and then apply Newton's 2nd law in normal and tangential directions. If you do it correctly, L should disappear from your equation.


m[kg] = 1.58;

 

[thrill3rnit3]

Where's your work?

 

[topgun08]

The below information may not be correct...

Perhaps start with drawing a Free Body Diagram at the degree angle. Their is T tension, the force downward mg, and the force balancing tension, mgsin(theta).

Summing the forces to find the centripetal Force one gets:
Centripetal Force = T - mgsin(theta)
---Apllying Newton's 2nd Law ---
ma = T - mgsin(theta)

in centripetal motion a = (v^2)/r where r is L.

Thus
mv^2/L = T - mgsin(theta)
T = mv^2/L + mgsin(theta)

The only issue is that we have two variables (T and L) and only one equation. So we need another equation. We turn to using Energy.

Original PE = New PE + KE
mgL = mg(.5L) + .5mv^2
L = v^2/g

plugging back into original equation one solves for T

I think this is right, but maybe wait for a more advanced member to comment.

 

[sfsy1]

Original PE = New PE + KE
mgL = mg(.5L) + .5mv^2
L = v^2/g

The change in GPE is (sin45)Lgm, not 0.5Lgm.

 

[rwisz]

I would approach this problem by first understanding the physical principles at play. In this case, we are dealing with a pendulum, which is a simple harmonic oscillator. This means that the motion of the pendulum can be described by the conservation of energy and Newton's laws of motion.

To find the tension in the string, we need to consider the forces acting on the ball at the given position. At 45 degrees, the ball will have a velocity in the tangential direction and a force acting on it due to gravity in the normal direction.

Using Newton's second law, we can set up equations for the forces in the normal and tangential directions. In the normal direction, we have the force of gravity, which is equal to the mass of the ball (m) multiplied by the acceleration due to gravity (g). In the tangential direction, we have the tension in the string (T) acting in the opposite direction of the velocity (v).

By setting these equations equal to each other and solving for T, we can find the tension in the string at 45 degrees. This will give us a value in Newtons (N), which is the unit of force.

It is important to note that the length of the string (L) does not appear in this equation. This is because the tension in the string is dependent on the mass of the ball and the acceleration due to gravity, not the length of the string.

In conclusion, to find the tension in the string of a pendulum at a specific angle, we can use Newton's second law and set up equations for the forces acting on the ball. By solving for the tension, we can determine the force in Newtons at that particular angle.