Find tension of string in a pendulum

[Jtappan]

Homework Statement

A pendulum is 0.615 m long and the bob has a mass of 1.37 kg. When the string makes an angle of =14.1° with the vertical, the bob is moving at 1.40 m/s. Find the tangential and radial acceleration components and the tension in the string. [Hint: Draw an FBD for the bob. Choose the x-axis to be tangential to the motion of the bob and the y-axis to be radial. Apply Newton's second law.]
at = _____m/s2
ar = _____ m/s2
T = _______ N

Homework Equations

F=MA

The Attempt at a Solution

I have tried breaking up the forced using the FBD but I cannot get the right answer for any of them. I have no idea what I am doing wrong. For the tangential acceleration i got: 6.54 and 6.74 doing it two different ways. For tension I got 13.02 N and those are still not correct...

 

[Anadyne]

In the y (radial) direction there is T and a component of gravity.
In the x (tangential) direction, there is only the other component of gravity.

So figure out Fnet in the tangential direction then Fnet in the radial direction.

 

[ogb p]

To find the tension in the string, we need to use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration (F=ma). In this case, the net force acting on the bob is the tension in the string.

First, let's draw a free body diagram for the bob. The forces acting on the bob are the tension in the string (T), the weight of the bob (mg), and the radial component of the tension (Tr). The tangential component of the tension (Tt) is the force that causes the bob to accelerate tangentially.

Next, we can break up the forces into their components. The tangential component of the tension (Tt) is equal to Tsinθ, where θ is the angle the string makes with the vertical. Similarly, the radial component of the tension (Tr) is equal to Tcosθ.

Since we know the mass of the bob and its tangential acceleration, we can use Newton's second law to solve for the tension in the string. We can set the equation equal to the tangential component of the tension (Tt) and solve for T.

Tsinθ = ma
Tsin14.1° = (1.37 kg)(1.40 m/s2)
T = 13.02 N

Therefore, the tension in the string is 13.02 N.

To find the tangential and radial acceleration components, we can use the equations at = rα and ar = rω2, where r is the length of the string and α is the angular acceleration.

Since the bob is moving at a constant speed, its angular acceleration is 0 and therefore its tangential acceleration is also 0. The radial acceleration can be found by substituting the given values into the equation.

ar = (0.615 m)(1.40 m/s2)2
ar = 1.12 m/s2

Therefore, the tangential acceleration is 0 m/s2 and the radial acceleration is 1.12 m/s2.