Calculating Tension of a Pendulum at 4.0 m/s

[Morhas]

Homework Statement

A 1.2 m long pendulum reaches a speed of 4.0 m/s at the bottom of its swing.
http://members.shaw.ca/barry-barclay/Self-Tests/test07/q02.gif
What is the tension in the string at this position?

Homework Equations

Fnet=Mv^2/r

The Attempt at a Solution

Im my FBD I had FT acting up, and fg acting down.

Ft-Fg=mv^2/r
Ft-mg=mv^2/r
Ft -(9.8)(3)=(3)(4.0)^2/(1.2)
Ft=40 +(9.8)(3.0)

EDIT Realized my mistake less than a second after posting this. :) Mods can delete.

 

[anathema]

I would like to point out that your solution is incorrect. The equation you used, Fnet = Mv^2/r, is only valid for circular motion. The motion of a pendulum is not circular, it is an example of simple harmonic motion. Therefore, the correct equation to use is Fnet = -kx, where k is the spring constant and x is the displacement from equilibrium.

To find the tension in the string at the bottom of the swing, we need to first find the displacement at that position. Using the given information, we know that the length of the pendulum is 1.2 m and the speed at the bottom is 4.0 m/s. We can use the equation for the velocity of a pendulum, v = √(gL(1-cosθ)), where g is the acceleration due to gravity and θ is the angle of displacement. At the bottom of the swing, θ = 0, so the equation simplifies to v = √(gL). Plugging in the given values, we get v = √(9.8*1.2) = 3.43 m/s.

Now, we can use the equation Fnet = -kx to find the tension. At the bottom of the swing, the displacement is equal to the length of the pendulum, so x = 1.2 m. We also know that the net force is equal to the weight of the pendulum, which is mg. Therefore, we have:

mg = -kx
k = -mg/x
k = -(3*9.8)/1.2
k = -24.5 N/m

Finally, we can use this value of k in the equation Fnet = -kx to find the tension at the bottom of the swing:

Ft = -kx
Ft = (-24.5)(1.2)
Ft = -29.4 N

Therefore, the tension in the string at the bottom of the swing is 29.4 N.

 

[baba89]

I would like to point out that the formula used in the attempt at a solution is incorrect. The correct formula for calculating the tension in a pendulum string is T=mgcosθ, where θ is the angle between the string and the vertical direction. In this case, θ would be 90 degrees since the pendulum is at the bottom of its swing. Therefore, the tension in the string would simply be equal to the weight of the pendulum, which is mg. However, the value of g should be taken as 9.8 m/s^2, not 9.8 N. So the correct calculation would be T= (3 kg)(9.8 m/s^2) = 29.4 N.