Pendulum and Oscillating Motion

[cstout]

Homework Statement

A pendulum is 0.8 m long and the bob has a mass of 1.0 kg. At the bottom of its swing, the bob's speed is 1.8 m/s. What is the tension in the string at the bottom of the swing?

I don't even know how to get started on this problem, I think it has something to do with using the sin or cos but I can't find an example problem like this in my book.

 

[Tedjn]

At the bottom of its swing, the only two factors putting forces on the bob must be the rope (tension) and gravity (weight). Thus, the two together must be the net force. What else is special about the motion of a pendulum bob? How is the velocity changing?

 

[Moetasim]

I can offer some guidance on how to approach this problem. First, we need to understand the basic principles of pendulum and oscillating motion. A pendulum is a weight suspended from a pivot point that can freely swing back and forth. This motion is called oscillation and is governed by the laws of physics, specifically the principles of energy and motion.

To solve this problem, we can use the equation for the tension in a string, which is given by T = mgcosθ, where T is the tension, m is the mass of the bob, g is the acceleration due to gravity, and θ is the angle between the string and the vertical direction. In this case, we can assume that the angle is 90 degrees since the bob is at the bottom of its swing.

Next, we need to find the value for g, which is approximately equal to 9.8 m/s^2. We can also use the equation for velocity in a pendulum, which is given by v = √(2gl(1-cosθ)), where v is the velocity, g is the acceleration due to gravity, and l is the length of the pendulum. In this case, we know the velocity (1.8 m/s) and the length (0.8 m), so we can solve for g.

Once we have the value for g, we can plug it into the equation for tension and solve for T. This will give us the tension in the string at the bottom of the swing.

In summary, to solve this problem, we need to use the equations for tension and velocity in a pendulum, as well as the known values for mass and length. By using these principles, we can determine the tension in the string at the bottom of the swing.