Speed of Pendulum: Solving for Bob at Bottom of String

[Klaven]

Homework Statement

A 2.0 M long pendulum released from rest with the support string at an angle of 25 degrees with the vertical. What is the speed of the bob at the bottom of the string?

Homework Equations

PE = mgy
KE = 1/2mv^2
Trig functions

The Attempt at a Solution

I just need help getting the problem started, in the potential energy formula, we have two unknowns(unless the 2.0 m has to do with the location of the bob, but i am not certain).

Thanks in advance :]

 

[Fluent]

Yes, the 2.0m has something to do with the location of the bob. Use the bottom of the pendulum's course (2.0 m) as the reference point (at this point the PE is 0 and the KE is at a maximum).

Ill give you a shove in the right direction. Let's say the height of the bob at it's location at 25 degrees to the vertical is 2.0 - (2.0)cos25.

Hope this helps.

 

[thomate1]

I would first begin by defining the problem and identifying what information is given and what is needed. In this case, we are given the length of the pendulum (2.0 m), the angle of the support string (25 degrees), and we are asked to find the speed of the bob at the bottom of the string.
Next, I would consider the physical principles and equations that are relevant to this problem. In this case, we can use the equations for potential energy (PE = mgy) and kinetic energy (KE = 1/2mv^2) to solve for the speed of the bob. Additionally, we can use trigonometric functions to relate the angle of the support string to the vertical direction.
To begin solving the problem, we can first calculate the potential energy at the top of the pendulum (where it is released from rest). This will be equal to the kinetic energy at the bottom of the pendulum (where the bob is located). We can then set these two energies equal to each other and solve for the velocity (v) using the mass (m) and the height (y) of the bob.
Using trigonometric functions, we can also determine the vertical height (y) of the bob at the bottom of the string. This will involve using the length of the pendulum and the angle of the support string. Once we have determined the height (y), we can substitute it into the equation for kinetic energy and solve for the velocity (v).
In conclusion, we can use the equations for potential and kinetic energy, along with trigonometric functions, to solve for the speed of the bob at the bottom of the string. By clearly defining the problem and utilizing relevant physical principles and equations, we can successfully solve for the desired quantity.