# 2008 us physics olympiad pendulum in electric field

• timetraveller123
In summary: OK now i get the solution what it essentially means is that there is combined effective "gravity" pointing not directly down but at an angle of θo and then when you do the coordinate transformation such that the effective "gravity" is pointing directly down you get the equation from then on its just mathematical manipulation am i right?
timetraveller123

1. Homework Statement

i was solving the 2008 semi final us physics olympiad paper when i got stuck on question B2 in part 2
the link takes you a pdf with questions and solution however i don't understand the soution to B2 i get part ai) but not part aii) how do you prove the motion is simple harmonic and i am not sure how they derive the period in that way

## Homework Equations

T = 2π/ω
f = q E
V = Ed
f = mg
sin θ ≈ tan θ ≈ θ

## The Attempt at a Solution

i tried to turn the coordinate system such that the equilibrium is in a vertical position but failed miserably i also tried taking a force approach and also failed i have no idea how to start please help

vishnu 73 said:
i tried to turn the coordinate system such that the equilibrium is in a vertical position but failed miserably i also tried taking a force approach and also failed i have no idea how to start please help
Please show us your attempt. If you just say that you attempted it we have no way of knowing where you went wrong.

vishnu 73 said:
sin θ ≈ tan θ ≈ θ
Note that this is true only for small angles. The way the problem is stated, there is no guarantee that ##\theta_0## or ##\theta## is small. What is small in the problem is the difference ##\theta - \theta_0##.

Orodruin said:
Please show us your attempt. If you just say that you attempted it we have no way of knowing where you went wrong.Note that this is true only for small angles. The way the problem is stated, there is no guarantee that ##\theta_0## or ##\theta## is small. What is small in the problem is the difference ##\theta - \theta_0##.
the problem is i know no way of how to start
i don't even how to set up the differential equation for this problem and i meant θ - θ0 is small not the actual angle itself
the reason why i say that is that because the force due to electric field and gravity are constant throughout the motion then why should there be a restoring force unlike the spring oscillator in which there is a restoring force thus there is SHM

Last edited:
vishnu 73 said:
the problem is i know no way of how to start
i don't even how to set up the differential equation for this problem and i meant θ - θ0 is small not the actual angle itself
the reason why i say that is that because the force due to electric field and gravity are constant throughout the motion then why should there be a restoring force unlike the spring oscillator in which there is a restoring force thus there is SHM

Well, you said that you wanted to try to write the problem in a rotated coordinate system. What do you get when you do that?

Also, the gravitational force on a standard pendulum is constant - yet it performs SHM for small angles. Do you understand why?

Orodruin said:
Well, you said that you wanted to try to write the problem in a rotated coordinate system. What do you get when you do that?

Also, the gravitational force on a standard pendulum is constant - yet it performs SHM for small angles. Do you understand why?

oh wait i forgot that while force remains the same the tangential components and the radial components of the force change let me try again give me some time

OK now i get the solution what it essentially means is that there is combined effective "gravity" pointing not directly down but at an angle of θo and then when you do the coordinate transformation such that the effective "gravity" is pointing directly down you get the equation from then on its just mathematical manipulation am i right?

## 1. What is the concept behind the 2008 US Physics Olympiad Pendulum in Electric Field?

The 2008 US Physics Olympiad Pendulum in Electric Field is a theoretical problem that challenges students to apply their knowledge of electric fields and pendulum motion to solve a complex physics problem.

## 2. How does the electric field affect the motion of the pendulum in this problem?

The electric field exerts a force on the charged pendulum, causing it to deviate from its natural path and follow a curved trajectory. This force is dependent on the strength and direction of the electric field, as well as the charge and mass of the pendulum.

## 3. What are the key equations used to solve the 2008 US Physics Olympiad Pendulum in Electric Field?

The main equations used in this problem are the equations of motion for a pendulum and Coulomb's Law. Additionally, students may also need to use the equations for electric potential and electric field intensity.

## 4. How can I prepare for a problem like the 2008 US Physics Olympiad Pendulum in Electric Field?

To prepare for this type of problem, it is important to have a strong understanding of basic physics principles such as electric fields and pendulum motion. Practice solving similar problems and familiarize yourself with the relevant equations and their applications.

## 5. What are the key takeaways from solving the 2008 US Physics Olympiad Pendulum in Electric Field?

Solving this problem requires critical thinking and the ability to apply various physics concepts to a complex scenario. It also highlights the importance of understanding the relationship between different physical quantities and how they affect the motion of objects.

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