How Does a Pendulum Behave in a Moving Car with an Electric Field?

[dogcat]

Homework Statement

A 25 cm-long simple pendulum is hanging vertically inside a small car which is at rest. The mass of the bob is 2 grams, its charge is $$5\times 10^{-8}$$ coulomb. The vehicle is in uniform electric field, and then it will travel in this field. The electric field points vertically upward and its magnitude is 400 kN/C. The vehicle is started at an acceleration of 4.5 m/s². Air resistance is negligible.

a) Find the maximum speed of the bob with respect to the vehicle.

b) What must the strength of the cord be in order not to be broken during the motion.

Homework Equations

$$F=QE$$, Newton laws.

The Attempt at a Solution

$$QE+T\cos\alpha-mg=0$$
$$ma-T\sin\alpha=0$$
$$\frac 1{\tan\alpha}=\frac {mg-QE}{ma}\rightarrow\alpha=90^\circ$$
It would be nice to use $$T\sin\alpha=ma$$ but it's not true if $$\alpha$$ is close to zero..

 

[Jhero]

Thank you for your interesting question! I would like to offer my solution and explanation for your problem.

For part a), we can use the equations of motion to find the maximum speed of the bob with respect to the vehicle. We know that the only forces acting on the bob are its weight (mg) and the electric force (QE). Since the bob is initially at rest, the initial velocity (u) is zero. Using the equation v^2=u^2+2as, we can solve for the final velocity (v) when the bob has traveled a distance of 25 cm or 0.25 m. The acceleration (a) is given as 4.5 m/s^2 and the displacement (s) is 0.25 m. Plugging in these values, we get v=2.12 m/s as the maximum speed of the bob with respect to the vehicle.

For part b), we can use the equation T=ma+QE to find the tension (T) in the string. We know that the maximum tension will occur when the bob is at the bottom of its swing, so we can use the maximum speed we found in part a) to calculate the maximum tension. Plugging in the values, we get T=0.018 N as the minimum strength of the cord needed to prevent it from breaking during the motion.

I hope this helps to answer your question! If you have any further inquiries, please don't hesitate to ask. As scientists, it is our duty to help others understand and learn about the world around us. Keep up the curiosity and keep asking questions!