# Pendulum inside a small car

1. Apr 14, 2009

### dogcat

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

$$F=QE$$, Newton laws.

3. 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..