pseudo force (non-inertial frames)

Question

In an accelerating car (a = 4 m/s² forward), a pendulum bob of mass 0.2 kg hangs at equilibrium making an angle θ with the vertical. Neglect air resistance. Find tan θ.

RankGuru · Accepted Answer

1. **Analyze in Non-Inertial Frame**: For an observer inside the accelerating car, the bob is in equilibrium, but a **pseudo force** must be added.
2. **Forces on Bob**:
   - **Weight**: $mg$ downwards.
   - **Pseudo Force**: $ma$ backwards (opposite to car acceleration).
   - **Tension**: $T$ along the string.
3. **Equilibrium Equations**:
   - Vertical: $T \cos 	heta = mg$
   - Horizontal: $T \sin 	heta = ma$
4. **Divide Equations**: $\frac{T \sin 	heta}{T \cos 	heta} = \frac{ma}{mg} \implies 	an 	heta = \frac{a}{g}$.
5. **Substitute Values**: $	an 	heta = \frac{4}{10} = 0.40$.
6. **Final Result**: The tangent of the angle is **$0.40$**.

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pseudo force (non-inertial frames)

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