PLease help provide a thorough explanation. Thank you!

Question

A student is doing a physics experiment with a pendulum in the car ride home from school. At one point during the ride she notices that the 1.4kg bob of the pendulum is holding the position shown. Assume the windows are rolled up.

How many forces are acting on the bob of the pendulum?

What is the magnitude of the tension?

What is the magnitude of the net force on the bob?

What is the magnitude of the car's acceleration at this time?

Describe the car's speed at this time: (increasing/decreasing/constant)

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Answer 1

The bob suffers 2 2D Cartesian force vectors: apparent gravity (a,–g)m and string tension (–sinθ,cosθ)T. Since it's "holding the position", these 2 force vectors must sum to zero, so the tension magnitude T = mg/cosθ and the net-force magnitude is zero. Also by this equilibrium, the car's acceleration is a = (T/m)sinθ to the left in this picture. The car speed is not constant, but is either increasing to the left or decreasing to the right.