Physics question?

Question

A car is accelerating at a rate of 2.3m/s^2. a mass of 250 g is hanging from the ceiling on a string 1.2m long. What is the angle that the string makes with the verticle

Answer 1

consider a fbd of the mass, use T as the tension of the string and θ as the angle of the string w/r/t vertical

Vertical forces
m*g-T*cos(θ)=0
Horizontal forces
T*sin(θ)-m*a=0
the a is actually towards the back of the car assuming the car is accelerating forward.
Let's do some algebra
T*cos(θ)=m*g
T*sin(θ)=m*a

divide the two equations to get

Tan(θ)=a/g
θ=13.2 degrees to the rear of the car from vertical.

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