- #1
modulus
- 127
- 3
Homework Statement
A simple pendulum (massless string, neglect friction) is supended from the ceiling of a car taking a turn of radius 10m at a speed of 36km/h. Find the angle made by the string of the pendulum wih the vertical if this angle does not change during the turn. Take g=10ms-2
Homework Equations
The centripetal acc of the car (and the bob of the pendulum too, aince it moves along with the car)= v2/r
The Attempt at a Solution
My instinct told me that the pendulum's bob should move away from the centre of the car's circle of motion. But, the bob would also move in a circle along with car, which implies that there is a centripetal force on the bob. I think the centripetal acceleration will be provided by the tension in the string.
So, I equated the tension to the component of gravitation along the string:
T = mg secѳ
And I took the component of tension which pointed towards the center of the circle of motion of the car, and equated it to the centripetal acceleration on the bob:
T sinѳ = mv2/r
Combining the two, I got:
mg tanѳ = mv2/r
ѳ = 45®
My answer was right, but what I couldn’t understand was why the pendulum would move away from the center of the car’s circle of motion. What compells the string of the bob to do so. There wasn’t any force acting on the bob away from thecenter of the circle.
And, that question has been bugging me a lot. I think my method might also be wrong, because I can’t even justidy my opening statement to solve the problem.
Please help.