Forces on a ball in a moving car

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AI Thread Summary
The discussion focuses on analyzing the forces acting on a 1 kg ball hanging from a rope in a car that accelerates at 5 m/s². It is established that the ball does experience acceleration due to the car's movement, which causes it to swing backward, forming a 10-degree angle with the vertical. Participants express uncertainty about calculating the ball's acceleration and the tension in the rope, considering the effects of gravity and the car's acceleration. The tension force is suggested to be calculated using the formula t = mg / cos(10 degrees). Overall, the thread seeks guidance on breaking down the forces into their components to solve the problem effectively.
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Homework Statement



a) A 1 kg ball hands from a 1m rope in a car accelerating at 5 m/s^2, Does the ball have an acceleration?if so what are the magnitude and direction of the balls acceleration

b) suppose the ball makes a 10 degree angle witht he vertical. If possible determine the truck's velocity, if possible determine the truck's acceleration.

Homework Equations



F=ma? lol

The Attempt at a Solution



a) Ok so i assume the ball would have an acceleration but how do i fugre it out? I know gravity acts on it and the tension of the rope acts on it...and i assume if the car is accelerating then the ball will swing backwards and settle in a position where the rope is slanting towards the back side of the car... but how do i actually calculate them? do i break down the forces in the x and y components? would then the y component be gravity straight down or gravity along the angle at which the rope is bent or what?



b) Well i know we can't determine velocity at least, but we should be able to determine the acceleration...but how?

if it makes a 10 degree angle to the vertical...then the force of tension on the rope would be t = mg / cos(10 degrees) (is this right)? I really have no idea how to do either part, can i get a hint of where to start
 
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(a) What is the ball's motion relative to the car?

(Hint: the answer is simpler than you might think.)
 
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