Finding acceleration from the angle made by a hanged ball.

[Mohamed BOUCHAKOUR]

Homework Statement

A ball with a mass of 200g, is hanged on the roof of a bus with a rope (it's mass is negligible), when the bus starts moving, the rope makes an angle of 18°.
What's the acceleration of the bus?

Homework Equations

ΣF=m.a

The Attempt at a Solution

The first thing i thought of is air friction, but it related to speed not acceleration, and the ball is inside the bus, it would be negligible.
Nothing exept that came to my mind.

 

[kuruman]

You're right, air resistance is not an issue because the air moves with the bus. How about drawing a free body diagram?

 

[PeroK]

Homework Statement

A ball with a mass of 200g, is hanged on the roof of a bus with a rope (it's mass is negligible), when the bus starts moving, the rope makes an angle of 18°.
What's the acceleration of the bus?

Homework Equations

ΣF=m.a

The Attempt at a Solution

The first thing i thought of is air friction, but it related to speed not acceleration, and the ball is inside the bus, it would be negligible.
Nothing exept that came to my mind.

You can ignore the air resistance. Two questions:

What happens to something inside the bus that is attached to the bus?

What happens to something inside the bus that is not attached to the bus?

 

[Mohamed BOUCHAKOUR]

You're right, air resistance is not an issue because the air moves with the bus. How about drawing a free body diagram?

Yeah, but the only forces i can think of are gravity and rope.

 

[Mohamed BOUCHAKOUR]

If somthing is attached

You can ignore the air resistance. Two questions:

What happens to something inside the bus that is attached to the bus?

What happens to something inside the bus that is not attached to the bus?

If somthing is attached, it accelerate at the same rate as the bus.
And if it's not (ignoring friction) it would roll back.
But how does that help me?

 

[PeroK]

If somthing is attached, it accelerate at the same rate as the bus.

Yes.

And if it's not (ignoring friction) it would roll back.

Is the ball in this case rolling back?

 

[Mohamed BOUCHAKOUR]

Is the ball in this case rolling back?

In a way yes(the 18° angle) , but then the rope prevents it from continuing,

 

[PeroK]

In a way yes(the 18° angle) , but then the rope prevents it from continuing,

What does that mean in the ground frame?

What does someone outside the bus see happen to the ball? Is it rolling/stationary/accelerating?

 

[Mohamed BOUCHAKOUR]

What does that mean in the ground frame?

What does someone outside the bus see happen to the ball? Is it rolling/stationary/accelerating?

Accelerating

 

[PeroK]

Accelerating

So now you know all the forces on the ball. Or, at least, can calculate them.

 

[Mohamed BOUCHAKOUR]

So now you know all the forces on the ball. Or, at least, can calculate them.

Still can't see it...

 

[PeroK]

Still can't see it...

Have a think and draw a free-body diagram.

 

[Mohamed BOUCHAKOUR]

Have a think and draw a free-body diagram.

I think I've got it, thanks for the help ✌✌