Conceptual question regarding tension

[nietzsche]

Homework Statement

Suppose you are in the back of a truck with a ball hanging by a string from the ceiling of the truck. If the truck is moving at a constant velocity on a smooth track, you will not know that you are moving. But if the truck is accelerating, you will see the ball and string make an angle, and the ball will tend to want to "stay behind". Why is this?

Homework Equations

The Attempt at a Solution

I just don't understand why this happens. If I draw a free body diagram of the ball (suppose the truck is accelerating to the right), I can see that there is a diagonal tension force, which can be split up into x and y components. The y component of the tension force will balance out with the force of gravity. And all that will be left is the x component of the tension force, which will cause the ball to accelerate with the truck.

Maybe this will help me clarify my question. Suppose the ball is taped to the end of the rigid metal rod and suspended from the ceiling of the truck. Then when the truck accelerates, the ball and rod will remain straight (perpendicular to the ceiling). What is the difference between this example and the string example?

 

[Troels]

Maybe this will help me clarify my question. Suppose the ball is taped to the end of the rigid metal rod and suspended from the ceiling of the truck. Then when the truck accelerates, the ball and rod will remain straight (perpendicular to the ceiling). What is the difference between this example and the string example?

No it won't - Unless of course you have clamped the rod to the ceiling (clamped is the term used to indicate that the position and first derivative of rod is fixed at the end). In that case it should be obvious that the horizontal force from the accelerating truck is balanced by a tension on the clamp.

But if the rod is allowed to swing freely, you will see it swing out as the truck accelerates

 

[nietzsche]

sorry, I'm not familiar with the terminology. i did mean clamp.

i just don't see why the string makes a diagonal. i mean, intuitively, it's very easy to easy that it does happen. but why doesn't the string just stay straight while the truck is accelerating? what's the difference between a clamped metal rod and a loose string?

if i had to guess, i'd say it's because the ball is trying to resist the motion and wants to stay where it is. but i don't understand the science behind that.

 

[Doc Al]

Maybe this will help me clarify my question. Suppose the ball is taped to the end of the rigid metal rod and suspended from the ceiling of the truck. Then when the truck accelerates, the ball and rod will remain straight (perpendicular to the ceiling). What is the difference between this example and the string example?

The difference is that the rigid rod can exert a sideways force to accelerate the ball. The string cannot--the string can only pull along its length.

 

[nietzsche]

I'm sorry, I'm still not sure I understand.

So let's say the truck is accelerating. Then the string and ball will form a diagonal, as the ball tries to "stay behind". The truck is exerting a horizontal force on the string, so how can the string end up giving a VERTICAL force to the ball? After all, the ball will higher up in the air if it forms a diagonal.

I think I'm just confused as to how a FBD of the system would look like.

 

[Doc Al]

So let's say the truck is accelerating. Then the string and ball will form a diagonal, as the ball tries to "stay behind".

OK.

The truck is exerting a horizontal force on the string, so how can the string end up giving a VERTICAL force to the ball?

The truck exerts a diagonal force on the string, equal to the string tension. (The string is attached to the ceiling of the truck.) The string tension exerts a diagonal force on the ball, which has both horizontal and vertical components.

After all, the ball will higher up in the air if it forms a diagonal.

So?

I think I'm just confused as to how a FBD of the system would look like.

Only two forces act on the ball: The force of the string tension (at a diagonal) and gravity (down).