Calculating Tension in Friction & Pulley: Solving for a=3 m/s^2

[gracy]

I think the top part of the string should be

 

[haruspex]

I think the top part of the string should beView attachment 81886

That cannot be string, or the pulley would fall down. Must be a rod.
The upper part of the string runs drom the wall to the pulley. How much longer does that get when the car advances 1m?

 

[gracy]

How much longer does that get when the car advances 1m?

Same as distance covered by small block.

 

[haruspex]

Same as distance covered by small block.

No. Forget the block for the moment, and concentrate on the car, the pulley, the wall, and the length of string from wall to pulley. If the car moves 1m further from the pulley, how much longer is that part of the string?

 

[gracy]

How much longer does that get when the car advances 1m?

Total length of string - length of the top part of the string ?

 

[haruspex]

Total length of string - length of the top part of the string ?

No, I'm asking about that top part of the string, the part that runs horizontally from the wall to the pulley.

 

[gracy]

Total length of string -(minus) length of the top part of the string .Right?/QUOTE]

 

[gracy]

Thank you for your patience .

 

[haruspex]

If the car moves 1m further from the wall, how much further is the pulley from the wall? So how much longer is the piece of string from the wall to the pulley?

 

[gracy]

1 meter?

 

[haruspex]

1 meter?

Right. So what would be the change in length of the lower part of the string, the part that runs from the block to the pulley?

 

[gracy]

So what would be the change in length of the lower part of the string

1 meter .

 

[haruspex]

1 meter .

Longer or shorter?

 

[gracy]

Longer or shorter?

Shorter?

 

[haruspex]

Shorter?

Right. So how much closer is the block to the pulley?

 

[gracy]

So how much closer is the block to the pulley?

1 meter.so distance covered by block is 1 meter,right?

 

[haruspex]

1 meter.so distance covered by block is 1 meter,right?

It is one metre closer to the pulley. But the pulley has moved how far?

 

[gracy]

But the pulley has moved how far?

1 meter?

 

[haruspex]

1 meter?

Right. So the pulley is one metre further from the wall, and the block is one metre closer to the pulley. So how far has the block moved away from the wall?

 

[gracy]

So how far has the block moved away from the wall?

1 meter.

 

[gracy]

Right. So how much closer is the block to the pulley?

It is one metre closer to the pulley. But the pulley has moved how far?

Right. So the pulley is one metre further from the wall, and the block is one metre closer to the pulley. So how far has the block moved away from the wall?

By all these questions do you want to say that distance covered by car=distance covered by block

 

[BvU]

No: if the block would NOT be connected to the wall by this wire (and it would NOT move wrt the flat car), THEN the distance covered by the block would be equal to the distance covered by the flat car. So

So the pulley is one metre further from the wall, and the block is one metre closer to the pulley. So how far has the block moved away from the wall?

try again. You have one more attempt left

 

[gracy]

Is my post #70 correct?

 

[BvU]

As incorrect as #71, since to me these two appear equivalent. The block moves on the car, so distance covered by car $\ne$ distance covered by block

 

[gracy]

Distance covered by block would be equal to shorter length of string(the region of string which connects block and pulley).That is block will reach where pulley was.

 

[BvU]

That is still saying the block moved by 1 meter ([edit] well, not really, but never mind (*) ). Is it also what you mean to say ?

Would it help you if you made a drawing of the intial situation and one of the situation where the flat car has moved over some distance ?

Or perhaps you do a little experiment where you attach a wire to a fixed point (the wall) on one end and to some object (the block) on the other. Let you finger play the role of the pulley and move your finger by 10 cm. How far did the object move ?

(*) you can easily see that can't be right: imagine the car is fifty meters long and moves by 1 m. No way the block is "where the pulley was".

 

[gracy]

It is one metre closer to the pulley

That's why I answered that Distance covered by block would be equal to shorter length of string(the region of string which connects block and pulley).That is block will reach where pulley was.

 

[gracy]

It is one metre closer to the pulley.

How to interpret it.

 

[BvU]

If the pulley moves 1 m away from the wall, it has to reel in the block by 1 m. So the pulley moves 1 m and pulls in the block by 1m. Over what distance has the block moved wrt the wall ?

The length itself of the shorter section has nothing to do with it. It's about how much that length has changed that's relevant.

 

[gracy]

It's about how much that length has changed .

1 meter?

 

[gracy]

So the pulley is one metre further from the wall,

Does that mean distance between wall and pulley is 1 meter?

 

[BvU]

Yes, that length has changed 1 meter: the pulley reeled it in by 1 meter. he pulley itself moved by 1 meter. How much has the block moved wrt the wall ?

 

[BvU]

No, distance between pulley and wall is not one meter. It has changed by 1 meter. If it was 10 m before, it now is 11 m.

 

[gracy]

How much has the block moved wrt the wall ?

2 meter?

 

[BvU]

Hurray ! (but: why the ? question mark?)
So, to summarize the last umpteen posts: when the cart moves 1 thing, the block moves 2 things (meters, inches, millimeters, whatever distance).

Now, next step: if the cart is accelerated by 3 m/s², what must be the acceleration of the block ?

 

[haruspex]

2 meter?

Hooray!
So for each metre the car moves, the block moves 2 m.
If the car's acceleration is a, what is the block's acceleration?

 

[BvU]

Fun with ropes and pulleys

Haru: you continue please. Bedtime for me. Grcy: good luck!

 

[gracy]

acceleration of the block =2 multiplied by trucks acceleration
i.e 6 m/s^2

 

[gracy]

So T-150=30 multiplied by6
T=330 N

 

[gracy]

Bedtime for me

Even I am going to sleep.

 

[haruspex]

So T-150=30 multiplied by6
T=330 N

You got it. Sleep well.

 

[gracy]

"haruspex" and BVU bigThanks for all your answers .And BVU sorry for that question mark

 

[gracy]

You both are true homework helper.BVU you used the whiteboard so nicely.Very neat diagram
.Next time when Calculus master will visit physics forum,will get homework done.

 

[gracy]

if the acceleration of the block = 2 * truck acceleration, then the force required in the string = m * a
then add the friction force

Really fast service ,I got this after 88 you in 10 th post.