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

[Calculus Master]

1. If flat car is given an acceleration a = 3 m/s^2 starting from rest, compute tension (in N) in the light inextensible string connected to block A of mass 30 kg. Coefficient of friction between block and flat car is = 0.50.

Neglect mass of pulley and its friction. Take g = 10.
2. Friction = $\mu N$
F = ma
ma = mg - T3. No idea. I couldn't approach the problem. Please tell me how to approach these types.

 

[pcm]

1. If flat car is given an acceleration a = 3 m/s^2 starting from rest, compute tension (in N) in the light inextensible string connected to block A of mass 30 kg. Coefficient of friction between block and flat car is = 0.50.

Neglect mass of pulley and its friction. Take g = 10.
2. Friction = $\mu N$
F = ma
ma = mg - T3. No idea. I couldn't approach the problem. Please tell me how to approach these types.

Write the Newton's laws in the frame of the ground. It is an inertial frame. Write down all the forces(along both axes). Also observe that for every meter the car moves, block A moves by 2 meter.

 

[DaPi]

Take g = 10.

I hope the original problem gave some units for g!

 

[haruspex]

In case pcm's post is not clear enough, it's the forces on the block that matter. You don't need to analyse forces on the cart since its motion is a given.

 

[gracy]

I also want it's answer.Please guide how to start?

 

[haruspex]

I also want it's answer.Please guide how to start?

What are the horizontal forces acting on the block? What is the acceleration of the block? What equation does that give you?

 

[gracy]

What are the horizontal forces acting on the block?

Friction and tension.

 

[gracy]

What is the acceleration of the block?
Same as acceleration of the car(truck)?

 

[gracy]

What equation does that give you?

Net force on the block=mass of the block multiplied by acceleration of the truck.

 

[dean barry]

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

 

[gracy]

then add the friction force

why should I add?

 

[dean barry]

acceleration force is forward (say + ve) and friction force is rearward (say - ve), the tension force is the difference.
adding gets the same result.

 

[haruspex]

acceleration force is forward (say + ve) and friction force is rearward (say - ve), the tension force is the difference.
adding gets the same result.

Yes, it produces the same equation, but I feel it would be less confusing for gracy to stick to the normal formulation $\Sigma F_x = m a_x$.
gracy, do you see why the acceleration of the block is not the same as the acceleration of the truck?

 

[gracy]

acceleration force is forward (say + ve) and friction force is rearward

But according to
The page number 6 of attached pdf
the direction of friction force should be forward.

 

[haruspex]

But according to
The page number 5 of attached pdf
the direction of friction force should be forward.

That's a different situation. In the textbook example, the only force accelerating the block is the friction, so of course it must be acting in the forward direction. In this thread, there is a string pulling on the block.
Friction always opposes relative motion of the two surfaces in contact. Which way does the block move relative to the truck?

 

[gracy]

Which way does the block move relative to the truck?

rearward.

 

[gracy]

if the acceleration of the block = 2 * truck acceleration

Why?

 

[haruspex]

rearward.

Yes, sorry, I meant in this thread, which way does it move relative to the "flat car".

 

[haruspex]

Why?

What is the acceleration of the block relative to the car?
Does the total length of the string change?

 

[gracy]

which way does it move relative to the "flat car".

After Considering pull on block by string?

 

[gracy]

Does the total length of the string change?

No,it is for sure.

 

[haruspex]

After Considering pull on block by string?

Of course.

 

[gracy]

Tension in string is pulling the block in forward direction, right?

 

[haruspex]

Tension in string is pulling the block in forward direction, right?

Right.

 

[gracy]

So,to find in which direction the block will move,I need to know force is larger in which direction,i.e tension +force by truck in forward direction should be greater than force of friction then only block will move in forward direction.

 

[haruspex]

So,to find in which direction the block will move,I need to know force is larger in which direction,i.e tension +force by truck in forward direction should be greater than force of friction then only block will move in forward direction.

You know which way the block will move relative to the car (since the string neither stretches nor breaks).
And what do you mean by "force by truck in forward direction"? There are only two horizontal forces on the block.

 

[gracy]

I only know force of friction (static in nature) i.e 0.5 multiplied by 30 multiplied by 10=150 N.

 

[gracy]

what do you mean by "force by truck in forward direction"? There are only two horizontal forces on the block.

As truck is moving and block is in contact with the truck will not it exert any force?

 

[haruspex]

As truck is moving and block is in contact with the truck will not it exert any force?

Yes, friction. What else?

 

[gracy]

When we board in bus ,we are initially (before getting in bus)at rest,but then start traveling at the speed of bus,As per Newton's first law some external must acts on us.What's that?Is it fiction ?
You may find this trivial,but seriously that's why I was thinking that flat car does exert force on block.

 

[haruspex]

When we board in bus ,we are initially (before getting in bus)at rest,but then start traveling at the speed of bus,As per Newton's first law some external must acts on us.What's that?Is it fiction ?
You may find this trivial,but seriously that's why I was thinking that flat car does exert force on block.

No, it's not fiction, it's friction. The bus is stationary when you board. You are standung, say. When the bus starts, if there were ni friction between your shoes and the bus floor you would remain still, your shoes sliding, until you hit the back of the bus.

 

[gracy]

Is it fiction ?

typo.

 

[gracy]

Is my calculation in post #37 correct?

 

[haruspex]

Is my calculation in post #37 correct?

If you mean #27, yes. So,
- which way does that friction force act?
- are there any other horizontal forces on the block other than friction and the string tension?
- what is the sum of horizontal forces on the block?
- what is the acceleration of the block?

 

[gracy]

If you mean #27,

Yes.

 

[gracy]

As tension force never pushes it always pulls .So block should move forward.

 

[gracy]

Is there any tension force in the end which is tied to wall (I have pointed out that end in my below diagram)

I think there should be.

 

[haruspex]

As tension force never pushes it always pulls block should move forward.

In particular, forward relative to the car. So friction acts the other way, agreed? What, then, is the sum of forces?

 

[haruspex]

Is there any tension force in the end which is tied to wall (I have pointed out that end in my below diagram)

View attachment 81877
I think there should be.

Yes. What is the relationship between the tension there and the tension at the end attached to the block?

 

[gracy]

They should be same.As string and pulley is massless(assumption)

 

[gracy]

Wait,I think I am getting the solution now.

 

[haruspex]

They should be same.As string and pulley is massless(assumption)

Right.

 

[gracy]

I wish Mass of flat car was given!

 

[haruspex]

I wish Mass of flat car was given!

As I posted previously, you don't care about the mass of the car or the forces on it because you know exactly how it is moving. Concentrate on the forces on the block and its acceleration.

 

[gracy]

Is it correct.

 

[haruspex]

Is it correct.
View attachment 81878

Whether or not it is correct, it is irrelevant. Please just answer my questions in post ##34.

 

[gracy]

- which way does that friction force act

Backward.

- are there any other horizontal forces on the block other than friction and the string tension?

No.

what is the sum of horizontal forces on the block?

T-150N =30Kg multiplied by acceleration of the block.

what is the acceleration of the block?

Here I am struggling.

 

[haruspex]

Backward.

No.

T-150N =30Kg multiplied by acceleration of the block.

Here I am struggling.

Ok so far.
The string is of constant length. If the car moves 1m, the top part of the string gets how much longer? What does that tell you about the length of the lower part? How far has the block moved?

 

[gracy]

Sorry,actually I am really pedantic.

the top part of the string

Did you mean the part of string indicated?

 

[haruspex]

Sorry,actually I am really pedantic.Did you mean the part of string indicated?

Yes.