What Is the Time for Log A to Move 1 Meter on a Diagonal Plane?

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Homework Help Overview

The problem involves two logs, A and B, with equal weights, connected by a rope over frictionless wheels. Log A is on a diagonal plane, while log B is on a horizontal surface. The discussion centers around calculating the time it takes for log A to move 1 meter and the tension in the rope.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the acceleration of log A and question whether it could be zero. They suggest analyzing the forces acting on both logs and applying Newton's second law.
  • There is a focus on the relationship between the tensions in the rope and the implications of the smooth surfaces on friction.
  • Some participants express confusion about the setup and seek clarification on the forces involved, particularly regarding friction and the angles.
  • Further questions arise about additional forces acting on log B and how they affect the system's state of rest.

Discussion Status

The discussion is active, with participants providing guidance on analyzing forces and equations. Some participants have shared their calculations and reasoning, while others are encouraged to revisit their approaches and clarify their understanding of the problem. There is no explicit consensus, but productive dialogue is ongoing.

Contextual Notes

Participants note that the problem involves a frictionless setup, but later discussions introduce the concept of friction for additional questions. The angle of the diagonal plane has been corrected during the discussion, indicating a focus on accurate problem setup.

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Homework Statement


Log A weighs 20Kg is laid on a diagonal smooth plane with a diagonal angle of 27 37 degree, log A is tied by a rope to the head of the plane and there through a wheel with no friction the rope descend vertically to the bottom of the plane and through another friction-less wheel is tied to log B that weighs 20 Kg and is laid on a smooth horizontal plane' the last part of the rope tied to log B is horizontal

Homework Equations


1. what is the time in which log A will move a 1 meter distance on the plane if it starts from rest?
2. what is the tension in the rope attached to both logs?

The Attempt at a Solution


is acceleration here 0? or maybe 6? I'm a bit lost would appreciate any help, thx!

physics1.jpg


[edit: fixed typo in given angle (picked up correction from post #3 -- Moderator]
 
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JAZZ541 said:
is acceleration here 0? or maybe 6?
Well, you know the acceleration can't be zero, else the first question would not make sense.

Do this: Analyze the forces acting on A and on B. Apply Newton's 2nd law to each.
 
Ty!
Is this correct? btw angle is 37 and not 27
physics2.jpg
 
Well, you don't show arrows. (Forces have direction.) And what does "f" represent? How do t1 and t2 relate?
 
f - friction ohh, but they said smooth surface, so no friction
and T1 = T2?
 
JAZZ541 said:
f - friction ohh, but they said smooth surface, so no friction
Right.

JAZZ541 said:
and T1 = T2?
Right. The tension is the same throughout the rope.
 
I'm sorry I had to go ill try and work on it some more and come back later
 
JAZZ541 said:
I'm sorry I had to go ill try and work on it some more and come back later
No worries. Give it a shot and then come back and show what you've done.
 
Thank u for your patience!
I have this:

1.

m1(A)g = m2(B)g = 20Kg

X = 1m

mag • sinα – T = m1a

T = m2a

mag • sinα -T + T = m1a + m2b

200 • 0.60 = a(m1 + m2)

a = 120/40 = 3m/s

X = V0T + at^2 /2

1 = 0 + 3t^2/2

2 = 3t^2

t = 0.816s

2.

T = m2a

T = 20 • 3 = 60N

there are two more questions about this problem:

3.
If there is a friction between log B and the horizontal surface what is the minimal static coefficient of friction in which if the system is in a state of rest then it will remain in that state?

4.
If the kinetic and static coefficient of friction is mu = 0.25, how long will it take log A to travel a 2 meter distance on the plane (the rope is weightless)?

how should I approach that?

Thx again!
 
  • #10
JAZZ541 said:
m1(A)g = m2(B)g = 20Kg

X = 1m

mag • sinα – T = m1a

T = m2a

mag • sinα -T + T = m1a + m2b

200 • 0.60 = a(m1 + m2)

a = 120/40 = 3m/s
Good!
(1) Your first equation should be: ##m_1 = m_2 = 20## Kg
(2) Careful with units. Acceleration has units of m/s^2.
(3) It's almost always better to stick to symbols as long as possible before plugging in numbers. Here's how I'd do it:
Since the masses are the same, I'd use "m" for both masses. And since the acceleration is the same, I'd use "a" for that.
##mg\sin\theta - T = ma##
##T = ma##
Adding them, we get:
##mg\sin\theta = 2ma##
And so on.

Note that the mass cancels out! So it doesn't matter (at least for this part of the question).
JAZZ541 said:
X = V0T + at^2 /2

1 = 0 + 3t^2/2

2 = 3t^2

t = 0.816s
Good!

JAZZ541 said:
2.

T = m2a

T = 20 • 3 = 60N
Good!
 
  • #11
JAZZ541 said:
3.
If there is a friction between log B and the horizontal surface what is the minimal static coefficient of friction in which if the system is in a state of rest then it will remain in that state?
(1) What additional force acts on B? (Use symbols, not numbers.)
(2) What is the acceleration?

Redo your force equations with this in mind.

JAZZ541 said:
4.
If the kinetic and static coefficient of friction is mu = 0.25, how long will it take log A to travel a 2 meter distance on the plane (the rope is weightless)?
This is similar to the first part, only now there is an additional force acting on B.
 
  • #12
TY!

Doc Al said:
(1) What additional force acts on B? (Use symbols, not numbers.)
(2) What is the acceleration?
a = 0 ?

Doc Al said:
Redo your force equations with this in mind.
mgsinα = T = f = mumg ?
 
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  • #13
Good!

(I fixed your quotes.)
 
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  • #14
Then:
mu = sin37° = 0.6
Ty very very much for your patience and guidance!
 
  • #15
JAZZ541 said:
Then:
mu = sin37° = 0.6
Yep!

JAZZ541 said:
Ty very very much for your patience and guidance!
You are welcome.
 

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