- #1
How can i find the acceleration for this constraint?
- Thread starter yy205001
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- Acceleration Constraint
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Homework Help Overview
The discussion revolves around determining the acceleration of a 2 kg block on a frictionless table, influenced by a pulley system with a hanging mass. Participants explore the relationships between the blocks' accelerations and the constraints imposed by the system.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants discuss drawing free body diagrams (FBDs) for both blocks and applying Newton's laws. Questions arise about the relationship between the accelerations of the blocks and the constraints of the pulley system.
Discussion Status
Some participants have provided guidance on the need for more detailed force diagrams and equations. There is ongoing exploration of how the constraints affect the motion of the blocks, with some participants expressing uncertainty about the relationship between their accelerations.
Contextual Notes
Participants note the importance of understanding the constraint imposed by the pulley system, particularly in terms of how the distance moved by one block relates to the other. There is mention of the need to clarify the units of tension and acceleration in their equations.
- #2
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As we welcome you to these forums, you first should show more of an attempt before we can assist. You need to draw force diagrams of each block and apply Newton's laws. Do you think the acceleration of the blocks are the same?
- #3
yy205001
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as long as they are in the same system, i think they have the same acceleration
- #4
gneill
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yy205001 said:
You'll have to show more effort. What is the constraint imposed by the pulley system on the relative motions of the blocks? Did you draw FBD's for both blocks? What are the resulting force equations?
- #5
- #6
gneill
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yy205001 said:
Okay. In your diagram you depict two "T" forces acting on the 2kg block, so why do you say the resulting force is T? How are the accelerations of the blocks related?
- #7
yy205001
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gneill said:
sorry, it should be 2T. Are they having the same acceleration, this is my main problem.
- #8
gneill
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The rope and pulley system place a constraint on the motions. If the 1kg block moves down a distance d, how far will the 2kg block slide?
- #9
yy205001
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will it slides a distance d as well??
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- #10
gneill
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yy205001 said:
Nope. Do a rope segment length calculation. Remember that the rope's total length is constant.
- #11
yy205001
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yea,i got d/2. Is it correct??
- #12
gneill
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Yes, that's fine. That then will be the constraint connecting the motions of the blocks. It will apply to distance moved, velocities, and accelerations.yy205001 said:
- #13
yy205001
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gneill said:
i still cannot get it
- #14
yy205001
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gneill, do you mean the acceleration of the hanging mass is twice the acceleration of the mass on the horizontal surface??
- #15
gneill
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yy205001 said:
Yes, it must be due to the constraint...
Convert your FBD force equations to acceleration for each block. Use the constraint equation for acceleration to solve.
- #16
yy205001
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In the x-direction, the Net force is 2*T.
Let a1 be the acceleration of the mass on horizontal surface,
a2 be the acceleration of the hanging mass.
"F=m*a", so:
2*T = 2*a1
T = a1
In the y-direction, the Net force is mg-T, where m is 1kg,so:
m*g-T = m*a2
where T = a1
→m*g-a1=m*a2
Then,sub in a2=2*a1
m*g-a1=m*2*a1
So, i can find out the acceleration of a1, thus find a2?
Let a1 be the acceleration of the mass on horizontal surface,
a2 be the acceleration of the hanging mass.
"F=m*a", so:
2*T = 2*a1
T = a1
In the y-direction, the Net force is mg-T, where m is 1kg,so:
m*g-T = m*a2
where T = a1
→m*g-a1=m*a2
Then,sub in a2=2*a1
m*g-a1=m*2*a1
So, i can find out the acceleration of a1, thus find a2?
- #17
gneill
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Tension has units of Newtons (force). It is not an acceleration (m/s2).yy205001 said:
Use the relationship F = ma that you've written to turn the net force into an acceleration, hence a = F/m. So that would make a1 = ?
Again you're mixing units. Forces (like m*g) are not accelerations (m/s2).
Just write the accelerations for each block separately at first; Don't try to apply the constraint until you have those expressions. You should have:
a1 = (something in terms of m1 and T)
a2 = (something in terms of m2 and T and g)
After you have them you can use the constraint equation to eliminate one of the accelerations...
- #18
yy205001
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yes, i got the correct answer finally, thank you so much!