Acceleration and Tension in a Two-Block System on an Inclined Plane

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In summary, we have two blocks of mass m connected by a massless, unstretchable string that rolls on a massless, frictionless pulley. At time t=0, both masses are released from rest. We are asked to find the acceleration of both masses and the tension T in the string. The free body diagrams for the two masses show that the only force acting on the mass on the inclined plane is mgsinθ, which is less than the weight of the first mass. The slope of the incline does not affect the mass or the gravitational acceleration. Since the floor is frictionless, there is no resistance, but inertia is still present. This means that the first mass will start moving immediately when pulled, and the
  • #1
SakuRERE
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Homework Statement


two blocks of mass m sit on a frictionless surface and are connected by a massless, unstrechable string that rolls on a massless, frictionless pulley as shown. the second mass sits on an inclined tipped at an angle θ relative to horizontal. at time t=0, both masses are released from rest.
a) find the acceleration of both masses (magnitude, but indicate directions for each mass on the figure).
b) find the tension T in the string.
upload_2018-10-5_22-44-6.png


Homework Equations


Σf=ma

The Attempt at a Solution


I can solve this one, but the only problem i am facing is that i see the whole system stationary. i can't indicate the direction of the acceleration and find the a of both masses. i just need to know will they move, and if yes how could that happen. i know that the incline will reduce the weight of the mass so the only force on the mass on the incline is mgsinθ, and this is even less from the first mass's weight.
or is it like since the floor is frictionless then the first mass will be moved and (so the system) by any Tension force even though it's very small. but what about the inertia then?
 

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  • #2
The first mass is not being lifted. So the force to move it only needs to overcome friction - of which there is none.
 
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  • #3
.Scott said:
The first mass is not being lifted. So the force to move it only needs to overcome friction - of which there is none.
then no friction means no resistance (inertia)?

i am sorry if i am asking basic questions, but for some reasons it's been a long time since i studied physics and i am trying to regain the flexibility of thinking that i used to have. however it appears that i am still lacking some basic information.

thanks in advance
 
  • #4
SakuRERE said:
then no friction means no resistance (inertia)?
Inertia and resistance are two separate things.
There is no friction, so when you pull it it will start moving immediately.
But yes, there will be inertia. So the mass will begin to accelerate from stationary - gaining speed for as long as it is pulled - or until it hits that pulley.
 
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  • #5
SakuRERE said:

Homework Statement


two blocks of mass m sit on a frictionless surface and are connected by a massless, unstrechable string that rolls on a massless, frictionless pulley as shown. the second mass sits on an inclined tipped at an angle θ relative to horizontal. at time t=0, both masses are released from rest.
a) find the acceleration of both masses (magnitude, but indicate directions for each mass on the figure).
b) find the tension T in the string.
View attachment 231730

Homework Equations


Σf=ma

The Attempt at a Solution


I can solve this one, but the only problem i am facing is that i see the whole system stationary. i can't indicate the direction of the acceleration and find the a of both masses. i just need to know will they move, and if yes how could that happen. i know that the incline will reduce the weight of the mass so the only force on the mass on the incline is mgsinθ, and this is even less from the first mass's weight.
or is it like since the floor is frictionless then the first mass will be moved and (so the system) by any Tension force even though it's very small. but what about the inertia then?
Have you drawn free body diagrams for the two masses? If so, what are the force balance equations for the two masses?
 
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  • #6
Chestermiller said:
Have you drawn free body diagrams for the two masses? If so, what are the force balance equations for the two masses?
upload_2018-10-5_23-53-42.png
this is the fbd or the two masses
 

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  • #7
SakuRERE said:

The Attempt at a Solution


I can solve this one, but the only problem i am facing is that i see the whole system stationary. i can't indicate the direction of the acceleration and find the a of both masses. i just need to know will they move, and if yes how could that happen.

Does it snow in your country? Have you ever been on a sledge? Rolled down s hill on a bike?

These are all examples of objects on a slope with no (or minimal) friction
i know that the incline will reduce the weight of the mass so the only force on the mass on the incline is mgsinθ, and this is even less from the first mass's weight.

Weight = mass * g

The angle of the slope doesn't change either mass or g.

or is it like since the floor is frictionless then the first mass will be moved and (so the system) by any Tension force even though it's very small. but what about the inertia then?

If there is a net force on an object it MUST accelerate. F=ma so a=F/m. The objects mass only effects how fast it accelerates.

Draw separate free body diagrams for each block.

I also recommend you try and build it using two toy cars (The wheels will help reduce friction) or even two ice cubes.
 
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  • #8
SakuRERE said:
View attachment 231733 this is the fbd or the two masses
So, if you eliminate T from these two equations, what do you get?
 
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  • #9
Chestermiller said:
So, if you eliminate T from these two equations, what do you get?
adding the two equations
T = m a
+ mgsinθ - T= m a
________________________
mgsinθ = 2m a
and by eliminating m from both sides:
a= (g sinθ)/2
so, sir, you want me to conclude that the acceleration cannot be zero unless the θ itself is zero which can't be (since it's inclined). so there is definitely an acceleration! was it?

Thanks in advance
 
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Related to Acceleration and Tension in a Two-Block System on an Inclined Plane

1. Will this system move if there is no external force acting on it?

According to Newton's First Law of Motion, an object will remain at rest or in motion in a straight line at a constant speed unless acted upon by an external force. Therefore, if there is no external force acting on the system, it will not move.

2. What factors determine the movement of a system?

The movement of a system is determined by various factors such as the type and magnitude of external forces acting on it, the mass and inertia of the system, and any frictional or resistive forces present.

3. Can the movement of a system be predicted?

Yes, the movement of a system can be predicted using Newton's Laws of Motion and other principles of physics. By understanding the forces and factors affecting the system, it is possible to accurately predict its movement.

4. How can we control the movement of a system?

The movement of a system can be controlled by manipulating the external forces acting on it. For example, by applying a force in a specific direction, we can change the speed and direction of the system's movement.

5. Are there any limitations to predicting the movement of a system?

While we can use scientific principles to predict the movement of a system, there are some limitations. These include uncertainties in measurement and calculations, as well as the complexity of certain systems that may exhibit chaotic or unpredictable behavior.

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