Mass Sliding at An Angle; find mass of one

In summary: Friction and normal?Friction and normal?Weight and normal force are perpendicular to the string. Friction and tension are parallel to the string.
  • #1
cassienoelle
63
0

Homework Statement


M1 and M2 are two masses connected as shown.
(M1 on hypotenuse of triangle, M2 on right side, (adjacent to right angle)) (Pulley at corner of them, Angle Theta is on the opposite corner)
The pulley is light and frictionless. Find the mass M1, given that M2 (4.50 kg) is moving downwards and accelerates downwards at 3.09 m/s2, that θ is 20.0°, and that μk is 0.450.



Homework Equations


The total force (which is the total mass times the acceleration) is equal to the sum of the forces. The normal force is NOT simply "m1g"--WHY?



The Attempt at a Solution

 
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  • #2
It would be better if you could show us a diagram of what you are talking about. :smile:
 
  • #3
cassienoelle said:

Homework Statement


M1 and M2 are two masses connected as shown.

I couldn't see the "as shown"?
 
  • #4
cassienoelle said:

Homework Statement


M1 and M2 are two masses connected as shown.
(M1 on hypotenuse of triangle, M2 on right side, (adjacent to right angle)) (Pulley at corner of them, Angle Theta is on the opposite corner)
The pulley is light and frictionless. Find the mass M1, given that M2 (4.50 kg) is moving downwards and accelerates downwards at 3.09 m/s2, that θ is 20.0°, and that μk is 0.450.



Homework Equations


The total force (which is the total mass times the acceleration) is equal to the sum of the forces. The normal force is NOT simply "m1g"--WHY?



The Attempt at a Solution


OK, I was expecting "as shown" to be a diagram.

The Normal force is perpendicular to the slope [that is what the "Normal" means - as in Tangent and normal ... Tangent, parallel to surface; Normal, perpendicular to surface.]
mg is vertically down, so you need to use some components to calculate the Normal force.
 
  • #5
cassienoelle said:

Homework Statement


M1 and M2 are two masses connected as shown.
(M1 on hypotenuse of triangle, M2 on right side, (adjacent to right angle)) (Pulley at corner of them, Angle Theta is on the opposite corner)
The pulley is light and frictionless. Find the mass M1, given that M2 (4.50 kg) is moving downwards and accelerates downwards at 3.09 m/s2, that θ is 20.0°, and that μk is 0.450.



Homework Equations


The total force (which is the total mass times the acceleration) is equal to the sum of the forces. The normal force is NOT simply "m1g"--WHY?



The Attempt at a Solution


Without the string, M2 would accelerate down at g - either 9.8, 9.81 or 10 depending which value you have been advised to use.
The fact it accelerates at only 3.09 means the string is providing a force trying to prevent the acceleration. This force is due to two contributions.
Part of it will be friction between M1 and the slope.
Part of it will be the component of the weight force of M1 acting down the slope.
 
  • #6
yes, but what components?
 
  • #7
IMAGE:
https://s3.lite.msu.edu/res/msu/physicslib/msuphysicslib/09_Force_and_Motion/graphics/prob75_fricpullplane.gif
 
Last edited by a moderator:
  • #8
cassienoelle said:
IMAGE:
https://s3.lite.msu.edu/res/msu/physicslib/msuphysicslib/09_Force_and_Motion/graphics/prob75_fricpullplane.gif

No image present.
 
Last edited by a moderator:
  • #9
cassienoelle said:
yes, but what components?

We always take components parallel to and perpendicular to something convenient,
Here that is parallel to the slope and perpendicular to the slope.

You want those components of M1g.
 
  • #10
The picture should be attached now.
 

Attachments

  • masssliding.gif
    masssliding.gif
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  • #11
cassienoelle said:
IMAGE:
https://s3.lite.msu.edu/res/msu/physicslib/msuphysicslib/09_Force_and_Motion/graphics/prob75_fricpullplane.gif

You have to work out to get the image. We can only see it if we log-in and we certainly don't want your username and password posted here.
 
Last edited by a moderator:
  • #12
Ok, first let's make the equation for the M2 block.
What are the forces acting on the M2 block? :smile:
 
  • #13
On the M2 block there is gravity and normal force ?
 
  • #14
cassienoelle said:
On the M2 block there is gravity and normal force ?

Read post 5 and think about it.
 
  • #15
cassienoelle said:
On the M2 block there is gravity and normal force ?

You are forgetting one force "Tension". :smile:
Now form the equation for M2 block.
 
  • #16
M2 : T - mg = ma
?
 
  • #17
cassienoelle said:
M2 : T - mg = ma
?

Yep, that's right.
Now plug in the values and find tension. :)
 
  • #18
Pranav-Arora said:
Yep, that's right.
Now plug in the values and find tension. :)

is the acceleration negative because the box is falling down?
 
  • #19
cassienoelle said:
is the acceleration negative because the box is falling down?

No. :)
 
  • #20
k, so T = 58.05N
 
  • #21
I haven't calculated it so i am assuming it as right. :)

So for the M1 block, what are the forces acting on it? Think about this one carefully and form the equation. :smile:
 
  • #22
Tension, weight, and normal force?
 
  • #23
cassienoelle said:
Tension, weight, and normal force?

You again missed one "Friction" :)
So now form the equation.
 
  • #24
Honsestly, I have zero clue how to form the equation.
 
  • #25
cassienoelle said:
Honsestly, I have zero clue how to form the equation.

Ok, i give you a clue.
We have weight, normal, friction and tension.

The tension acts upwards along the string. We have two components for weight. Can you find them?
 
  • #26
well i know that : weight = mass * gravity
 
  • #27
cassienoelle said:
well i know that : weight = mass * gravity

Weight is acting downwards but we need to find what effect does it have along the inclined plane. For that you need to take component of mg along the inclined plane. Can you do that? :smile:
 
  • #28
W = cos20 * T
?
 
  • #29
cassienoelle said:
W = cos20 * T
?

That's completely absurd.
I think you are not able to picture out what i am talking about. Ok here's a picture:-

2m7yals.png


Can you find the component (the yellow arrow)?
 
  • #30
No, I can't.
 
  • #31
cassienoelle said:
No, I can't.

Aren't you knowing about vectors? Are you trying to do these questions yourself without any guidance?
If not, then this question should not bother you much. :)
 
  • #32
I know about vectors. But yes, I am trying to do these with almost no guidance. It's an online course and I have no idea what's going on. I would appreciate it if you would stop making me feel like an idiot. I came onto this website for the guidance.
 
  • #33
cassienoelle said:
I know about vectors. But yes, I am trying to do these with almost no guidance. It's an online course and I have no idea what's going on. I would appreciate it if you would stop making me feel like an idiot. I came onto this website for the guidance.

Really? Did i make you feel like that. I am very sorry if i did so.:frown:

Ok i will tell you how to do so in a minute. I am making pictures to make you understand. :)
 
  • #34
I want to just tell you that these question are categorized under Laws of Motion. :)
If you are not familiar with these, then i suggest you to complete the Khan Academy videos on Laws of Motion. :)

Here's the explanation:-
Let us consider an object of mass m kept on an inclined plane as shown in the figure.
16iwirp.png


The blue arrows indicate forces. Now to find the component along the inclined plane, draw a straight line as shown in the figure. The straight line is along the force mg.
21d4u2q.png


Now in triangle ABC, angle BAC is 90-[itex]\theta[/itex]. Now its easy to have the components. The components are shown in the figure below.

i3bdza.png


So we have found out the components.
So now can you tell me what’s the normal reaction force here?

(Ask if you have any doubts, because this is a very important concept, don't miss this one)
 
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  • #35
cassienoelle said:
On the M2 block there is gravity and normal force ?

I am not happy with your terminology use here.
You use the term Normal force - you should be using the full name Normal Reaction Force.
this reminds you it is referring to a force, perpendicular to a surface, which comes about as the action-reaction pair of something applying a force to the surface.

For M2, there is no surface involved, so there will be no Normal Reaction Force.

M2 does have a string attached. That means M2 will pull on the string, and the string will pull on the mass [that is an action reaction pair]. One of that pair acts on M2 - the string pulling the mass. We can say that force is due to the Tension in the string if you like.

So the forces acting on M2 are Weight [due to Gravity] and Tension.

M1 can have a Normal Reaction Force, since it is touching a surface.
Because the surface is rough there may be a Friction Force.
There is also, of course, the weight of M1.

Weight acts vertically down.
Friction acts parallel to the surface.
The Normal Reaction force acts at right angles to the surface [of course it does! That is why it is called the Normal Reaction Force].
 
<h2>1. What is mass sliding at an angle?</h2><p>Mass sliding at an angle refers to the motion of an object with a certain mass sliding down a surface at an angle, influenced by the force of gravity.</p><h2>2. How is the mass of an object determined in mass sliding at an angle?</h2><p>The mass of an object can be determined by using the equation m = F/gsinθ, where m is the mass, F is the force of gravity, and θ is the angle of the surface.</p><h2>3. What factors affect the mass of an object in mass sliding at an angle?</h2><p>The mass of an object is affected by the force of gravity, the angle of the surface, and the coefficient of friction between the object and the surface.</p><h2>4. How does the angle of the surface impact the mass in mass sliding at an angle?</h2><p>The angle of the surface affects the mass by changing the direction and magnitude of the force of gravity acting on the object. A steeper angle will result in a greater force of gravity and therefore a greater mass.</p><h2>5. Can the mass of an object change during mass sliding at an angle?</h2><p>No, the mass of an object remains constant during mass sliding at an angle. However, the weight of the object may change due to the varying force of gravity depending on the angle of the surface.</p>

1. What is mass sliding at an angle?

Mass sliding at an angle refers to the motion of an object with a certain mass sliding down a surface at an angle, influenced by the force of gravity.

2. How is the mass of an object determined in mass sliding at an angle?

The mass of an object can be determined by using the equation m = F/gsinθ, where m is the mass, F is the force of gravity, and θ is the angle of the surface.

3. What factors affect the mass of an object in mass sliding at an angle?

The mass of an object is affected by the force of gravity, the angle of the surface, and the coefficient of friction between the object and the surface.

4. How does the angle of the surface impact the mass in mass sliding at an angle?

The angle of the surface affects the mass by changing the direction and magnitude of the force of gravity acting on the object. A steeper angle will result in a greater force of gravity and therefore a greater mass.

5. Can the mass of an object change during mass sliding at an angle?

No, the mass of an object remains constant during mass sliding at an angle. However, the weight of the object may change due to the varying force of gravity depending on the angle of the surface.

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