Mass Sliding at An Angle; find mass of one

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Homework Help Overview

The problem involves two masses, M1 and M2, connected over a frictionless pulley, with M1 on an inclined plane and M2 hanging vertically. The goal is to determine the mass M1 given that M2 (4.50 kg) is accelerating downwards at 3.09 m/s², with an angle θ of 20.0° and a coefficient of kinetic friction μk of 0.450.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the forces acting on both masses, including gravity, normal force, tension, and friction. There are questions about the components of forces acting on M1 and M2, particularly regarding the normal force and its calculation.

Discussion Status

Participants are actively engaging in clarifying the setup and forces involved. Some have provided insights into the components of forces, while others are seeking further clarification on forming equations for the masses. There is a mix of understanding and confusion, with some participants offering guidance and others expressing uncertainty.

Contextual Notes

There is a noted absence of a diagram that could aid in visualizing the problem setup. Additionally, some participants mention the need for a clearer understanding of vector components and the terminology used in discussing forces.

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

Homework Statement


M1 and M2 are two masses connected as shown.

I couldn't see the "as shown"?
 
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.
 
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.
 
yes, but what components?
 
IMAGE:
https://s3.lite.msu.edu/res/msu/physicslib/msuphysicslib/09_Force_and_Motion/graphics/prob75_fricpullplane.gif
 
Last edited by a moderator:
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:
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
    2.4 KB · Views: 560
  • #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.
 

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