How to I find what needs to be the mass of an object in a friction problem?

In summary, the coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.42 between mass mA and the table. To keep the system from starting to move, the minimum value of mA must be determined. To keep the system moving at constant speed, the value of mA must also be determined. The equations Fs <= uN and Fk = uN can be used, along with the knowledge that the tension in the rope must be equal to or greater than the force pulling down on mass mB. Two force-body diagrams can be drawn to solve the problem, with one equation for the x-direction and two equations for the y-direction. The equations can then be solved to find the tension in the rope
  • #1
Mustachio
9
0

Homework Statement



In the figure the coefficient of static friction between mass mA and the table is 0.50, whereas the coefficient of kinetic friction is 0.42.
(a) What minimum value of mA will keep the system from starting to move?
(b) What value of mA will keep the system moving at constant speed?

3HZVZ.gif



Homework Equations


So I know that

Fs <= uN
Fk = uN

But I don't know what to do when I lack the Newtons.

Can anyone give me a hint on where to start?


The Attempt at a Solution

 
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  • #2
If the system isn't moving, what must be the tension in the rope?
 
  • #3
Would it be 0 because it'd be at equilibrium when not moving?
 
  • #4
If someone asked you to support that hanging mass mB by holding the upper end of the rope, what force would your arm have to exert? It would not be zero.
 
  • #5
A force greater or equal to that of the force that is pulling down mb?
 
  • #6
A force of how many Newtons?
 
  • #7
Can I multiply 2 * 9.8(m/s^2) to get the mkg/s^2 = N unit?
 
  • #8
Mustachio said:
Can I multiply 2 * 9.8(m/s^2) to get the mkg/s^2 = N unit?
Yes.
 
  • #9
So I made 2 FBDs.

...... ^ N
......|
......|
mSn...mKn...|.... T
<---<--------|---------->
......|
......|
......| Ma(g)
...... vT
|
|
o
|
|
2g

And I derived 2 sets of equations.For the first FBD I got
X: T - mkN - msN = (Ma)a
Y: N - (Ma)g = 0

Second one I got

Y: T - 2g = 2a.

Do I have the problem set it up right?
 
  • #10
Mustachio said:
For the first FBD I got
X: T - mkN - msN = (Ma)a
What do mkN and msN stand for? If those are supposed to be the friction forces, realize that only one acts at any given time; it's either static or kinetic friction.

Y: N - (Ma)g = 0
OK.

Second one I got

Y: T - 2g = 2a.
OK. (What's a?)
Do I have the problem set it up right?
To solve the problem, answer the question I asked before:
If the system isn't moving--or is moving at constant speed--what must be the tension in the rope?
 
  • #11
I don't understand the question. :\
 
  • #12
Mustachio said:
I don't understand the question. :\
What does your equation for MB tell you? (What's the acceleration?)
 

FAQ: How to I find what needs to be the mass of an object in a friction problem?

How do I calculate the mass of an object in a friction problem?

To calculate the mass of an object in a friction problem, you will need to use the formula F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force. You can rearrange this formula to solve for the mass of the object by dividing both sides by the coefficient of friction (μ) and the normal force (N). The resulting formula is m = F/(μN), where m is the mass of the object in kilograms (kg).

What is the coefficient of friction and how does it affect the mass of an object in a friction problem?

The coefficient of friction is a measure of the amount of resistance that an object experiences when moving against another surface. It is represented by the symbol μ and is dependent on the materials and surfaces in contact. The coefficient of friction can affect the mass of an object in a friction problem because it is a factor in the formula for calculating the mass (m = F/(μN)). A higher coefficient of friction will result in a larger mass needed to overcome the resistance.

3. How can I determine the normal force in a friction problem?

The normal force is the perpendicular force exerted by a surface on an object in contact with it. In order to determine the normal force in a friction problem, you will need to consider the forces acting on the object. If the object is on a flat surface, the normal force will be equal to the weight of the object. However, if the surface is inclined, you will need to use trigonometry to calculate the normal force.

4. What units should I use for the mass in a friction problem?

In a friction problem, the mass of the object is typically measured in kilograms (kg). This is the standard unit for mass in the International System of Units (SI). However, if you are given the mass in other units such as grams (g) or pounds (lbs), you will need to convert it to kilograms before using it in the formula (m = F/(μN)).

5. Are there any other factors that I should consider when calculating the mass of an object in a friction problem?

In addition to the coefficient of friction and the normal force, there are a few other factors that you may need to consider when calculating the mass of an object in a friction problem. These include the angle of inclination of the surface, the type of motion (static or kinetic), and any external forces acting on the object. It is important to carefully consider all of these factors to ensure an accurate calculation of the mass.

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