Finding Minimum A for Equilibrium in a Two Block Problem

In summary, the conversation discusses determining the angle in a circle with a string arcing over it and using equations to find the tension and weight in a system for equilibrium. The equations are discussed and confirmed to be correct, and the possibility of finding a different variable in the same system is mentioned.
  • #1
goodOrBad
25
2
Homework Statement
Given the weight of block A, friction coefficients and an angle determine the max.weight of B for which the system will stay in balanc
Relevant Equations
fg=µ1N

T2=T1e^(µ2β)
FRIC.png
 
Physics news on Phys.org
  • #2
You have ##\beta=\alpha+90^o##. Check that.
 
  • #3
So it should be -90? I don really understand how I have to determine the angle
 
  • #4
goodOrBad said:
So it should be -90? I don really understand how I have to determine the angle
Did you draw a diagram of the circle with radii to the ends of where the string arcs over it?
 
  • #5
1d0483c8ed1e67925615789ffb5e00d3.gif

no, but it does seem like the rope arcs over a 90 degree area
 
  • #6
goodOrBad said:
View attachment 269851
no, but it does seem like the rope arcs over a 90 degree area
If the upper section of the string were horizontal it would be 90 degrees. But it isn't.
Mark the ends of string contact on that circle.
 
  • #7
Okay so
cos30T1=0.3*500
T1=173.205
B=173.205*e^(0.2*300* π/180)=493.574N
 
  • #8
goodOrBad said:
cos30T1=0.3*500
That looks like a big step backwards.
What is wrong with the equations you had previously, ##T_1\cos(30)=\mu_1N=\mu_1(500+T_1\sin(30))##?
goodOrBad said:
e^(0.2*300* π/180)
300? Where did that come from? Or did you mean 30o?
No, not 30o either.
Did you draw the diagram I described?
 
  • #9
then beta should be 60 right?
WhatsApp Image 2020-09-22 at 12.01.47.jpeg
 
  • #11
Great then this should be correct
WhatsApp Image 2020-09-22 at 13.00.29 (1).jpeg
 
  • #13
WhatsApp Image 2020-09-22 at 13.40.42.jpeg

Thank you now I have one more question, what if almost everything was the same but... I was given weight of B and needed to find A, would I be able to use T2=T1e^(µ2β)
 
  • #14
goodOrBad said:
View attachment 269881
Thank you now I have one more question, what if almost everything was the same but... I was given weight of B and needed to find A, would I be able to use T2=T1e^(µ2β)
To find the minimum A for equilibrium? Sure - why should the equations change?
 
  • Like
Likes goodOrBad

FAQ: Finding Minimum A for Equilibrium in a Two Block Problem

What is a two block problem?

A two block problem refers to a physics problem that involves two blocks connected by a string or rope. The blocks may be on an incline or a horizontal surface, and the problem typically involves calculating the forces and accelerations acting on the blocks.

How do I solve a two block problem?

To solve a two block problem, you will need to use Newton's laws of motion and apply them to each block separately. You will also need to consider any external forces acting on the blocks, such as friction or tension in the string. It may also be helpful to draw a free body diagram for each block to visualize the forces acting on them.

What are some common mistakes when solving a two block problem?

Some common mistakes when solving a two block problem include forgetting to consider all the forces acting on the blocks, using incorrect values for mass or acceleration, and not properly accounting for the direction of forces. It is important to carefully read and understand the problem before attempting to solve it.

Can I use any equations to solve a two block problem?

Yes, there are several equations that can be used to solve a two block problem, such as Newton's second law (F=ma), the equations for friction, and the equations for tension in a string. However, it is important to only use equations that are applicable to the specific problem at hand.

Are there any tips for solving a two block problem more efficiently?

One tip for solving a two block problem more efficiently is to break the problem down into smaller parts and solve each part separately. This can help to simplify the problem and make it more manageable. It is also helpful to double-check your calculations and make sure all units are consistent throughout the problem.

Back
Top