Finding Mass of Block B in Triangle with Pulley & Friction Coefficients

In summary, the conversation discusses a scenario involving a triangle with two blocks attached by a rope and a frictionless pulley. The goal is to find the mass of one of the blocks, given information about the static equilibrium and friction coefficients of both blocks. The problem arises with deciding the direction of the static frictional force, which can lead to two different answers. The conversation also mentions using free-body diagrams and solving a system of equations to find the correct mass.
  • #1
skaterbasist
13
0
I have a conceptual problem regarding the following scenario:

Try to imagine a triangle with two blocks on each side, attached together with a rope, and a pulley at the tip of the triangle.

Block A & B are attached to each other through a rope. Blocks A & B are in static equilibrium, each on an inclined plane of angle theta and phi. The pulley at the top of this triangle has a frictionless pulley. Block A has a static friction coefficient of 0.1, and block B has a static coefficient of 0.2. Block A has a mass of 10kg, and we are asked to find the mass of Block B with the given information.

Now, my problem is, in which direction do we assume the static frictional force to be? Since the two blocks are in static equilibrium, do we assume that that the static force is up the plane in each separate free-body diagram? Do we assume that the tendency of friction and movement is in one particular direction and then draw a free-body diagram, with the static frictional force going up on one side and down on the other side [of the surfaces in the triangle]? And why does the mass of block B depend on which assumption we use [I tried solving the problem and got 4.87kg when we assumed the direction of friction to go in one direction and 7.66kg when we assumed the direction of friction to go in the other direction).

I'm having difficulties understanding which assumptions to use to find the correct mass of block B.

Please keep in mind that the problem is assuming that both block A and B are in static equilibrium with no motion or movements.

Thank you!
 
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  • #2


Is this homework?

You have seven variables, (Wa; WB; T; Fa; Fb; Ra and Rb)

You are given one and can generate six linear equations: Either vert an horiz equilibrium or parallel and normal equilibrium at A and B; and two friction equations.

You should therefore be able to solve the system uniquely with the friction forces being + or - according to whether you guessed their direction correctly or not.

You have not stated the values of theta and phi so I cannot check your working, but I expect there is an erithmetic error is you have two answers.
 

FAQ: Finding Mass of Block B in Triangle with Pulley & Friction Coefficients

What is the purpose of finding the mass of Block B in a triangle with a pulley and friction coefficients?

The purpose of finding the mass of Block B is to determine the amount of force needed to move the block in a given system. This information is important in understanding the dynamics of the system and can be used to make predictions and calculations.

How is the mass of Block B calculated in this scenario?

The mass of Block B can be calculated using the formula: mass = (force x distance) / (acceleration x slope). This formula takes into account the force applied to the block, the distance it moves, the acceleration of the system, and the slope of the triangle.

What factors can affect the accuracy of the calculated mass of Block B?

The accuracy of the calculated mass of Block B can be affected by factors such as measurement errors, friction in the system, and variability in the values of the pulley and friction coefficients. It is important to take these factors into consideration and minimize their impact for a more accurate result.

How do the pulley and friction coefficients impact the calculation of Block B's mass?

The pulley and friction coefficients play a crucial role in the calculation of Block B's mass. The pulley coefficient affects the amount of force needed to move the block while the friction coefficient affects the resistance to movement. These values must be accurately measured and accounted for in the calculation to get a precise result.

Can the same method be used to find the mass of different objects in various systems?

Yes, the same general method can be used to find the mass of different objects in various systems. However, the specific formula and values used may vary depending on the specific system and its dynamics. It is important to understand the principles behind the calculation and adapt them accordingly for different scenarios.

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