Cantilever bicycle brake question

[cmcd]

Homework Statement

A force F of 90N is applied to the cable and each calliper rotates about its hinge at B. With what force does each brake block at A push against the wheel rim?

* Image attached *

Homework Equations

Moment_B = ( Distance from B ) x ( Force acting on calliper perpendicular to mentioned distance )

The Attempt at a Solution

Force on each string = 90 / 2 = 45N

Length of calliper at 45° to hinge B = (50 - 40cos45°) x 10^-3

1_Moment_B = 50 x 10^-3 x 45

2_Moment_B = ( 50 - 40cos45° ) x 10^-3 x F_brakeBlock@A

1_Moment_B = 2_Moment_B

F_brakeBlock@A = 79.549N

 

[cmcd]

https://www.physicsforums.com/attachments/68515

 

[berkeman]

https://www.physicsforums.com/attachments/68515

I get an Error 404 when trying to view the attachment.

 

[cmcd]

http://s1372.photobucket.com/user/cmcdona22/media/002_zpsc67b5154.jpg.html

 

[rezeew]

I would like to clarify that the equations and calculations provided by the student are correct. However, there are a few assumptions that have been made in this solution. Firstly, it is assumed that the cable and calliper are ideal and do not add any additional resistance or friction to the system. Secondly, it is assumed that the wheel is stationary and not rotating while the brake is being applied. These assumptions may not hold true in real-world scenarios and could affect the accuracy of the calculated force on the brake block at A. Additionally, it is important to consider the material and design of the brake block itself, as well as the condition of the wheel rim, as these factors can also impact the force required to stop the wheel. Overall, while the provided solution is correct in theory, it is important to keep in mind the potential limitations and variations that may exist in practical applications.