How Does a Cat Affect the Acceleration of a Modified Atwood Machine?

[agnosticus]

Homework Statement

Given in this problem is a modified Atwood Machine (block A sits on a horizontal surface with a massless rope attached which goes horizontally over a frictionless pully attached to the edge of the "cliff" which is attached downward to block B)



W of A = 45.0 N, W of B = 25.0 N, mu = 5/9

A 45 N cat falls asleep on box A. If box B is now set in motion, what is it's acceleration (magnitude and direction)?

Homework Equations

f[tex]_{kA}[/tex] = ([tex]\mu[/tex])n

The Attempt at a Solution

50N = (5/9)(90N). I then have found the net force on block B and found it to be -9.80 m/s[tex]^{2}[/tex]. The correct answer for this is 2.13 m/s[tex]^{2}[/tex] upward. What am I missing?

 

[anathema]

Thank you for your post. Your calculations are on the right track, but there are a few things that you may have missed.

Firstly, when a cat falls asleep on box A, its weight will now be included in the total weight of block A. Therefore, the weight of block A should be 90 N (45 N + 45 N from the cat).

Secondly, when finding the net force on block B, you must also take into account the tension in the rope. This tension will be equal to the weight of block A (90 N) since the rope is massless. Therefore, the net force on block B will be 90 N - 25 N = 65 N.

Finally, to find the acceleration of block B, you must use Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration (F = ma). In this case, the mass of block B is not given, but it can be calculated using its weight and the acceleration due to gravity (m = W/g). Once you have the mass, you can solve for the acceleration (a = F/m).

I hope this helps you in finding the correct answer. Let me know if you have any further questions.

 

[baba89]

Based on the given information, it seems that the Atwood Machine in this problem has been modified to include a horizontal surface and a friction coefficient. This may affect the calculations and result in a different acceleration than expected. It is important to carefully consider all the given parameters and equations before attempting to solve the problem. In this case, it may be helpful to draw a free body diagram and analyze the forces acting on each block separately. Additionally, double checking the calculations and units may also help in finding the correct answer.