Masses & Pulley: Balancing Forces with mA, mB, mC

[KMjuniormint5]

In the figure below, three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The masses are mA = 22.0 kg, mB = 40.0 kg, mC = 30.0 kg.

figure:

Pulley-----------mA
|
|
|
mB
|
mC

Now I apply Fnet = ma so. . .

the massA in the x direction would be T1 (tension) = (mA)(ax) and in the Y direction n-(mA)(g) = (mA)(ay).
the massB in the y direction would be T1-T2 - (mB)(g) = (mB)(ay)
the massC in the y direction would be T2 - (mC)(g) = (mC)(ay)

but in the equations above wouldn't acceleration in the x direction (ax) = 0? and accel. in the y (ay)direction be (9.8 m/s^2 aka gravity (g))

 

[learningphysics]

No ax isn't 0. The acceleration of mA towards the left equals the acceleration of the hanging masses downwards...

using your conventions ax = -ay.

so you have 3 equations with 3 unknowns... T1, T2 and ax.

One "trick" you can use to simplify calculating T1 and ax, is to take mB and mC together as one system. that way you get 2 equations with 2 unknowns, T1 and ax.

But the 3 equations you have seem fine.

 

[ogb p]

Yes, you are correct. In this scenario, the acceleration in the x direction (ax) would be zero because the pulley and cords have negligible friction and mass, so there is no net force acting in that direction. The acceleration in the y direction (ay) would be equal to the acceleration due to gravity (g) as it is the only force acting in that direction. Therefore, the equations you have written are correct and can be used to calculate the tensions (T1 and T2) in the cords. It is important to consider all forces acting on each mass in order to accurately calculate the tensions and ensure that the system is in equilibrium.

 

[m2003]

I can confirm that your understanding of the forces and equations involved in this system is correct. The acceleration in the x-direction will indeed be zero, as there are no external forces acting on the masses in that direction. The only forces acting in the y-direction are the tension forces from the cords and the force of gravity, which is equivalent to the acceleration due to gravity (g).

To fully analyze this system, we would need to consider the direction and magnitude of the tension forces in the cords. However, based on the information given, it appears that the system is in equilibrium, meaning that the forces are balanced and there is no net acceleration. This is a common occurrence in systems involving pulleys, as the tension forces in the cords can counteract the force of gravity and create a balanced system.

Overall, your understanding of the forces and equations involved in this system is accurate. Keep up the good work!