Newton's Second Law in NON-inertial frame of reference

[Spiewgels]

Homework Statement

The steel ball is suspended from the accelerating frame by the two cords A and B. The angles (they are on the inside) are both 60 degrees.

Determine the acceleration of the frame which will cause the tension in A to be twice that in B. The acceleration is going to the right and the cord A is to the right of the moving frame.

Provide your answer in m/s/s with one decimal point accuracy

Homework Equations

I want to know how to relate the forces on the inside of the accelerating frame to the accelerating frame itself.

The Attempt at a Solution

Thus far, I have drawn free body diagrams to the inside cords and steel ball. I broke down the components of cord A and B and found the x-coordinate of cord A to be Acos60 and y-coordinate of Asin60. I got these same results for cord B. Combining knowns I've determined both cords tension to be .87w where w equals the weight of the ball. I'm now stuck and don't know how this relates to the moving frame where I think the force is F=ma(of x) and a(of x)=F/m...Have I screwed up this entire problem?

 

[Dick]

You've apparently solved the problem of a ball hanging in a gravitational field using F=mg. In an frame with acceleration vector a, the equivalent force is given by F=ma (obviously) in the direction opposite to the acceleration. So redraw your force diagram, but this time instead of drawing the 'external' force as pointing straight down, let it point at some angle. Your job is to determine that angle so you get the right tension relation.

 

[m2003]

I would like to clarify that Newton's Second Law applies to both inertial and non-inertial frames of reference. In a non-inertial frame, the acceleration of the frame must be taken into account when calculating the forces acting on objects within the frame. In this scenario, we can use the equations of motion for a non-inertial frame to relate the forces acting on the cords and the steel ball to the acceleration of the frame itself.

To determine the acceleration of the frame, we can use the fact that the tension in cord A is twice that in cord B. This means that the net force in the x-direction must be equal to zero, as there is no acceleration in that direction. Therefore, we can set up the equation:

2Tsin60 - Tsin60 = ma

Where T is the tension in cord A, m is the mass of the steel ball, and a is the acceleration of the frame. Solving for a, we get:

a = T/m = (2Tsin60 - Tsin60)/m = T/m = 0.5g

Where g is the acceleration due to gravity. Therefore, the acceleration of the frame is 0.5g to the right.

I hope this helps clarify the relationship between the forces on the inside of the accelerating frame and the frame itself. It is important to consider the acceleration of the frame when analyzing forces in a non-inertial frame.