Solve Constrained Motion: Aa, Ab, Ac, Ad

[makeez]

http://img101.photolava.com/2009/10/21/engr-vswpt7nk.jpg
An old exam paper practice question. I can get up to b) but i am having trouble with the tensions.

I got for Aa=-10mms-2 Ad=-5mms-2, while Ac is given to be 20mms-2 and Ab=0mms-2.
Is this corrent and if so how do I go about solving question c?

This was done by creating the constraints.
2Aa + 2Ab + Ac = 0
2Ad - Aa - Ab = 0

 

[tiny-tim]

Welcome to PF!

Hi makeez! Welcome to PF!

(question c is the tension in the strings)

Start with good ol' Newton's second law for mass C … F_net = ma

 

[tomcue]

I would like to clarify that the given values of Aa, Ab, Ac, and Ad represent accelerations, not tensions. The tensions in the system can be calculated using Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). In this case, the net force is the sum of all the forces acting on the object, which includes the tension in the strings.

To solve for the tensions, you can start by drawing a free body diagram of the object and labeling all the forces acting on it. The tensions in the strings can be represented as T1 and T2. Since the object is in equilibrium, the net force acting on it is equal to zero. This means that the sum of all the forces in the x-direction and the y-direction must equal zero.

In the x-direction, we have:
T1 + T2 = 0

In the y-direction, we have:
2T1 + 2T2 + mg = 0

Using the constraints given in the question, we can substitute for the accelerations and solve for the tensions:
2(-10) + 2(0) + 20 = 0
-20 + 20 = 0
0 = 0

2(-5) - (-10) - 0 = 0
-10 + 10 = 0
0 = 0

This indicates that the tensions in the strings are equal and opposite, and they are both equal to 10m. Therefore, the tension in each string is 10m.

To solve for part c, we can use the same approach and set up a system of equations using the constraints and the known values of Aa, Ab, Ac, and Ad. From there, we can solve for the unknown acceleration and then use Newton's second law to calculate the tensions in the strings.

In conclusion, as a scientist, I would recommend approaching this problem by first clarifying the given values and then using the appropriate equations and principles to solve for the unknown quantities. It is important to carefully consider the physical meaning of each variable and to use proper units in the calculations.