Help Finding the Tension between 2 Masses

[ttk3]

Three blocks on a frictionless surface are connected by massless strings, with M1 = 1.10 kg, M2 = 2.80 kg, and M3 = 3.50 kg. Due to the force F acting on M3, as shown, the system accelerates to the right. Given that T1 is 2.90 N, calculate T2.

I found the acceleration of the problem using F1 = m1 (T1 / (M1 + M2)). Where do I go from here?

 

[learningphysics]

So is T1 between M2 and M3, and T2 between M1 and M2?

I don't understand how you got the acceleration... can you describe or upload a picture?

 

[m2003]

To find the tension between the two masses, we can 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, we can set up two equations, one for the horizontal direction and one for the vertical direction, and solve for the unknown tension (T2).

In the horizontal direction, we know that the net force acting on the system is equal to the force applied on M3 (F), which is also equal to the sum of the tensions on M1 and M2 (T1 + T2). Therefore, we can write the equation: F = (M1 + M2 + M3)a. Substituting in the known values, we get F = (1.10 kg + 2.80 kg + 3.50 kg)a. Solving for acceleration, we get a = F / (1.10 kg + 2.80 kg + 3.50 kg) = F / 7.40 kg.

In the vertical direction, we can set up a similar equation, taking into account the weight of the blocks (M1g, M2g, and M3g) and the tension on M3 (T2). Since the system is on a frictionless surface, there is no frictional force to consider. Therefore, our equation becomes: T2 - M1g - M2g - M3g = 0. Substituting in the known values, we get T2 - (1.10 kg)(9.8 m/s^2) - (2.80 kg)(9.8 m/s^2) - (3.50 kg)(9.8 m/s^2) = 0. Solving for T2, we get T2 = (1.10 kg + 2.80 kg + 3.50 kg)(9.8 m/s^2) = 7.40 kg(9.8 m/s^2) = 72.52 N.

Therefore, the tension between the two masses is 72.52 N, given the known force applied on M3 and the tension on M1. It is important to note that this solution assumes that the system is in equilibrium, meaning that the acceleration is constant and there is no net force in any direction. If the system is not in equilibrium, the tension between the two masses may be