Three blocks are located on a horizontal frictionless table. They are connected by a massless cord, as shown in the figure, and pulled to the right. The masses of the three blocks are m1 = 38 kg, m2 = 37 kg, and m3 = 17 kg.
a.) The pulling force is equal to T3 = 45 N. What is the acceleration of the system?
b.) What is the tension T1?
c.) What is the tension T2?
I found that the acceleration is 0.489 but I can't figure out how to find the tensions.
To find the tensions in the system, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, we have three masses connected by a massless cord, so we can consider them as a single system.
a) The pulling force is applied to the system through block 3, so the net force is equal to this force. Therefore, the net force acting on the system is 45 N.
Using Newton's second law, we can write:
Net force = (m1 + m2 + m3) * acceleration
Substituting the given values, we have:
45 N = (38 kg + 37 kg + 17 kg) * acceleration
Now, we can solve for the acceleration:
acceleration = 45 N / (38 kg + 37 kg + 17 kg)
acceleration = 0.489 m/s^2
As you correctly found, the acceleration of the system is 0.489 m/s^2.
b) To find the tension T1, we can consider the forces acting on block 1. It experiences two forces: the tension in the cord pulling it to the right and the tension in the cord pulling it to the left.
Since the system is accelerating to the right, the sum of the forces acting on block 1 must be equal to its mass multiplied by its acceleration. Let's denote T1 as the tension pulling block 1 to the right and T2 as the tension pulling block 1 to the left.
We can write:
T1 - T2 = m1 * acceleration
Substituting the given values:
T1 - T2 = (38 kg) * (0.489 m/s^2)
Now, we need additional information to solve for T1 or T2. We could use the fact that the tension in the cord connecting blocks 2 and 3 is known, or we need to know more about the pulley system or the relationship between T1 and T2.
c) Similarly, to find the tension T2, we can consider the forces acting on block 2. It also experiences two forces: the tension in the cord pulling it to the right and the tension in the cord pulling it to the left.
Again, considering the acceleration of the system, we can write:
T2 - T3 = m2 * acceleration
Substituting the given values:
T2 - 45 N = (37 kg) * (0.489 m/s^2)
Now, we can solve for T2:
T2 = (37 kg) * (0.489 m/s^2) + 45 N
Unfortunately, without additional information, we cannot determine the exact values of T1 and T2.