How does acceleration affect tension?
In a typical case of two objects, one pulling another with a rigid link in-between, the higher acceleration of the first results in a higher tension in a link.
Here is why.
Assume the mass of the first (pulling) object is
The force of tension acts on the first object against its movement, it slows this object down. The force of tension acts on the second object towards the direction of movement since this is the only force that causes its moving forward.
These two forces, one acting on the pulling object and another acting on the pulled one, have opposite direction and the same absolute value. Let's choose the direction of the movement as the positive. Then the tension force acting on the first object is negative (
The combination of forces acting on the first body is positive
The second Newton's law gives us:
The only force acting on the second object is
Let's solve the system these two equations for
The solution is (skipping the trivial manipulations):
As we see, acceleration is proportional to the force