a 1.29 kg ball is connected by means of two massless strings to a vertical, rotating rod. The strings are tied to the rod and are taut. The tension in the upper string is 38 N.

The length of both strings is 1.70m and the distance between the strings on the rod is 1.7.

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To find the tension in the lower string, we can use the concept of equilibrium.

In equilibrium, the sum of the forces acting on an object is zero. In this case, the forces acting on the ball are its weight (mg) and the tension in the two strings.

Let's break down the forces acting on the ball:

1. Weight (mg): The weight of the ball can be calculated using the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity.
Given: mass (m) = 1.29 kg, acceleration due to gravity (g) = 9.8 m/s^2
Therefore, weight (W) = (1.29 kg) x (9.8 m/s^2) = 12.642 N

2. Tension in the upper string (T1): Given as 38 N.

3. Tension in the lower string (T2): This is what we need to find.

Since the ball is in equilibrium, the sum of the vertical forces (in the upward direction) must equal the sum of the vertical forces (in the downward direction).

The vertical forces acting upward are the tension in the upper string (T1) and the tension in the lower string (T2).

The vertical force acting downward is the weight of the ball (W).

So we can write the equation:
T1 + T2 = W

Now we can substitute the given values:
38 N + T2 = 12.642 N

To find T2, we simply need to subtract 38 N from both sides of the equation:
T2 = 12.642 N - 38 N

Therefore, the tension in the lower string is:
T2 = -25.358 N (Note that the negative sign indicates that the tension in the lower string is acting in the opposite direction to T1, i.e., downward).