A 0.50 kg ball that is tied to the end of a 1.2 m light cord is revolved in a horizontal plane with the cord making a 30° angle, with the vertical

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To find the tension in the cord, we need to consider the forces acting on the ball.

In this case, there are two forces: the tension in the cord (T) and the weight of the ball (mg).

The weight of the ball can be calculated using the formula:

Weight (mg) = mass (m) × acceleration due to gravity (g)

Given that the mass of the ball is 0.50 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:

Weight (mg) = 0.50 kg × 9.8 m/s^2 = 4.9 N

Now, let's analyze the forces acting on the ball in the horizontal plane. We have the weight acting vertically downwards (mg) and the tension in the cord (T) acting at an angle of 30° with the vertical.

To find the vertical component of the tension (T_vertical), we can use trigonometry:

T_vertical = T × cos(30°)

And to find the horizontal component of the tension (T_horizontal), we can also use trigonometry:

T_horizontal = T × sin(30°)

Since the ball is not in vertical equilibrium (it is rotating in a horizontal plane), we know that the vertical component of the tension must balance the weight:

T_vertical = mg

Plugging in the values we know:

T × cos(30°) = 4.9 N

Now, we can solve for T:

T = 4.9 N / cos(30°)

Using a calculator:

T ≈ 5.64 N

So, the tension in the cord is approximately 5.64 N.