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 determine the tension in the cord, we can use the principles of circular motion and centripetal force.
First, let's analyze the forces acting on the ball:
- Tension force (T) acting towards the center of the circle, which provides the centripetal force.
- Weight force (mg) acting vertically downward.
- Horizontal component of the tension force (T_h) acting opposite to the horizontal component of the weight force.
To find the tension in the cord, we need to resolve the weight force into its horizontal and vertical components:
- The vertical component of the weight force is given by mg * cos(30°).
- The horizontal component of the weight force is given by mg * sin(30°).
Since the ball is in equilibrium, the net force acting on it should be zero. Therefore, the horizontal component of the tension force must balance the horizontal component of the weight force.
Thus, T_h = mg * sin(30°).
To find the tension in the cord, we can use the Pythagorean theorem:
T² = T_h² + T_v²
Substituting the known values into the equation, we have:
T² = (mg * sin(30°))² + (mg * cos(30°))²
The mass is given as 0.50 kg. The acceleration due to gravity (g) is approximately 9.8 m/s². By substituting these values, the equation becomes:
T² = (0.50 kg * 9.8 m/s² * sin(30°))² + (0.50 kg * 9.8 m/s² * cos(30°))²
Simplifying further, we calculate:
T² = (0.50 * 9.8 * 0.5)² + (0.50 * 9.8 * 0.866)²
T² = (2.45)² + (4.25)²
T² = 6.0025 + 18.0625
T² = 24.065
Taking the square root of both sides, we find:
T ≈ √24.065
T ≈ 4.906 N
Therefore, the approximate tension in the cord is 4.906 Newtons.