Two racquetballs, each having a mass of 200 g, are placed in a glass jar as shown in in the figure below. Their centers lie on a straight line that makes a 45° angle with the horizontal.
To calculate the forces acting on the racquetballs, we need to consider the weight of each ball and the tension in the string.
1. Weight of the racquetballs:
The weight of an object is given by the formula: weight = mass * acceleration due to gravity (g).
In this case, the mass of each racquetball is given as 200 g = 0.2 kg. The acceleration due to gravity, g, is approximately 9.8 m/s^2.
So, the weight of each ball would be: weight = 0.2 kg * 9.8 m/s^2 = 1.96 N.
2. Tension in the string:
At 45 degrees angle, the forces acting on the racquetballs can be resolved into vertical and horizontal components. The net force acting on each racquetball in the vertical direction is zero since they are in equilibrium.
Therefore, the tension in the string can be calculated from the horizontal forces acting on each ball. Each ball experiences an equal and opposite horizontal force from the other ball through the string.
Using trigonometry, we can determine the horizontal component of the weight of each ball:
horizontal force = weight * cos(45°).
For each ball:
horizontal force = 1.96 N * cos(45°).
Finally, the tension in the string is the sum of these horizontal forces acting on each ball: Tension = 2 * horizontal force.
Now, you can substitute the value for the horizontal force to calculate the tension in the string.