A tetherball leans against the smooth, frictionless post to which it is attached. The string is attached to the ball such that a line along the string passes through the center of the ball. The string is 1.30 long and the ball has a radius of 0.170 with mass 0.440 .
What is the tension in the rope?
What is the force the pole exerts on the ball?
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To determine the tension in the rope, we need to consider the forces acting on the ball. There are two forces at play here: the gravitational force acting downward and the tension force in the rope acting upward.
1. Calculate the gravitational force (weight) acting on the ball:
The weight of the ball is given by the formula: weight = mass * gravitational acceleration.
In this case, the mass of the ball is 0.440 kg, and the standard gravitational acceleration is approximately 9.8 m/s^2. Therefore, the weight of the ball is:
weight = 0.440 kg * 9.8 m/s^2 = 4.312 N.
2. Determine the force the pole exerts on the ball:
Since the pole is smooth and frictionless, the pole exerts only a normal force on the ball. This normal force acts vertically upward and is equal in magnitude and opposite in direction to the gravitational force.
Therefore, the force the pole exerts on the ball is equal to the weight of the ball (since there is no horizontal force):
force by pole = 4.312 N.
3. Calculate the tension in the rope:
To find the tension in the rope, we need to consider the net force acting on the ball. Since the ball is in equilibrium (not moving), the net force is zero.
The tension in the rope balances the weight of the ball and is equal in magnitude and opposite in direction:
tension = 4.312 N.
Thus, the tension in the rope is 4.312 N and the force the pole exerts on the ball is also 4.312 N.