TWo identical l-5.0-kg balls, Figure P5.85
each 25.0 cm in diameter, are suspended
by two 35.0-cm wires (Fig. P5.85). The
entire apparatus is supported by a
single 18.0-cm wire, and the surfaces
oi the balls are perf'ectly smooth.
(a) Find the tension in each of the three
wires. (b) How hard does each ball
push on the other one?
To find the tension in each of the three wires and how hard each ball pushes on the other, we can use Newton's laws of motion.
(a) Finding the tension in each wire:
1. Calculate the weight of each ball:
The weight of an object can be determined using the formula: weight = mass * gravity, where gravity is approximately 9.8 m/s^2.
Given that each ball has a mass of 5.0 kg, the weight of each ball is:
weight = 5.0 kg * 9.8 m/s^2 = 49.0 N
2. Find the tensions in the two vertical wires:
Since the balls are in equilibrium (not accelerating), the tension in each of the two vertical wires must equal the weight of each ball. Therefore, the tension in each of the vertical wires is 49.0 N.
3. Find the tension in the horizontal wire:
The horizontal tension can be found by considering the net force acting on the system in the horizontal direction. Since the ball arrangement is symmetrical, the horizontal forces acting on each ball cancel each other out. Thus, the tension in the horizontal wire must be zero (0 N).
Therefore, the tension in each of the three wires is as follows:
Tension in vertical wires: 49.0 N
Tension in horizontal wire: 0 N
(b) Finding the force exerted by each ball on the other:
Since the balls push each other, they exert equal and opposite forces on each other according to Newton's third law.
Therefore, each ball pushes on the other with a force of 49.0 N.