A 2940 kg demolition ball swings at the end of a 16.9 m cable on the arc of a vertical circle. At the lowest point of the swing, the ball is moving at a speed of 8.28 m/s. Determine the tension in the cable.
To determine the tension in the cable, we can use the principle of centripetal force. At the lowest point of the swing, the gravitational force and the tension force in the cable combine to provide the centripetal force required to keep the demolition ball in circular motion.
The centripetal force is given by the equation:
Fc = m * v^2 / r
Where:
Fc = centripetal force
m = mass of the demolition ball (2940 kg)
v = velocity of the demolition ball (8.28 m/s)
r = radius of the circular path (cable length - height from lowest point to center of circle)
First, let's calculate the radius of the circular path using the given information. The length of the cable is 16.9 m, and the height from the lowest point to the center of the circle can be calculated as follows:
h = cable length - radius
Since the radius is half the cable length, we have:
h = 16.9 m - (16.9 m / 2)
h = 16.9 m - 8.45 m
h = 8.45 m
Now, we can substitute the values into the formula to calculate the centripetal force:
Fc = (2940 kg) * (8.28 m/s)^2 / (8.45 m)
Calculating this gives us:
Fc = 2940 kg * (8.28 m/s)^2 / 8.45 m
Fc = 24677.9048 N
Therefore, the centripetal force required at the lowest point is approximately 24677.9048 N.
Since the tension force in the cable provides the necessary centripetal force, the tension in the cable is also 24677.9048 N.