Final answer:
The tension in the rope at the ball's lowest point is 85.5 N, which consists of the gravitational force acting on the ball (60 N) plus the centripetal force (25.5 N) due to the ball's circular motion.
Step-by-step explanation:
To determine the tension in the rope when a 60 N ball is swinging as a pendulum through its lowest point at a speed of 5.0 m/s, we must consider both the gravitational force and the centripetal force required to keep the ball moving in a circular path.
The tension in the rope at the lowest point consists of two components: the weight of the ball (which is the gravitational force) and the centripetal force needed for circular motion. The gravitational force is simply the weight of the ball, which is given as 60 N. The centripetal force (Fc) can be calculated using the formula Fc = m*v2/r, where m is the mass of the ball, v is the velocity, and r is the radius (length of the rope).
Firstly, we need to find the mass of the ball using the gravitational force equation Fg = m*g. Given that Fg is 60 N and g is 9.8 m/s2 (the acceleration due to gravity), we can solve for m yielding m = Fg/g = 60 N / 9.8 m/s2 = 6.12 kg approximately.
Now, we can calculate the centripetal force required: Fc = m*v2/r = 6.12 kg * (5.0 m/s)2 / 6.0 m = 25.5 N approximately.
The total tension in the rope is the sum of the gravitational force and the centripetal force: T = Fg + Fc = 60 N + 25.5 N = 85.5 N.
Therefore, the tension in the rope at the ball's lowest point during its pendulum swing is 85.5 N.