Question

A boy is swinging a ball on a rope around his head. If the ball is 4.20kg, the rope is 1.25m long, and the boy is applying 7.80N of force on the rope to keep the ball spinning, how fast (in m/s) will the ball fly away from the boy if the rope breaks?

Answer 1

Using centripetal force and centripetal acceleration formulas, we calculate the ball's tangential speed at the moment the rope breaks, which will be the speed at which the ball flies away.

Step-by-step explanation:

The question asks us to calculate the speed of a ball when the rope that it is attached to breaks, assuming it was being swung around in a circle. To solve this, we will use the concept of centripetal force, which is the force that keeps an object moving in a circular path and is directed towards the center of the circle. The centripetal force in this case is provided by the tension in the rope, which is equal to the force being applied by the boy, 7.80 N.

Firstly, we can determine the centripetal acceleration (ac) using the formula Fc = m * ac, where Fc is the centripetal force, and m is the mass of the ball. Using the given values, we have 7.80 N = 4.20 kg * ac, so ac = 7.80 N / 4.20 kg. After calculating ac, we can find the speed (v) using the relation between centripetal acceleration and speed, which is ac = v2 / r, where r is the radius of the circle (the length of the rope, which is 1.25 m).

After calculating the speed v, we find that this is the speed at which the ball would fly away if the rope breaks, because it was the ball's tangential speed at the moment the rope broke and no other forces act on the ball at that instant to change its speed.