Question

A ball, which weighs 9.8 N, is tied to the end of a light string, l - 0.5 m in length. When the ball swings in its arc, the tension in the string is 14.3 N at the bottom of the arc. What is the ball's acceleration at the bottom of the arc? What is the ball's speed at the bottom of the arc?

Answer 1

The ball's acceleration at the bottom of the arc is 1459.18 m/s². The ball's speed at the bottom of the arc is 27.03 m/s.

Step-by-step explanation:

At the bottom of the arc, the ball's acceleration can be found using the equation: Tension = mass*acceleration. Rearranging the equation, acceleration = Tension/mass. Plugging in the values given, we get:

acceleration = 14.3 N / 0.0098 kg = 1459.18 m/s².

The ball's speed at the bottom of the arc can be found using the equation: centripetal force = mass*velocity²/radius. Rearranging the equation for velocity, we get:

velocity = sqrt(centripetal force*radius/mass)

Plugging in the values given:

velocity = sqrt(14.3 N * 0.5 m / 0.0098 kg) = sqrt(729.18) = 27.03 m/s