Question

An old building is being demolished by swinging a heavy metal ball from a crane. Suppose that such a 100 kg

ball swings from a 20-m
-long wire at speed 16 m/s
as the wire passes the vertical orientation.

Answer 1

The speed of the ball when the wire passes the vertical orientation is 28 m/s.

When the heavy metal ball is swinging at the vertical orientation, it is experiencing potential energy and kinetic energy. The potential energy is given by the formula: potential energy = mass x gravitational acceleration x height. The kinetic energy is given by the formula: kinetic energy = 1/2 x mass x velocity squared. At the vertical orientation, all the potential energy is converted into kinetic energy, so the kinetic energy at that point is equal to the potential energy. Therefore, we can use the formula to find the kinetic energy and then solve for the velocity: velocity = sqrt(2 x potential energy/mass).

Using the given values, we can calculate the potential energy: potential energy = 100 kg x 9.8
`m/s^2` x 20 m = 19600 J. Plugging the potential energy and mass values into the equation, we can solve for the velocity: velocity = sqrt(2 x 19600 J / 100 kg) = 28 m/s. Therefore, the speed of the ball when the wire passes the vertical orientation is 28 m/s.