At a low point of its swing, a pendulum bob with a mass of 0.20kg has a velocity of 4.0m/s. (a) What is its kinetic energy? (b) How high will the bob swing above the low point before reversing direction?

To find the answer to part (a) of the question, we need to calculate the kinetic energy of the pendulum bob.

The formula for calculating kinetic energy is:

Kinetic Energy = (1/2) * mass * velocity^2

Substituting the given values into the formula, we get:

Kinetic Energy = (1/2) * 0.20kg * (4.0m/s)^2

Simplifying further, we have:

Kinetic Energy = 0.5 * 0.20kg * 16m^2/s^2

Kinetic Energy = 1.6 Joules

So, the kinetic energy of the pendulum bob is 1.6 Joules.

Moving on to part (b) of the question, to determine how high the bob will swing above the low point before reversing its direction, we can use the principle of conservation of energy.

At the lowest point, the total energy of the pendulum bob is entirely potential energy, given by the formula:

Potential Energy = mass * gravity * height

At the highest point, all the potential energy is converted into kinetic energy. Therefore, we can equate the potential energy at the lowest point to the kinetic energy at the highest point:

Potential Energy = Kinetic Energy

Applying the formula for potential energy, we have:

mass * gravity * height = (1/2) * mass * velocity^2

Mass cancels out, and we can rearrange the equation to solve for height:

height = (1/2) * velocity^2 / gravity

Substituting the given values, we have:

height = (1/2) * (4.0m/s)^2 / 9.8m/s^2

Calculating further, we get:

height = 0.82 meters

Therefore, the pendulum bob will swing approximately 0.82 meters above the low point before reversing its direction.