The Physics of a Swing: Understanding Kinetic and Potential Energy

George is pushing his 20kg son, Jake, on the swing at the park. He pulls his son up to a height of 2m, pauses, and lets him go. What is Jake's kinetic energy before his dad lets go of the swing? What is Jake's kinetic energy at the lowest point? What is Jake's velocity at the top of the lowest point?

Jake's velocity at the lowest point of the swing is 7 m/s.

What is kinetic and potential energy?

Potential energy is the energy stored in any object or system due to the position or arrangement of its parts. It is, however, unaffected by factors outside of the object or system, such as air or height. Kinetic energy, on the other hand, is the energy of moving particles in an object or system.

To solve this problem, we need to use the conservation of energy principle, which states that the total energy in a system remains constant.

At the highest point, Jake has potential energy (due to his position above the ground), but no kinetic energy (since he is not moving).

As he swings down, his potential energy is converted to kinetic energy, and at the lowest point of the swing, he has the maximum kinetic energy and minimum potential energy. Then, as he swings back up, the process is reversed.

To calculate Jake's potential energy at the top of the swing, we use the formula:

PE = mgh

where m is the mass of Jake, g is the acceleration due to gravity (9.8 m/s²), and h is the height above the ground. Substituting in the values, we get:

PE = (20 kg)(9.8 m/s²)(2 m) = 392 J

This is Jake's potential energy at the top of the swing. At this point, he has no kinetic energy.

At the lowest point of the swing, Jake has converted all of his potential energy into kinetic energy. We can use the conservation of energy principle to find his kinetic energy at this point:

KE = PE

where KE is kinetic energy and PE is potential energy. Substituting in the values, we get:

KE = 392 J

This is Jake's kinetic energy at the lowest point of the swing.

To find Jake's velocity at the lowest point, we can use the formula for kinetic energy:

KE = (1/2)mv²

where v is velocity. Rearranging the formula to solve for v, we get:

v = √((2KE)/m)

Substituting in the values, we get:

v = √((2(392 J))/(20 kg)) = 7.0 m/s

This is Jake's velocity at the lowest point of the swing.