How do you calculate the kinetic and potential energy?

Question

How do you calculate the kinetic and potential energy of an gravitational pendulum?

Answer 1

Not sure what a "gravitational" pendulum is. But here's a bit of physics that may help you work the problem. Potential energy = PE = mgh; where mg is the weight of the bob on the end of the pendulum and h is the height of that bob above its low point in the swing. (NB: h is just the vertical distance, there is no horizontal component in doing PE.)

Now, the second bit of physics. PE = mgh = 1/2 mv^2 = KE = kinetic energy; where v = the total velocity vector v = dx/dt + dy/dt or in scalar v^2 = (dx/dt)^2 + (dy/dt)^2. In other words, all that work to raise the bob h distance becomes PE = mgh. And when the pendulum swings back down, that PE is converted to KE minus friction losses if any.

Since you mention no friction mgh = 1/2 mv^2 so that v^2 = 2gh or, as it is usually given, v = sqrt(2gh), which is the total velocity magnitude at the bottom of the swing.

Answer 2

Kinetic Energy= mv² (mass times velocity squared) Potential Energy + Kinetic Energy + Heat lost to friction = Total energy What this basically means is that whenever the spring is pulled back fully, all the energy is potential, and none is kinetic. Once the spring is released, the potential energy is being transformed into kinetic energy. Kinetic energy is the energy of movement. Half way through the release, when the car has the most kinetic energy, it has the least potential energy. The total amount of energy is the same, but it is converted from potential to kinetic. However, energy is lost due to friction. Friction causes energy to be converted to heat. At the end, when the car comes to a stop, all energy has been lost to friction and converted to heat.