0.21 Phy1190: energy -- kinetic and mechanical energy  (Page 6/8)

Mechanical energy possessed by the dart

At that point in time, the dart has gravitational potential energy due to its height above the floor and the suction cup haselastic potential energy due to having been deformed within its elastic limit.

The slightest air leak will cause the suction cup to return to its original shape, thereby causing the dart to pop off the target. Then the gravitationalpotential energy possessed by the dart will cause it to fall to the floor.

Total mechanical energy

The total amount of mechanical energy possessed by an object is the sum of the potential and kinetic energy possessed by the object. Therefore,

TME = PE + KE

where

• TME represents the total mechanical energy
• PE represents the total potential energy
• KE represents the kinetic energy

Because the potential energy can be of two forms,

TME = PEs + PEg + KE

where

• TME represents the total mechanical energy
• PEs represents the potential energy due to deformation such as stretching, compressing, twisting, etc.
• PEg represents the potential energy due to gravity
• KE represents the kinetic energy

Energy is a scalar quantity

As mentioned earlier, energy is a scalar and not a vector quantity. Therefore, the total mechanical energy is simply the sum of the three types ofenergy possessed by the object. There are no angles or directions to contend with when computing the sum.

Conversion of energy between types

Over the course of time, a moving object can convert the types of energy between the different forms. A good example is the pendulum on a clock, or a child sittingmotionless in a swing that is in motion.

When the pendulum reaches its highest point...

There is an instant in time where a swinging pendulum is at its highest point and it is not moving. At that instant, it has no kinetic energy but it has maximum gravitational potential energy.

When the pendulum reaches its lowest point...

As the pendulum goes through the lowest point in its swing, it has the greatest speed and therefore the greatest amountof kinetic energy. If you define the zero height reference as the height of the pendulum at that point, then it has no potential energy at that point in time.

Swapping kinetic energy for potential energy

Therefore, the total mechanical energy of the pendulum is swapped back and forth between kinetic energy and potential energy in a very smooth way.

If the pendulum were swinging in a friction-free environment, it would continue thatprocess forever. The total amount of mechanical energy would stay the same but at any instant in time would be divided between potential and kinetic energy.

Of course, there is no such thing as a friction-free environment and a small amount of energy is dissipated by friction each time the pendulum swings througha cycle. Over time, therefore, the total mechanical energy in the pendulum would be depleted and the pendulum would stop swinging.

Pendulum clocks have springs

That is why pendulum clocks have springs or weights that store potential energy and impart a small amount ofenergy into the pendulum mechanism during each swing.