0.21 Phy1190: energy -- kinetic and mechanical energy  (Page 2/8)

There's that little brother again

When your little brother throws a ball and scores a solid hit on your back (not a glancing blow), thevelocity of the ball goes to zero upon contact and the kinetic energy possessed by the baseball is released into your body. This can sometimes cause pain, particularlyif the ball possesses a lot of kinetic energy.

Forms of kinetic energy

Kinetic energy comes in a variety of forms, including:

• rotational, which is due to rotational motion such as a wheel on a bicycle
• translational, which is due to the movement of an object from one location to another location

I will concentrate on translational kinetic energy in this module and will deal with other forms of kinetic energy in future modules.

Two factors control the amount of kinetic energy

The amount of translational kinetic energy possessed by a moving object depends on two factors:

1. The mass of the object.
2. The velocity of the object.

How did the object attain its current velocity?

Note that it doesn't matter how the object attained its current velocity. The object may have attained its current velocity by accelerating very slowly over aperiod of years. The object may have fallen off a tall bookshelf and attained its current velocity fairly quickly as a result of the acceleration of gravity. Or, the object may have been shot out of a cannondue to an explosion of gun powder and acquired its current velocity very quickly.

With regard to the kinetic energy currently possessed by the object, the only things that are important are:

1. What is the mass of the object?
2. What is the current velocity of the object?

Calculating kinetic energy

We know that an object can have motion (and hence kinetic energy) at the current time only if work was done on the object earlier to put it in motion. We also know that thekinetic energy will be equal to the work that was performed on the object to put it in motion with the possible loss of kinetic energy due to friction or otherfactors over time.

Knowing those things, and assuming that the object gained its current velocity as a result of constant acceleration, we can derive an equation thatrepresents the kinetic energy possessed by the object.

The definition of work -- review

Recall the definition of work:

work = force * displacement * cos(theta)

where

• theta is the angle between the direction of displacement and the line of action of the force.

In this case, we might as well assume that theta is 0 degrees.

The equation for work

Therefore, W = f*d

where

• W represents work, and ultimately kinetic energy
• f represents force
• d represents distance or displacement

Acceleration is caused by force

We also know that a given force applied to an object will produce a given acceleration, as in

f = m*a

where

• f represents force
• m represents mass
• a represents acceleration

Distance traveled by an object under constant acceleration

In an earlier module, you learned that when an object is subjected to a constant acceleration, the distance traveled by the object in a given time isrepresented by