0.21 Phy1190: energy -- kinetic and mechanical energy  (Page 7/8)

Where does the potential energy come from

That raises another issue. What happens to the clock when the spring or weights expend all of their stored energy. The answer is that eventually the pendulum will stopswinging and the clock will stop running unless a human imparts more energy intothe spring or weight system that keeps the clock running.

Twenty-four hours of controlled energy transfers

I can still remember my grandfather winding the spring on his pendulum clock as the last thing he did before going to bed each night. He was convertingpotential energy derived from food into elastic potential energy in the clock's spring.

During the next 24 hours, that elastic potential energy would be converted to a combination of gravitational potential energy and kinetic energy in thependulum, which would move the hands on the clock to indicate the correct time.

The next night, my grandfather would start the process all over again by imparting energy into the clock's spring.

Sample calculations

I will present and explain sample calculations involving both kinetic energy and mechanical energy in this section.

Kinetic energy

A roller coaster car

What is the kinetic energy possessed by a 1378 pound roller coaster car that is moving with a speed of 60 ft/sec?

Answer:

Enter the following expression into the Google search box:

0.5*1378lb * (60ft/s)^2

The resulting kinetic energy is 1.045 * 10^5 joules.

Similarly, you could enter the following into the Google search box:

0.5*625kg * (60ft/s)^2

and you would get the same answer of 1.045 * 10^5 joules.

As you can see, it doesn't matter whether you use English units or SI units for mass and velocity,as long as you do the calculation correctly. The answer is the same, because the kinetic energy of the object doesn't change just because you express thosequantities in different units.

More on the roller coaster car

What would be the kinetic energy of another car with the same mass but with three times the speed?

Answer:

We don't even need to evaluate the equation to answer this question. We know that the kinetic energy varies as the square of the speed, so if we triple thespeed, we will increase the kinetic energy by a factor of 3*3=9. Therefore,

KE = 9*1.045 * 10^5 joules = 9.405 * 10^5 joules

Dead Fred the daredevil

Dead Fred, the daredevil possessed a kinetic energy of 18000 joules just prior to hitting a solid brick wall on his motorcycle. If his mass was 176 pounds, what was his speed?

Answer:

KE = 0.5*m*v^2, or

v^2 = KE/(0.5*m), or

v = sqrt(KE/(0.5*m)), or

v = sqrt(18000joules/(0.5*176pound))

Enter the right-hand expression above into the Google search box and you should get a velocity of

v = 21.24 m/s

Mechanical energy

A dart gun

A dart with a mass of 0.1 kg leaves the muzzle of a dart gun with a velocity of 10 m/s. The child is holding the dart gun at a position that is 1 m above theground. At that instant,

1. What is the potential energy of the dart?
2. What is the kinetic energy of the dart?
3. What is the total mechanical energy of the dart?
4. Assuming no losses of energy due to friction or other causes, what is the change in the total mechanical energy of the gun at the instant the dart exits the gun?