Newton's law of conservation states that energy of an isolated system remains a constant. It can neither be created nor destroyed but can be transformed from one form to the other.
Implying the above law of conservation of energy in the case of pendulum we can conclude that at the bottom of the swing the entire potential energy gets converted to kinetic energy. Also the potential energy is zero at this point.
Mathematically also potential energy is represented as
Potential energy= mgh
Where m is the mass of the pendulum.
g is the acceleration due to gravity
h is the height from the bottom z the ground.
At the bottom of the swing,the height is zero, hence the potential energy is also zero.
The kinetic energy is represented mathematically as
Kinetic energy= 1/2 mv^2
Where m is the mass of the pendulum
v is the velocity of the pendulum
At the bottom the pendulum has the maximum velocity. Hence the kinetic energy is maximum at the bottom.
Energy can neither be created e destroyed. It can only be transferred from one form to another. Implying this law and the above explainations we conclude that at the bottom of the pendulum,the potential energy=0 and the kinetic energy=294J as the entire potential energy is converted to kinetic energy at the bottom.
All spontaneous processes release free energy
Investigators are most likely to use the case history method when they study <span>a rare behavior or an unusual person.
They do this to obtain some sort of basis that they could use as a pointer to make their decision regarding the similar case (after figuring out the difference in situation between each period)</span>
Answer:
a)30.14 rad/s2
b)43.5 rad/s
c)60633 J
d)42 kW
e)84 kW
Explanation:
If we treat the propeller is a slender rod, then its moments of inertia is
a. The angular acceleration is Torque divided by moments of inertia:
b. 5 revolution would be equals to 
rad, or 31.4 rad. Since the engine just got started
c. Work done during the first 5 revolution would be torque times angular displacement:
d. The time it takes to spin the first 5 revolutions is
The average power output is work per unit time
or 42 kW
e.The instantaneous power at the instant of 5 rev would be Torque times angular speed at that time:
or 84 kW
One of the useful forns of the formula for electrical power is: Power = (voltage squared) / (resistance). Knowing that power is proportional to (voltage squared), we can see that if the voltage is reduced to 1/2, the power is reduced to 1/4 of its original value. The 220volt/60watt appliance, when operated on 110 volts, dissipates 60/4 = 15 watts.
