Answer to Question #219980 in Mechanical Engineering for rashi

Question

Mechanical systems highly depend on energy transfer. Piledrivers, Windmills are some commonly seen mechanical systems that depend on such a mechanism. Explain the effects of energy transfer of at least two such mechanical systems with uniform acceleration.

Answer 1

Windmill System

Under constant acceleration, the kinetic energy of an object having mass m and velocity v is equal to the work done W in displacing that object from rest to a distance s under a force F.

E = W = Fs

According to Newton’s Law, we have: F = ma. Hence, E = mas. Using the third equation of motion: v ²+u² +2as, we get: a=(v²-u²)/2s

Since the initial velocity of the object is zero, u = 0 , we get: a=$v$²/2s

E=(v²/2s)ms

Piledrivers

Work = force X distance = (weight of hammer) X (height of hammer) = (mass of hammer ) X (acceleration due to gravity) X (height) . In lifting the hammerhead, we act as the energy source and the hammer acts as the energy receiver.

The work we do becomes the gravitational potential energy stored in the hammerhead. Consequently, we define gravitational potential energy as the product of an object's mass, the acceleration due to gravity, and the object's height above some reference point: Gravitational potential energy= (mass of hammer) X (acceleration due to gravity) X (height)

Gravitational potential energy=mgh

KE=(1/2)mv²

GPE=mgh

2KE/v²=m...1

GPE/gh=m...2

2KE/v²=GPE/gh

GPE=gh.2KE/v²