# ## SUDESHNA  PAUL  EDUCATIONAL COMPANION

#### Brake applied by car    Work on Inclined Plane    Energy Conservation on an Incline

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A Car  moving at uniform velocity, is suddenly brought to rest ,by application of brakes. Its velocity falls to zero instantly and so its kinetic energy .

# when the car is in uniform velocity

Equation :       (1/2)mv2 = fkd1

when the car brakes are applied

Equation :    Fd= (1/2)mv2 – (1/2)mv2f  + fkd

F = force applied by the brakes

fk =  frictional force of the ground

m = mass of the ground

d1= distance covered by the car before brakes are applied

d = distance covered by the car after brakes are applied

v = uniform velocity of the car

vf = final velocity after retardation by brakes (since the car comes to rest vf =0)

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As the ball rolls down the hill from its elevated position, its mechanical energy is transformed from potential energy to kinetic energy. At a height just above the ground, the majority of energy is in the form of kinetic energy. This is to say, energy due to vertical position has been transformed into energy due to motion  Three different incline angles could be used to represent the three different paths up the mountain The amount of work done to raise the cart from the floor to the seat top is dependent upon the force applied to the cart and the displacement caused by this force

The amount of work done by a force on any object is given by the equation

Work = F * d * cosine(Theta)

where F is the force, d is the displacement and Theta is the angle between the force and the displacement vector. The least steep incline (30-degree incline angle) will require the least amount of force while the most steep incline will require the greatest amount of force. Yet, force is not the only variable affecting the amount of work done Another variable is the displacement .the least steep incline would correspond to the largest displacement and the most steep incline would correspond to the smallest displacement. The final variable is Theta - the angle between the force and the displacement vector