Total ....X.... energy of a system is conserved, if the forces, doing work on it, are ........... .
Here, and refer to
conservative, mechanical
mechanical, conservative
mechanical, non-conservative
kinetic, conservative
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The principle of conservation of total mechanical energy can be stated as, the total mechanical energy of a system is conserved if the forces, doing work on it, are conservative.
A metallic wire of length metre extends by metre when stretched by suspending a weight from it. The mechanical energy stored in the wire is
Weight moves the centre of gravity of the spring through a distance
Mechanical energy stored Work done .
A steel ball of mass is thrown downward with velocity from height . It penetrates sand by . The change in mechanical energy will be
K.E. at the ground
P.E.
Change in energy
A ball is allowed to fall from a height of . If there is loss of energy due to air friction, then velocity of the ball when it hit the ground is
zero
At the lowest point, P.E. (gravitational P.E.). There is no work done on the bob by the tension as it is perpendicular to the displacement.
Potential energy is associated only to the gravitational force.
Calculate the K.E and P.E. of the ball half way up, when a ball of mass is thrown vertically upwards with an initial speed of .
Total energy at the time of projection
Half way up, P.E. becomes half the P.E. at the top i.e.
K.E. .
A spherical ball of mass is stationary at the top of a hill of height . It rolls down a smooth surface to the ground, then climbs up another hill of height and finally rolls down to a horizontal base at a height of above the ground. The velocity attained by the ball is
Using conservation of energy,
.
or or
A particle is moving in a circle of radius under the action of a force which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy for )
As we know,
As,
or,
Total energy Potential energy + kinetic energy
Now, from eqn (i) and (ii)
Total energy K.E. + P.E.
When a body is projected vertically up from the ground with certain velocity, its potential energy and kinetic energy at a point are in the ratio . If the same body is projected with double the previous velocity, then at the same point A the ratio of its potential energy to kinetic energy is
Let be the total energy then
When velocity is double then inital energy becomes .
So,
On solving, we get .
A mass is revolving in a vertical circle at the end of a string of length . By how much does the tension of the string at the lowest point exceed the tension at the topmost point?
The tension at the topmost point is given by
Centrifugal force acting outward while weight acting downward.
The tension at the lowest point
Centrifugal force and weight (both) acting downward
or
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