2019-03-01_Physics_Times

Total mechanical energy of a system remains constant, if only conservative forces are acting on a system of
particles and the work done by all other forces is zero.
  U K constant
Total mechanical energy  constant

The rate of doing work is called power.



( )

( )

( )

Work done W

Power P

Time t



Power is a scalar.
SI Unit: watt(W) (or) J/s
One horse power (H.P)=746 watt

Instantaneous Power, inst t .0

W

P Lt

  t

 

  

 

 It is also calculated by P Fvinst cosF v.



Average power is given by

Total work done

avg Total time

P 

A crane lifts a body of mass m with a constant
velocity ‘v’ from the ground, its power is
P Fv mgv 

When a liquid of density ‘’ coming out of a pipe
of area of cross section ‘A’ with a velocity ‘v’,
then the power of the motor is
2

(^113)
2 2
mv
P Av
t
  
Tension in the string at P is
2
cos
mv
T mg
r
 
When it is at lowest point ( 0 ), 
mv^2
T mg
r
  = maximum
When it is at highest point ( 180 ), 
mv^2
T mg
r
  = minimum
(I) Tension in the string at any point
2
cos
mv
T mg
r
  
At the lowest point  0 

11.Conservation of Mechanical Energy

12. Power

13. Applications on power

14. Vertical circular motion with constant

speed

15. Vertical circular motion with variable

speed

2

T mvA mg

r

  (maximum)

At the highest point  180 

2

T mvB mg

r

  (minimum)

(II) Condition for looping vertical circular motion

The minimum speed at highest point to just

complete the vertical circle is gr

For the body to continue along circular path

the minimum velocity at lowest point is 5 gr

(III) Condition for oscillation about the lowest

position

If 0  vA 2 gr, in this case, velocity