What average horsepower is developed by an 80 kg man while climbing in 10 s a flight of stairs that rises 6 m vertically
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What average horsepower is developed by an 80 kg man while climbing in 10 s a flight of stairs that rises 6 m vertically
A quarter horse power motor runs at a speed of 600 r.p.m. Assuming 40% efficiency, the work done by the motor in one rotation will be
Motor makes 600 revolution per minute
∴ n =
∴ Time required for one revolution sec
Energy required for one revolution = power × time
=
But work done = 40% of input
An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the engine is 60% . If g = 10 ms–2, the power of the engine is
Work output of engine = mgh =
Efficiency () =
∴ Input energy =
∴ Power = =
A force of acts on a body for 4 second, produces a displacement of The power used is-
An engine pump is used to pump a liquid of density ρ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is
Energy supplied to liquid per second by the pump
= = =
=
A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is
The hanging part of the chain has a length L/3 and mass M/3. The work required to lift it vertically through a height L/3 is (M/3)g(L/3) = MgL/9. However, since the chain is pulled horizontally, the work done is half of this value, which is MgL/18.
A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to –K/r2, where K is a constant. The total energy of the particle is
Here
∴ K.E.
Total energy
The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation , where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is
⇒
at ; and at ,
so, change in kinetic energy
A force (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particles is
While moving from (0,0) to (a,0)
Along positive x-axis, y = 0
i.e. force is in negative y-direction while displacement is in positive x-direction.
∴ W1 = 0
Because force is perpendicular to displacement
Then particle moves from (a, 0) to (a, a) along a line parallel to y-axis (x = +a) during this
The first component of force, will not contribute any work because this component is along negative x-direction while displacement is in positive y-direction (a,0) to (a,a). The second component of force i.e. will perform negative work
∴ =
So net work done on the particle W = W1 + W2
=
If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth R, is
Gain in potential energy
If h = R then
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