The engine of a train has to apply a force of \(4000N\) to overcome friction to run at a uniform rate of \(72\frac{km}{h}\). What is power developed by the engine?
Ans: \(P=80kW\).
An electric motor is used to lift an elevator and its load (total mass of 2000kg) to a height of \(20m\). The taken by the motor for the job is \(20s\). (a) What is the work done? (b) What is the rate at which work is done? (c) If, the efficiency of the motor is \(80\%\), at which rate is the energy supplied to the motor?
Ans:(a) \(W=\left(3.92\times10^{5}\right)J\), (b) \(P_{output}=\left(1.96\times10^{4}\right)W\) and (c) \(P_{input}=\left(2.45\times10^{4}\right)W\).
Water falls from a height of \(60m\) at the rate of \(15\frac{kg}{s}\) to operate a turbine. The loss due to frictional forces are \(10\%\) of initially available energy. How much power is generated by the turbine? Take: \(g=10\frac{m}{s^{2}}\).
Ans: \(P_{output}=8.1kW\).
A bus of mass \(10000kg\) is moving at a constant speed of \(10\frac{m}{s}\) up an inclined plane of \(15^{o}\). Calculate: the power of the engine?
Ans: \(P=253.6kW\).
A body of mass \(m\) is accelerated uniformly from rest to a speed \(v\) in time \(T\). Calculate: the instantaneous power delivered to the body in time \(t\).
Ans: \(P_{ins}=\frac{mv^{2}}{T^{2}}t\).
Water is raised from a well with a pump. The depth of the well is \(15m\) and water is raised at a rate of \(20\frac{kg}{s}\) and discharges at \(5\frac{m}{s}\). Calculate: the power of the motor.
Ans: \(P=3.25kW\).
The human heart discharges \(75ml\) of blood at each beat against a pressure of \(0.1m\) of Hg . Calculate: the power of heart assuming that pulse frequency is \(80\frac{beats}{min}\). Take: \(\rho_{Hg}=\left(13.6\times10^{3}\right)\frac{kg}{m^{3}}\).
Ans: \(P_{heart}=1.33kW\).
A well \(30m\) deep and \(3m\) in diameter contains water up to a depth of \(\). How long it will take by a \(5hp\) pump to empty it?
Ans: \(t=7008Sec\).
A man cycles up hill whose slope is 1 in 20 with a velocity of \(6.4\frac{km}{h}\) along the up hill. The weight of the man and the cycle is \(98kg\). What work per minutes he is doing? What is his horse power?.
Ans: \(W=5122.1J\) and \(P=0.114hp\).
A coolie takes 1 min to raise a box through a height of \(3m\). Another takes \(30s\) for the same job and does the same amount of work. Which one of these two has greater power and which one uses greater energy?
Ans: \(P_{2}=2P_{1}\) .
A pump on the ground floor of a building can pump up water to fill a tank of volume \(30m^{3}\) in \(15min\). If, the tank is \(40m\) above the ground and efficiency of the pump is \(30\%\). How much electric power is consumed by the pump?
Ans: \(P_{input}=43.6kW\).
A machine gun fires \(80\) bullets per minutes with a velocity of \(700\frac{m}{s}\). If, each bullet has a mass of \(60g\). Then; find the power developed by the gun?
Ans: \(P=19600W\).
An elevator that can apply a maximum load of \(1800kg\) (Elevator+Passenger) is moving up with a constant speed of \(2\frac{m}{s}\). The frictional force opposing the motion is [latex0]4000N[/latex]. Determine: the minimum power delivered by the motor to the elevator in watts as well as in horse power.
Ans: \(P=44000W\) or \(59hp\).
An engine of \(5kw\) power is used to pump water from a well of \(50m\) depth. Calculate: the quantity of water in kilolitres which it can pump out in one hours?
