Work, Energy and Power Numerical's Solution:

[2075 S / 2058]
A car of mass $1000 \; kg$ moves at a constant speed of $20 \; m/s$ along a horizontal road where the friction force is $200 \; N$. Calculate the power developed by the engine. [Click here for Solution]

[2075 B]
A water reservoir tank of capacity $250\;m^3$ is situated at a height of $20 \; m$ from the water level. What will be the power of an electric motor to be used to fill the tank in $3$ hours? Efficiency of motor is $70\;\%$ [Click here for Solution]

[2074 A / 2071 D]
A stationary mass explodes into two parts of mass $4 \; kg$ and $40 \; kg$. The initial kinetic energy of larger mass is $10 \; J$. What is the initial kinetic energy of the smaller mass and its velocity. [Click here for Solution]

[2074 B]
An explosive of mass M placed at a point explodes into one-third and two-third parts. If the initial kinetic energy of the smaller part is $1000 \; J$. What will be the initial kinetic energy of the bigger part? [Click here for Solution]

[2072 D]
You throw a $20 \; N$ rock vertically into the air from ground level. You observe that when it is $15 \; m$ above the ground, it is travelling at $25 \; m/s$ upward. Use the work-energy theorem to find (i) its speed as it left the ground and (ii) its maximum height. [Click here for Solution]

[2071 C]
A $650 \; kw$ power engine of a vehicle of mass $1.5 * 10^5\;kg$ is rising on an inclined plane of inclination $1$ in $100$ with a constant speed of $60\; km/hr$. Find the frictional force between the wheels of the vehicles and the plane. [Click here for Solution]

[2070 S - Set - A]
The constant force resisting the motion of a car of mass $1500 \; kg$ is equal to one fifteenth of its weight. When travelling at $48 \; km/h$, the car is brought to rest in a distance of $50 \; m$ by applying the brakes, find the additional retarding force due to the brakes (assumed constant) and heat developed in the brakes. [Click here for Solution]

[2070 S - Set - B]
A block of weight $150 \; N$ is pulled $20 \; m$ along a horizontal surface at constant velocity. Calculate the work done by the pulling force if the coefficient of kinetic friction is $0.2$ and the pulling force makes an angle of $60^0$ with the vertical. [Click here for Solution]

[2069 S]
A petrol engine car of mass $1500 \; kg$ and efficiency $15\;%$ accelerates from rest to $37 \; m/s$ in $10$ secs. If one gallon of petrol produces $1.38 * 10^8\;J$ of energy when burnt, how many gallons of petrol this car use during the acceleration? [Click here for Solution]

[2069 B]
A $0.15 \; kg$ glider is moving to the right on a friction less horizontal air track with a speed of $0.8 \; m/s$. It has a ahead on collision with a $0.3 \; kg$ glider that is moving to the left with a speed of $2.2 \; m/s$. Find the final velocity (magnitude and direction) of each glider if the collision is elastic. [Click here for Solution]

[2069 OLD / 2068]
A stationary mass explodes into two parts of mass $4$ units and $40$ units respectively. If the larger mass has an initial kinetic energy of $100 \; J$; what is the initial kinetic energy of the smaller mass? [Click here for Solution]

[2067]
A typical car weights about $1200 \; N$. If the coefficient of rolling friction is $\mu_r = 0.015$. What horizontal force is needed to make the car move with constant speed of $72 \; km/hr$ on a level road? Also calculate the power developed by the engine to maintain this speed. [Click here for Solution]

[2066]
A car of mass $1000 \; kg$ moves at a constant speed of $25 \; m/s$ along a horizontal road where frictional force is $200 \; N$. Calculate the power developed by the engine. [Click here for Solution]

[2063 S]
Sand drops vertically at the rate $2 \; kg/s$ on to a conveyer belt moving horizontally with a velocity of $0.1 \; m/s$. Calculate the extra power needed to keep the belt velocity. [Click here for Solution]

[2061]
A train of mass $2 * 10^5\; kg$ moves at a constant speed of $72 \; km/hr$ up a straight inclined against a frictional force of $1.28 * 10^5$ N. The inclined is such that the train rises vertically $1 \; m$ for every $100 \; m$ traveled along the incline. Calculate the necessary power developed by the train. [Click here for Solution]

[2058]
A ball A of mass $0.1 \; kg$ moving with a velocity $6 \; m/s$ collides directly with a ball B of mass $0.2 \; kg$ at rest. Calculate their common velocity if both balls move off together. If ball A had rebounded with a velocity of $2 \; m/s$ in the opposite direction after collision, what would be the new velocity of B? [Click here for Solution]

[2056]
A ball of mass $4 \; kg$ moving with a velocity $10 \; m/s$ collides with another body of mass $16 \; kg$ moving with $4 \; m/s$ from the opposite direction and then coalesces into a single body. Compute the loss of energy on impact. [Click here for Solution]

[2053]
A bullet of mass $20 \; gm$ travelling horizontally at $100 \; m/s$ embeds itself in the center of a block of wood mass $1 \; kg$ which is suspended by light vertical string $1 \; m$ in length. Calculate the maximum inclination of the string to the vertical. [Click here for Solution]

[2051]
A bullet of mass $10 \; gm$ is fired from a gun of mass $1 \; kg$ with a velocity of $100 \; m/s$. Calculate the ratio of the kinetic energy of the bullet and the gun. [Click here for Solution]

[2050]
Find the power of an engine in kilowatts which pulls a train of mass $600$ tonnes up an incline of $1$ in $100$ at the rate of $60 \; km/hr$. The weight of the engine is $200$ tonnes and the resistance due to friction is $50$ Newton's per tonne. [Click here for Solution]

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