D. C. Pandey Solutions for Chapter: Work, Energy and Power, Exercise 1: Excercise 1

An elevator in a building can carry a maximum of $10$ persons with the average mass of each person being $68 \mathrm{kg}$. The mass of the elevator itself is $920 \mathrm{kg}$ and it moves with a constant speed of $3 \mathrm{m} {\mathrm{s}}^{-1}$. The frictional force opposing the motion is $6000 \mathrm{N}$. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$ must be at least

A uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its ${\left(\frac{1}{n}\right)}^{\mathrm{th}}$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be,

A person of mass $M$ is sitting on a swing to length $L$ and swinging with an angular amplitude ${\mathrm{\theta }}_0$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance $l\left(l<<L\right)$ is close to,

A motor engine pumps $1800 \mathrm{L}$ of water per minute from a well of depth $30 \mathrm{m}$ and allows to pass through a pipe of cross-sectional area $30 {\mathrm{cm}}^2$. Then the power of the engine is (acceleration due to gravity, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$),

A ball of mass $2 \mathrm{kg}$ is thrown from a tall building with velocity, $v=\left(20\right) \hat{\mathrm{i}}+\left(24\right) \hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-1}$ at time $t=0 \mathrm{s}$. Change in the potential energy of the ball after, $t=8 \mathrm{s}$ is (the ball is assumed to be in air during its motion between $0 \mathrm{s}$ and $8 \mathrm{s}, \hat{\mathrm{i}}$ is along the horizontal and $\hat{\mathrm{j}}$ is along the vertical direction. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A mass of $2 \mathrm{kg}$ initially at a height of $1.2 \mathrm{m}$ above an uncompressed spring with spring constant $2\times {10}^4 \mathrm{N} {\mathrm{m}}^{-1}$ is released from rest to fall on the spring. Taking the acceleration due to gravity as $10 \mathrm{m} {\mathrm{s}}^{-2}$ and neglecting the air resistance, the compression of the spring in $\mathrm{mm}$ is,

A box of mass $3 \mathrm{kg}$ moves on a horizontal frictionless table and collides with another box of mass $3 \mathrm{kg}$ initially at rest on the edge of the table at height $1 \mathrm{m}$.
The speed of the moving box just before the collision is $4 \mathrm{m} {\mathrm{s}}^{-1}$. The two boxes stick together and fall from the table. The kinetic energy just before the boxes strike the floor is (Assume that acceleration due to gravity, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement $s$ is given as a function of time $\left(t\right)$ as,