Work, Energy and Power

A small block starts slipping down from a point B on an inclined plane AB, which is making an angle θ with the horizontal section BC. Section BC is smooth and the remaining section CA is rough with a coefficient of friction µ. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by µ = k tanθ. The value of k is

A body of mass 2 kg, is driven by an engine delivering, a constant power 1 J/s. the body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m)

A body $A$ $$ , of mass $m=0.1\mathrm{k}\mathrm{g}$ $$ has an initial velocity of $3\hat{i}{\mathrm{m}\mathrm{s}}^{-1}$ $\stackrel{}{}{}^{}$ . It collides elastically with another body, $B$ $$ of the same mass which has an initial velocity of $5\hat{j}{\mathrm{m}\mathrm{s}}^{-1}$ $\stackrel{}{}{}^{}$ . After collision, A moves with a velocity $\stackrel{?}{v}=4(\hat{i}+\hat{j})$ $\stackrel{}{}\stackrel{}{}\stackrel{}{}$ . The energy of $$ $B$ after collision is written as $\frac{}{}$ $\frac{x}{10}\mathrm{J}$ . The value of $x$ $$ is

A $60\mathrm{H}\mathrm{P}$ $$ electric motor lifts an elevator having a maximum total load capacity of $$ $2000\mathrm{k}\mathrm{g}$ . If the frictional force on the elevator is $4000\mathrm{N}$ $$ , the speed of the elevator at full load is close to: $\left(1\mathrm{H}\mathrm{P}=746\mathrm{W},\mathrm{g}=10{\mathrm{m}\mathrm{s}}^{-2}\right)$ $\left({}^{}\right)$

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being $68\mathrm{k}\mathrm{g}$ . The mass of the elevator itself is $920\mathrm{k}\mathrm{g}$ and it moves with a constant speed of $3\mathrm{m}/\mathrm{s}$ . 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 $\left(\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2\right)$  must be at least:

A particle of mass $$ $m$ is fixed to one end of a light spring having force constant $$ $k$ and unstretched length $\mathcal{l}$ $$ . The other end is fixed. The system is given an angular speed $\omega$ $$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

A ball of mass 10 kg moving with a velocity10√3ms-1along X – axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y– axis at a speed of 10m/s. The second piece starts moving at a speed of 20m/s at an angle θ° with respect to the X –axis. The configuration of pieces after collision is shown in the figure. The value of θ to the nearest integer is----------.

A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (take g = 9.8ms?²)

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = F₀[1 - ((t-T)/T)²]
Where F₀ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is:

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservation force F(x) acts on it. Suppose that E_mech = 8J, the incorrect statement for this system is: