Work, Energy and Power

A body is projected with a speed $u \mathrm{~ms}^{-1}$ at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $(3 / 4)$ th of the initial kinetic energy. The value of $\beta$ is

A block of mass 10 kg slides down a rough slope which is inclined at an angle of $45^{\circ}$ to the horizontal. The coefficient of sliding friction is 0.30 . When the block has slide 5 m , the work done on the block by the force of frictio...

A string of length $L$ and force constant $k$ is stretched to obtain extension $l$. It is further stretched to obtain extension $l_1$. The work done in second stretching is

An ideal massless spring $ S $ can be compressed 1 m by a force of 100 N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at $ 30^{\circ} $ to the horizontal. A 10 kg block $ M $ is released ...

A force of $ F=0.5 \mathrm{~N} $ is applied on lower block as shown in figure. The work done by lower block on upper block for a displacement of 3 m of the upper block with respect to ground is (Take, $ g=10 \mathrm{~m} / \mathrm{s}^{2} $ )

A pendulum of mass 1 kg and length $ l=1 \mathrm{~m} $ is released from rest at angle $ \theta=60^{\circ} $. The power delivered by all the forces acting on the bob at angle $ \theta=30^{\circ} $ will be (Take, $ g=10 \mathrm{~m} / \mathrm{...

The potential energy for a force field \(\mathbf{F}\) is given by \(u(x, y)=\cos (x+y)\). The force acting on a particle at position given by co-ordinates \((0, \pi / 6)\) is

A machine gun fires 300 bullets per min if the mass of each bullet is 10 g and the velocity of the bullets is 600 ms\(-\)1, the power (in kW) of the gun is

The bob of a pendulum of length 2 m lies at P, when it reaches Q, it losses 10% of its total energy due to air resistance.

The velocity of bob at Q is

A force F = a + bx acts on a particle in the x-direction where a and b are constants. The work done by this force during a displacement from x = 0 to x = d is

The work done by a force acting on a body is as shown in the following graph. The total work done in covering an initial distance of 40 m is

A time dependent force F = (8t) acts on a particle of mass 2 kg. If the particle starts from rest, the work done by the force during the first 1s will be

A ball of mass 0.5 kg is thrown up with initial speed 16 ms\(-\)1 and reaches maximum height of 9 m. How much energy is dissipated by air drag acting on the ball during the ascent?