Work Power and Energy

A force $$\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j + 2\overrightarrow k } \right)N$$ is applied over a particle which displaces it from its origin to the point $$\overrightarrow r = \left( {2\overrightarrow i - \overrightarrow j } \right)m.$$ The work done on the particle in joules is

When a rubber-band is stretched by a distance $$x$$, it exerts restoring force of magnitude $$F = ax + b{x^2}$$ where $$a$$ and $$b$$ are constants. The work done in stretching the unstretched rubber-band by $$L$$ is :

A body of mass m starts moving from rest along x-axis so that its velocity varies as $$\upsilon = a\sqrt s$$ where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is :

A uniform cable of mass 'M' and length 'L' is placed on a horizontal surface such that its (1/n)^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 pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take g = 9.8 ms^$$-$$2)

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of 0.8$$\sqrt {gh}$$. The value of workdone by the air-friction is :

A particle experiences a variable force $$\overrightarrow F = \left( {4x\widehat i + 3{y^2}\widehat j} \right)$$ in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x-y plane, then Kinetic Energy changes by :

Identify the correct statements from the following : A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. C. Work done by friction on a body sliding down an inclined plane is positive. D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero. E. Work done by the air resistance on an oscillating pendulum is negative. Choose the correct answer from the options given below :

A bullet of mass $$0.1 \mathrm{~kg}$$ moving horizontally with speed $$400 \mathrm{~ms}^{-1}$$ hits a wooden block of mass $$3.9 \mathrm{~kg}$$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $$20 \mathrm{~m}$$ before coming to rest. The coefficient of friction between the block and the surface is __________. (Given $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$ )