Work Energy and...

Two blocks A and B of masses m and 2m respectively placed on a smooth floor are connected by a spring. A third body C of mass m moves with velocity $$v_0$$ along the line joining A and B and collides elastically with A. At a certain instant of time after collision it is found that the instantaneous velocities of A and B are same then :

A force $$F = - K (y  \widehat i + x  \widehat j)$$ (where $$K$$ is positive constant) acts on a particle moving in the $$x-y$$ plane. Starting from the origin, the particle is taken along the $$x$$-axis to the point $$(a, 0)$$ and then parallel to $$y$$-axis to the point $$(0, a)$$. The total work done by the force $$F$$ on the particle is:

The work done by the varying force in changing the angular displacement from 0 to $$\theta $$ is

The work done by the spring in case (i):

A force $$F = - K (y  \widehat i + x  \widehat j)$$, (where $$K$$ is a +ve constant) acts on a particle moving in xy plane starting from origin, the particle is taken along the positive x-axis to the point ($$a, 0$$) and then parallel to y axis to the point ($$a, a$$). The total work done by force $$F$$ on the particle is

The work done by the tension T in the above process is

Two springs have their force constant as $$k_1$$ and $$k_2\:(k_1 > k_2)$$. When they are stretched by the same force

Calculate the work done on the tool by $$\vec{F}$$ if this displacement is along the straight line $$y =x$$ that connects these two points.

A ball attached to one end of a string swings in a vertical plane such that its acceleration at point A (extreme position) is equal to its acceleration at point B (mean position). The angle $$\displaystyle \theta $$ is

Which of the following statements is correct regarding the work done $$\vec{F}$$ along these two paths.