Work Energy and...

A block of mass $$10kg$$ is released on a fixed wedge inside a cart which is moved with constant velocity $$10 \ ms^{-1}$$ towards right. There is no relative motion between block and cart. Then work done by normal reaction on block in two seconds from ground frame will be $$(g=10 \ ms^{-2})$$:

A spring of natural length $$l$$ is compressed vertically downward against the floor so that its compressed length becomes $$\dfrac {l}{2}$$. On releasing, the spring attains its natural length. If $$k$$ is the stiffness constant of spring, then the work done by the spring on the floor is:

A spring of spring constant $$5\times 10^3$$ N/m is stretched initially by $$5$$ cm from the unstretched position. The work required to further stretch the spring by another $$5$$ cm is:

A spring of force constant $$k$$ is cut in two parts at its one-third length. When both the parts have same elongation, the work done in the two parts will be (Spring constant of a spring is inversely proportional to length of spring)

A pendulum was kept horizontal and released. Find the acceleration of the pendulum when it makes an angle $$ \theta $$ with the vertical.

A mass $${ m }_{ 1 }$$ with initial speed $${ v }_{ 0 }$$ in the positive $$x$$-direction collides with a mass $${ m }_{ 2 }=2{ m }_{ 1 }$$ which is initially at rest at the origin, as shown in figure. After the collision $${ m }_{ 1 }$$ moves off with speed $${ v }_{ 1 }={ v }_{ 0 }/2$$ in the negative $$y$$- direction, and $${ m }_{ 2 }$$ moves off with speed $${ v }_{ 2 }$$ at angle $$\theta$$. Find the velocity (magnitude and direction) of the centre of mass after the collision :

A body of mass $$m$$ is hauled from the Earth's surface by applying a force $$\vec{F}$$ varying with the height of ascent $$y$$ as $$\vec{F}=2(ay-1)mg$$, where $$a$$ is a positive constant. Find the work performed by this force $$W$$ and the increment in the body's potential energy $$\Delta U$$ in the gravitational field of the Earth over the first half of the ascent.

A brick of mass $$1.8$$ kg is kept on a spring of spring constant $$K = 490  N  m^{-1}$$. The spring is compressed so that after the release brick rises to $$3.6$$ m. Find the compression in the spring. (Take $$g= 10 \ m/s^2$$)

A particle P of mass m attached to vertical axis by two strings AP and BP of length l each. The separation AB=l. The point p rotates around the axis with an angular velocity $$\omega $$. the tension in two strings are $$ { T }_{ 1 }$$ and $$ { T }_{ 2 } $$
taut only if $$ \omega >\sqrt { \frac { 2g }{ l }  } $$

A spring of constant $$k$$ is fixed to a wall. A boy stretches this spring by distance $$x$$ and in the mean time the compartment moves by a distance $$s$$. The work done by boy with reference to earth is