Work Energy and...

Calculate the energy possessed by a stone of mass $$10\ kg$$ kept at a height of $$5\ m$$. 
Take $$g = 9.8\ m/s^{2}$$

The work done by the force $$\vec{F}=A(y^{2}\hat{i}+2x^{2}\hat{j})$$, where $$A$$ is a constant and $$x$$ & $$y$$ are in meters around the path shown is :

A ball of mass m moves towards a moving wall of infinite mass with a speed 'v' along the normal to the wall. The speed of the wall is 'u' toward the ball. The speed of the ball after elastic collision with wall is

A force $$\vec{F}=(3t\hat{i}+5\hat{j})$$ N acts on a particle whose position vector varies as $$\vec{S}=(2t^{2}\hat{i}+5\hat{j})$$ m, where $$t$$ is time in seconds. The work done by this force from $$t=0$$ to $$t=2s$$ is:

A particle of mass $$m_0,$$ travelling at speed $$v_0,$$ strikes a stationary particle of mass $$2m_0.$$ As a result, the particle of mass $$m_0$$ is deflected through $$45^o$$ and has a final speed of $$\dfrac{v_0}{\sqrt2}$$. Then the speed of the particle of mass $$2m_0$$ after this collision is 

A particle of mass $$m$$ moves along the quarter section of the circular path whose centre is at the origin. The radius of the circular path is $$a$$. A force $$\vec{F}=y\hat{i}-x\hat{j}$$ newton acts on the particle, where $$x, y$$ denote the coordinates of position of the particle. The work done by this force in taking the particle from point A ($$a, 0$$) to point B ($$0, a$$) along the circular path is

The force exerted by a compression device is given by $$ F(x) = kx (x-l)$$  for $$ 0 \leq  x \leq  l$$, where $$l$$ is the maximum possible compression, $$x$$ is the compression  and $$k$$ is the constant. Work done to compress the device by a distance $$d$$ will be maximum when 

An elastic string carrying a body of mass $$m$$ at one end extends by $$1.5\ cm$$. If the body rotates in vertical circle with critical velocity, the extension in the string at the lowest position is:

A force $$\vec F=(3t\hat i+5\hat j)$$N acts on a body due to which its displacement varies as $$\vec S=(2t^2\hat i-5\hat j)m$$. Work done by this force in $$2$$ second is

The world class Moses Mabhida football stadium situated in Durban has a symmetrical arc of length 350 m and a height of 106 m, as shown in the picture below on the left.
The picture on the right shows a funicular (Skycar), which takes tourists to the top of the arc. Suppose that the Skycar with tourists inside, starts from the base of the arc and travels a distance of 175 m along the arc to the viewing platform at the top. Assume that the work done by friction during the Skycars complete ascent is $$5.8\times 10^5J$$. If the combined mass of the Skycar and tourists is 5000 kg, then the work done by the motor that lifts the Skycar is approximately equal to,