Work Energy and...

If water is flowing in a pipe at a height 4m from the ground then its potential
energy per unit volume is (Reference is taken at ground, $g=10 \mathrm{m} / \mathrm{s}^{2} )$

Fig. shows a smooth curved track terminatingin a smooth horizontal part. A spring ofspring constant $400\mathrm { Nm }$ is attached at one end to the wedge fixed rigidly with the horizontal part. $A\ 40 \mathrm { g }$ mass is released from rest at a height of $5\mathrm { m }$ on the curved track. The maximum compression of the spring is $\left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right)$

A ball of mass 2 kg hits a floor with a speed of 4 m/s at an angle of $60 ^o$ with the normal.
If (e=1/2); then the change in the kinetic energy of the ball is

A bucket tied at the end of a $1.6m$ long string is whirled in a vertical circle with a constant speed. What should be the minimum speed so that the water from the bucket does not spill when the bucket  is at the highest position, (Take g=10m/s^2$$)

A stone tied to a piece of string is shrilled in a vertical cirlce with uniform speed. In  what position of the stone is the tension in the string greatest

A force acts on a 2$\mathrm { kg }$ object so that itsposition is given as a function of time as $x = 3 t ^ { 2 } + 5 .$ What is the work done by thisforce in first 5 seconds?

A body of mass 200 g moving on a test has final K.E. of 50 J after travelling a distance of 10 cm. Assuming 90% loss of energy due to friction. The initial speed of the body is 

Potential energy v/s displacement curve for one dimensional conservative field is shown. Force at A and B is respectively -

A circular road of radius 1000 m has banking angle $45^{\circ}$  The maximum safe speed $\left ( in ms^{-1} \right )$  of a car having a mass 2000 kg will be (if the coefficient of the friction  between tyre and road is 0.5) 

An escalator is moving downwards with a uniform speed u. A man of mass 'm' is running upwards or it at a uniform speed v.  If the height of the escalator is h, the work done by the man in going up the escalator is