Work, Energy and Power

An electric lift with a maximum load of 2000Kg (lift + passenger) is moving up with a constant speed $1.5{\mathrm{m}\mathrm{s}}^{-1}$ ${}^{}$ . The frictional force opposing the motion is 2000N${}^{}$ . The minimum power delivered by the motor to lift in watts is : $\left(\mathrm{g}=10{\mathrm{m}\mathrm{s}}^{-2}\right)$

The potential energy of a long spring when stretched by $2\mathrm{c}\mathrm{m}$  is $\mathrm{U}$ . If the spring is stretched by $8\mathrm{c}\mathrm{m}$ , potential energy stored in it will be:

A ball of mass 4 kg, moving with a velocity 10 ms?¹, collides with a spring of length 8m and force constant 100 Nm?¹. The length of compressed spring is x m. The value of x, to the nearest integer, is.

An object of mass m₁ collides with another object of mass m₂, which is at rest. After collision the objects move with equal speeds in the opposite direction. The ratio of the masses m₂: m₁ is :

The velocity-displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented by :

As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s²) The value of 'x' to the nearest integer is----------.

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is 10m/s and slows down with uniform deceleration, then magnitude effective retarding force on the bullet is 'x' N. The value of 'x' to the nearest integer is----------.

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to:

A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to 81/100 of the height through which it falls. Find the average speed of the ball. (Take g = 10 ms⁻²)

A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms?¹ goes up an inclined plane which makes an angle of 30° with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A?