Conservation of mechanical energyEdexcel International A Level Further Maths: Mind map

Exam questions on Conservation of mechanical energy

1. A ball of mass $0.2$ kg is thrown from a point $1.5$ m above horizontal ground with a speed of $12$ m s$^{-1}$. Air resistance is negligible. Take $g=9.8$ m s$^{-2}$.
   For the ball thrown vertically upwards, find its speed when it is $5$ m above the ground on the way up.2 marks
2. A particle of mass $2$ kg is released from rest at a point $A$ on a smooth plane inclined at $30^\circ$ to the horizontal. $A$ is $4$ m from the foot $B$ of the plane, measured along the plane. At $B$ the plane meets a rough horizontal surface with no loss of speed. The coefficient of friction between the particle and the horizontal surface is $0.4$. Take $g=9.8$ m s$^{-2}$.
   Find the speed of the particle when it has moved $2$ m along the horizontal surface.2 marks
3. A child of mass $30$ kg slides from rest down a straight slide of length $6$ m, with the top of the slide $3$ m above the bottom. At the bottom the child's speed is $5$ m s$^{-1}$. The resistance to motion is constant. Take $g=9.8$ m s$^{-2}$.
   Find the total mechanical energy lost by the child as she slides to the bottom.3 marks