Conservation of mechanical energyEdexcel International A Level Further Maths: Subtopic test

1. 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$^{-2}$.

   (a)

   The ball is thrown at an angle above the horizontal. Find the speed of the ball when it hits the ground.

   [1 mark]

   • A$13.2$ m s$^{-1}$
   • B$12.0$ m s$^{-1}$
   • C$10.7$ m s$^{-1}$
   • D$173$ m s$^{-1}$

   (b)

   The ball is instead thrown vertically upwards with the same speed from the same point. Find the greatest height of the ball above the ground.

   [1 mark]

   • A$7.35$ m
   • B$5.85$ m
   • C$8.85$ m
   • D$16.2$ m

   (c)

   For the ball thrown vertically upwards, find its speed when it is $5$ m above the ground on the way up.

   [2 marks]

   Total for question 1: 4 marks

2. 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$^{-2}$.

   (a)

   Find the speed of the particle when it reaches $B$.

   [1 mark]

   • A$8.85$ m s$^{-1}$
   • B$6.26$ m s$^{-1}$
   • C$39.2$ m s$^{-1}$
   • D$4.43$ m s$^{-1}$

   (b)

   Find the distance the particle travels along the horizontal surface before coming to rest.

   [1 mark]

   • A$10$ m
   • B$0.8$ m
   • C$6.26$ m
   • D$5.0$ m

   (c)

   Find the speed of the particle when it has moved $2$ m along the horizontal surface.

   [2 marks]

   Total for question 2: 4 marks

3. 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$^{-2}$.

   (a)

   Find the total mechanical energy lost by the child as she slides to the bottom.

   [3 marks]

   (b)

   Find the resistance to the child's motion and the acceleration of the child down the slide.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A skier of mass $70$ kg starts from rest and skis $100$ m down a straight slope inclined at $15^\circ$ to the horizontal. She then moves on to a horizontal section with no change in speed. The resistance to her motion is a constant $60$ N on the slope and a constant $140$ N on the horizontal section. Model the skier as a particle and take $g=9.8$ m s$^{-2}$.

   (a)

   Find the speed of the skier at the bottom of the slope.

   [6 marks]

   (b)

   Find the distance the skier travels on the horizontal section before she stops, and her speed when she has travelled $50$ m along it.

   [6 marks]

   Total for question 4: 12 marks

End of questions