Work done and energyAQA A-Level Further Maths: Subtopic test

1. 1
   A crate of mass 20 kg is pulled in a straight line across a horizontal floor by a horizontal force of 70 N. The crate moves 12 m. A constant resistance of 30 N opposes the motion.

   (a)

   Find the work done by the 70 N force.

   [1 mark]

   • A$360$ J
   • B$840$ J
   • C$1200$ J
   • D$480$ J

   (b)

   Find the work done against the resistance.

   [1 mark]

   • A$360$ J
   • B$480$ J
   • C$840$ J
   • D$2350$ J

   (c)

   The crate starts from rest. Find its speed after it has moved 12 m.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A ball of mass 0.4 kg is thrown vertically upwards from ground level with an initial speed of $14\text{ m s}^{-1}$. Air resistance may be ignored. Take $g=9.8\text{ m s}^{-2}$.

   (a)

   Find the initial kinetic energy of the ball.

   [1 mark]

   • A$5.6$ J
   • B$78.4$ J
   • C$2.8$ J
   • D$39.2$ J

   (b)

   Find the greatest height reached by the ball above the ground.

   [1 mark]

   • A$1.4$ m
   • B$20$ m
   • C$10$ m
   • D$14$ m

   (c)

   Use conservation of energy to find the speed of the ball when it is 6 m above the ground.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A skier of mass 70 kg starts from rest at the top of a straight slope inclined at $20^\circ$ to the horizontal and slides 80 m down the slope. A constant resistance of 50 N acts up the slope. Take $g=9.8\text{ m s}^{-2}$.

   (a)

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

   [3 marks]

   (b)

   At the bottom of the slope the skier moves onto level snow, where a constant horizontal resistance of 90 N acts. Find the distance the skier travels before coming to rest.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle $P$ of mass 0.5 kg is projected with speed $8\text{ m s}^{-1}$ up a line of greatest slope of a rough plane inclined at $30^\circ$ to the horizontal. The coefficient of friction between $P$ and the plane is 0.3. Take $g=9.8\text{ m s}^{-2}$.

   (a)

   (i) Show that the friction force acting on $P$ is 1.27 N, correct to 3 significant figures.
   (ii) Find the distance $P$ travels up the plane before it first comes to rest.

   [6 marks]

   (b)

   $P$ then slides back down the plane. Find its speed when it returns to its starting point, and explain why this is less than $8\text{ m s}^{-1}$.

   [6 marks]

   Total for question 4: 12 marks

End of questions