Forces and Newton's first lawEdexcel A-Level Maths: Subtopic test

1. 1
   A box of weight $200$ N rests on a rough horizontal floor. A horizontal force of $35$ N pushes on the box, but the box does not move. Model the box as a particle.

   (a)

   Find the magnitude of the normal reaction of the floor on the box.

   [1 mark]

   • A$35$ N
   • B$165$ N
   • C$235$ N
   • D$200$ N

   (b)

   Which statement about the friction (resistance) force on the box is correct?

   [1 mark]

   • AIt is $35$ N and acts in the direction opposite to the push.
   • BIt is $35$ N and acts in the same direction as the push.
   • CIt is zero, because the box is not moving.
   • DIt is $200$ N and acts in the direction opposite to the push.

   (c)

   The push is increased to $60$ N and the box now moves along the floor at a constant speed. State the magnitude of the resistance to the box's motion and justify your answer.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A car travels along a straight horizontal road at a constant speed of $25$ m s$^{-1}$. The engine provides a driving force of $1800$ N. Model the car as a particle.

   (a)

   Which statement about the resistance to the car's motion is correct?

   [1 mark]

   • AIt is $0$ N, because the car is not accelerating.
   • BIt is $1800$ N, equal to the driving force.
   • CIt is greater than $1800$ N, because the car is moving forwards.
   • DIt cannot be found without the mass of the car.

   (b)

   The driving force is increased to $2400$ N while the resistance stays the same. Which statement is correct?

   [1 mark]

   • AThe car continues at $25$ m s$^{-1}$, because the driving force is greater than the resistance.
   • BThe resultant force is $600$ N backwards, so the car slows down.
   • CThe resultant force is $600$ N forwards, so the car's velocity changes.
   • DThe resultant force is $4200$ N, because the forces add.

   (c)

   Explain why the engine must provide a driving force even though the car is moving at constant speed.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Three horizontal forces act on a particle: $\mathbf{F}_1=(3\mathbf{i}+5\mathbf{j})$ N, $\mathbf{F}_2=(-7\mathbf{i}+2\mathbf{j})$ N and $\mathbf{F}_3=(p\mathbf{i}+q\mathbf{j})$ N, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors. The particle moves with constant velocity.

   (a)

   Find the values of $p$ and $q$.

   [3 marks]

   (b)

   Find the magnitude of $\mathbf{F}_3$, and the acute angle between the line of action of $\mathbf{F}_3$ and the direction of $\mathbf{i}$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A skydiver of weight $850$ N is modelled as a particle. Air resistance acts on the skydiver while falling.

   (a)

   (i) With its parachute open, the skydiver falls vertically at a constant speed of $5$ m s$^{-1}$. State the two forces acting and find the air resistance.
   (ii) After landing, the skydiver stands at rest on horizontal ground while a steady horizontal wind drags the parachute with a horizontal force of $40$ N. Find the normal reaction of the ground and the friction force, stating the direction of each.

   [6 marks]

   (b)

   The skydiver leaves the aircraft with zero speed, with the parachute closed. Air resistance increases as the speed increases. Using Newton's first law, explain how the motion changes until a constant speed is reached before the parachute opens. A student claims that, to keep falling at constant speed, there must be a downward resultant force. Explain whether the claim is correct.

   [6 marks]

   Total for question 4: 12 marks

End of questions