Resolving forces and equilibrium of a particleEdexcel A-Level Maths: Subtopic test

1. 1
   A particle of weight 40 N is in equilibrium, supported by two light inextensible strings. String 1 makes an angle of $30^\circ$ with the upward vertical, and string 2 is horizontal.

   (a)

   Find the tension in string 1.

   [1 mark]

   • A$20.0$ N
   • B$34.6$ N
   • C$46.2$ N
   • D$80.0$ N

   (b)

   Find the tension in string 2.

   [1 mark]

   • A$20.0$ N
   • B$23.1$ N
   • C$34.6$ N
   • D$69.3$ N

   (c)

   String 2 will break if its tension exceeds 30 N. The strings stay at the same angles. Find the greatest weight that this arrangement can support.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A particle of mass 6 kg is placed on a smooth plane inclined at $25^\circ$ to the horizontal. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   The particle rests on the plane held by a force parallel to the plane. Find the magnitude of the normal reaction of the plane on the particle.

   [1 mark]

   • A$24.8$ N
   • B$58.8$ N
   • C$64.9$ N
   • D$53.3$ N

   (b)

   The particle is released from rest. Find the magnitude of its acceleration down the plane.

   [1 mark]

   • A$4.14\ \text{m s}^{-2}$
   • B$8.88\ \text{m s}^{-2}$
   • C$9.80\ \text{m s}^{-2}$
   • D$24.8\ \text{m s}^{-2}$

   (c)

   A horizontal force of magnitude $P$ N, in the vertical plane containing a line of greatest slope and directed towards the plane, holds the particle at rest on the plane. Find $P$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle of mass 2 kg is pulled up a smooth plane inclined at $30^\circ$ to the horizontal by a light string parallel to a line of greatest slope. The tension in the string is 20 N. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the acceleration of the particle and the magnitude of the normal reaction between the particle and the plane.

   [3 marks]

   (b)

   The string is cut when the particle is moving up the plane at $3\ \text{m s}^{-1}$. Find the time taken for the particle to come to instantaneous rest and the distance it moves up the plane in that time.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Particle $A$ of mass 4 kg lies on a smooth plane inclined at $30^\circ$ to the horizontal. It is attached to particle $B$ of mass 3 kg by a light inextensible string that passes over a smooth pulley fixed at the top edge of the plane. The string is parallel to a line of greatest slope and $B$ hangs freely. The particles are released from rest with the string taut. Take $g=9.8\ \text{m s}^{-2}$.

   (a)

   Find the acceleration of the particles and the tension in the string.

   [6 marks]

   (b)

   Initially $B$ is 0.7 m above the horizontal floor. $B$ does not rebound when it hits the floor, and $A$ does not reach the pulley. Find the total distance moved up the plane by $A$ from release until it first comes to rest.

   [6 marks]

   Total for question 4: 12 marks

End of questions