Coplanar Forces and Equilibrium · CAPE Applied Mathematics Unit 2

27 past-paper questions on Coplanar Forces and Equilibrium, part of Module 3: Particle Mechanics, from every CAPE Applied Mathematics Unit 2 paper on Quelpr.

1. 6(a)(i)9 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2If in the position of equilibrium P = 6 N, find the magnitude of the tension in OB.
2. 6(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2If in the position of equilibrium P = 6 N, find the magnitude of the (acute) angle of inclination OB makes with the vertical.
3. 6(b)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Find the magnitude of the (acute) angle of inclination OB makes with the vertical.
4. 6(b)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Find the magnitude of the pull, P.
5. 6(c)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Find the magnitude of ai + bj.
6. 6(c)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Find the angle of inclination of ai + bj to Ox.
7. 5(a)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Draw a diagram showing the forces acting on the car.
8. 6(b)(ii)7 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2If the block is of mass 70 kg and there is a frictional force opposing the motion of the block, find the magnitude of the frictional force.
9. 5(a)(i)5 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Draw a diagram to illustrate this information, and hence draw the coplanar force diagram.
10. 5(a)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Calculate the tension in the string.
11. 5(b)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Draw a force diagram to illustrate this information.
12. 5(b)(ii)7 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Find the LEAST value of P and the value of α when P is least.
13. 5(b)(iii)2 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Determine the LEAST value of P in terms of m when α = 30°.
14. 5(a)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Draw a force diagram to illustrate this information.
15. 5(a)(iii)4 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Calculate the force exerted by the string on the pulley.
16. 5(a)(i)9 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Use Lami's theorem, or otherwise, to show that the weight of the fixture is 50((cos θ)/√3 + sin θ).
17. 5(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Show that the tension in string B is TB = (100/√3) cos θ.
18. 6(a)(i)5 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the tractive force acting parallel to the plane.
19. 6(b)6 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2If the particle is just about to slip, find the coefficient of friction between the particle and the surface.
20. 6(a)(i)7 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Determine the horizontal force P.
21. 6(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Determine the frictional force.
22. 6(c)5 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2If the ropes are 60^\circ apart, determine the tensions in the ropes.
23. 5(a)(i)6 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Draw a clearly labelled diagram showing all the forces (tensions and weights), and the points P, Q, R and S.
24. 5(a)(ii)10 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Using your diagram, calculate the tension in the strings PQ and QR, and the weight, w.
25. 5(b)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Draw a diagram which illustrates the forces acting on the particle.
26. 5(b)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Determine the coefficient of friction.
27. 5(b)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Calculate the least force which, acting along the slope of the plane, will just cause the particle to move upwards.