HARD
AS and A Level
IMPORTANT
Earn 100

Four coplanar forces act on a particle, as shown in the following diagram. Show that the x component and y component of the resultant are equal. Hence, determine the direction of the resultant force.

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Important Questions on Forces in Two Dimensions

HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3E>Q 9
A boat of mass 1000 kg is pulled by three tugboats. One pulls due north with force 500 N, one pulls due east with force 350 N and one pulls on a bearing of 040° with a force of 250 N. Find the bearing and acceleration of the resultant motion.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3E>Q 10

In a competition of strength, four people pull a mass with ropes at different angles. The direction in which the mass moves determines the winner. Arjun wants the mass to go north, Bob wants it to go east, Chen wants it to go south and David wants it to go west. The men pull with the forces in the directions shown in the diagram. Find the direction of the resultant motion and determine who wins.

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HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3E>Q 11
A rowing boat of mass 120 kg is being pulled from rest by three boats. One pulls north with a force of 100 N, the second pulls on a bearing of 020° with a force of 80 N and the third pulls on a bearing of 045° with a force of 90 N. There is resistance from the water of 200 N directly against the motion. Find the bearing and acceleration of the resultant motion.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3E>Q 12
A hovercraft has an engine providing a force of 150 N on a bearing of 340°. The wind blows on a bearing of 310°, which means the hovercraft accelerates from rest on a bearing of 320°. Find the force of the wind on the hovercraft.
MEDIUM
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3E>Q 13
The wind is blowing a boat with force F. The motor of the boat can exert a driving force of D N, where D<F. Show with a diagram that, whatever direction the wind is taking the boat with the motor switched off, the motor is capable of deflecting the direction by a maximum of sin-1DF.
HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3E>Q 14
A building is unstable after a natural disaster. A car is stuck under the building and needs to be dragged out as quickly as possible, although the exact direction is less important. Three people can pull ropes, one due north, one at a bearing of 010° and one at a bearing of 030°. Akhil can pull with a force of 300 N, Ben can pull with a force of 240 N and Khadijah can pull with a force of 210 N. Find who should pull each rope to maximise the acceleration and what the net force will be.
MEDIUM
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>END-OF-CHAPTER REVIEW EXERCISE 3>Q 1

Three forces act on a particle in equilibrium in the horizontal plane, as shown in the diagram. Find the size of the unknown force F and the angle θ.

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HARD
AS and A Level
IMPORTANT
Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>END-OF-CHAPTER REVIEW EXERCISE 3>Q 2

Three forces act on a particle in equilibrium in the horizontal plane, as shown in the diagram. By resolving in a direction perpendicular to F, show that θ=47.2° and find F.

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