MEDIUM

AS and A Level

IMPORTANT

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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 $\sin^{- 1} \frac{D}{F} .$

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 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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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 4

Two people drag a car of mass

1200 kg

forward with ropes. One pulls with force

400 N

on a bearing of

005 ° .

One pulls with force

360 N

on a bearing of

352 ° .

Find magnitude of the acceleration and its direction to the nearest

0.1 ° .

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 5

A boat is in equilibrium held by a rope to the shore. The rope exerts a force $T$ at an angle $θ$ from north. The wind blows the boat with force $40 N$ in a northwest direction. The current pushes it south with a force of $50 N .$ Show that $T \sin θ = 20 \sqrt{2}$ and find an expression for $T \cos θ$ . Hence, show that $\tan θ = \frac{8 + 10 \sqrt{2}}{17}$ and find $θ$ and $T .$

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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 6

A car of mass

300 kg

is on a slope, which is at an angle of

5 °

to the horizontal. When it is pulled down the slope by a rope parallel to the slope with a force of

T,

it accelerates at

2 m s^{- 2} .

Find the acceleration of the car when it is pulled up the slope by a rope parallel to the slope with a force of

T .

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 8

A girl can drag a stone block of mass

18 kg

up a slope at an angle of

13 °

to the horizontal with an acceleration of

0.7 m s^{- 2} .

Assuming this is the maximum force she can exert to drag the block, find the mass of the heaviest stone block she would be able to drag up the slope.

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 13

A ball of mass

m kg

slides down a slope, which is at an angle of

θ °

to the horizontal. It passes two light gates

x m

apart. At the first gate, the speed of the ball is measured as

u m s^{- 1},

and at the second its speed is measured as

v m s^{- 1} .

Assuming the resistance is constant, show the resistance force has a total size of

\frac{m}{2 x} (2 xgsin θ + u^{2} - v^{2}) .

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.

Important Questions on Forces in Two Dimensions

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