Name: Applying Newton's Laws of Motion
Uploaded: 2019-07-19
Duration: 11 min 4 s
Description: In this video, we will understand the application of newton's laws of motion in solving problems. Let us learn more by watching this video.

Question

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.

Accepted Answer

Let the forces are $T_{1}, T_{2} & T_{3}$ .

The given problem is shown in the following diagram

The vertical and horizontal components are shown in the following diagram

Vertical component $R_{y} = T_{1} + T_{2} \cos (10 °) + T_{3} \cos (30 °)$

Horizontal component $R_{x} = T_{2} \sin (10 °) + T_{3} \sin (30 °)$

The magnitude of the resultant vector is $R = \sqrt{{R^{2}}_{x} + {R^{2}}_{y}}$

$R = \sqrt{{(T_{1} + T_{2} \cos (10 °) + T_{3} \cos (30 °))}^{2} + {(T_{2} \sin (10 °) + T_{3} \sin (30 °))}^{2}}$

This needs to be maximised in order to maximise acceleration

All cases for maximum resultant force are shown below

$T_{1} = 300 N, T_{2} = 240 N, T_{3} = 210 N \Rightarrow R = 733.04 N$

$T_{1} = 300 N, T_{2} = 210 N, T_{3} = 240 N \Rightarrow R = 731.58 N$

$T_{1} = 240 N, T_{2} = 300 N, T_{3} = 210 N \Rightarrow R = 734.31 N$

$T_{1} = 240 N, T_{2} = 210 N, T_{3} = 300 N \Rightarrow R = 730.81 N$

$T_{1} = 210 N, T_{2} = 240 N, T_{3} = 300 N \Rightarrow R = 731.71 N$

$T_{1} = 210 N, T_{2} = 300 N, T_{3} = 240 N \Rightarrow R = 733.76 N$

The highest result is the third of these arrangements.

So, $T_{1}$ (north) $= 240 N$ (Ben)

$T_{2} (10 °) = 300 N$ (Akhil)

$T_{3} (30 °) = 210 N$ (Khadijah)

Net force $R = 734.31 N$

Important Questions on Forces in Two Dimensions

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