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Chapter 1: Q1E (page 124)

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60掳. If Rover exerts a force of 270 N and Fido exerts a force of 300 N, find the magnitude of the resultant force and the angle it makes with Rover鈥檚 rope.

Short Answer

Expert verified

If two dogs Rover and Fido pull their ropes attached to a post with 270 Nand 300 N forces respectively having an angle 60掳between them, the resultant force is 493.86N and makes an angle 31.74掳 with Rover's rope.

Step by step solution

01

Given data

The magnitude of the force applied by Rover is

A鈫�=270N

The magnitude of the force applied by Fido is

B鈫�=300N

The angle between the two forces is

胃=60掳

02

Vector addition

The magnitude of vector sum of two vectors A鈫� and B鈫� with an angle 胃 between them is

R=A2+B2+2ABcos胃.....1

The angle made by the resultant vector with A鈫� is

f=tan-1Bsin胃A+Bcos胃.....2

03

Sum of two forces

From equation (1), the magnitude of sum of the two forces is

R=2702+3002+2脳270脳300cos60掳N=493.86N

From equation (2), the angle made by the resultant force with Rover's rope is

蠒=tan-1300sin60掳270+300cos60掳=tan-10.619=31.74掳

Thus, the resultant force is 493.86N and makes an angle 31.74掳 with Rover's rope.

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