A horizontal force of 12 N acts due east on a toy car, and a second horizontal force of 5 N acts due north on the same car at the same time. Fig. 1.1 shows ...
Question 1 Report
A horizontal force of 12 N acts due east on a toy car, and a second horizontal force of 5 N acts due north on the same car at the same time. Fig. 1.1 shows the two forces. What is the magnitude of the resultant force on the car?
Answer Details
The two forces act at right angles to each other (one due east, one due north). When forces are perpendicular, the magnitude of the resultant is found using Pythagoras' theorem:
\[R = \sqrt{F_1^2 + F_2^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \text{ N}\]
The resultant is 13 N, directed at an angle between north and east. Simply adding the forces (12 + 5 = 17 N) would only be correct if they acted in the same direction. Multiplying them (12 x 5 = 60 N) or subtracting them (12 - 5 = 7 N) are not valid operations for finding a resultant of perpendicular forces.
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