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Zorluk: OrtaScalars and Vectors

A crate on a smooth surface is simultaneously pulled by two horizontal forces. One force of magnitude 9.0 N9.0\text{ N} acts towards the East, and another force of magnitude 12.0 N12.0\text{ N} acts towards the North. What is the magnitude of the resultant force acting on the crate in newtons?

Cevap: 15 N

Cevap

The magnitude of the resultant force acting on the crate is 15.0 N15.0\text{ N}.
Because the two pulling forces are perpendicular, their resultant magnitude is calculated using vector addition via the Pythagorean theorem: R=9.02+12.02=15.0 NR = \sqrt{9.0^2 + 12.0^2} = 15.0\text{ N}.

Adım Adım Çözüm

1
Determine the angle between the two given vectors
The forces are perpendicular (90∘90^\circ).
East and North cardinal directions are orthogonal to each other.
2
Compute the resultant magnitude using vector synthesis
R=9.02+12.02=81+144=225=15.0 NR = \sqrt{9.0^2 + 12.0^2} = \sqrt{81 + 144} = \sqrt{225} = 15.0\text{ N}
For perpendicular force vectors, the resultant magnitude is the hypotenuse of the right triangle formed by the vector components.

Anahtar Kavram

Vector addition of perpendicular forces using the Pythagorean theorem
Tahmini Süre:1m 15s
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Scalars and Vectors

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