A crate on a smooth surface is simultaneously pulled by two horizontal forces. One force o… — JAMB UTME

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

Answer: 15 N

Answer

The magnitude of the resultant force acting on the crate is

15.0\text{ N}

Because the two pulling forces are perpendicular, their resultant magnitude is calculated using vector addition via the Pythagorean theorem:

R = \sqrt{9.0^2 + 12.0^2} = 15.0\text{ N}

Step-by-Step Solution

Determine the angle between the two given vectors

The forces are perpendicular (

90^\circ

East and North cardinal directions are orthogonal to each other.

Compute the resultant magnitude using vector synthesis

R = \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.

Key Concept

Vector addition of perpendicular forces using the Pythagorean theorem

Estimated Time:1m 15s

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