Question

the resultant of two perpendicular forces acting at a point is 15 n if one of the forces has magnitude of 12 n then the magnitude of the other force is

Answer 1

Answer:

Let,

A = 12N

B = ?

Angle = x = 90 degrees

R = 15N

We know,

R = (A^2 + B^2 + 2ABCosx)^(0.5)

or, 15 × 15 = 12×12 + B^2 + 0 (Cos 90 = 0)

or, 225 = 144 + B^2

or, B^2 = 81

or, B = 9N

Answer 2

Concept:

• Force
• Vector addition
• The process of adding two or more vectors together to create a vector sum is known as vector addition.
• Resolution of vectors
• Calculating the magnitude of a resultant vector

Given:

• Resultant force Fr = 15 N
• The first force component F₁ = 12 N
• The two force components are perpendicular to each other

Find:

• The second force component F₂

Solution:

For 2 perpendicular vectors, we find the resultant vector in the following manner

Resultant = √X²+Y²

Fr = √F₁²+F₂²

Fr² =  F₁²+F₂²

Fr = 15 N, F₁ = 12 N

15² = 12²+F₂²

225 = 144 + F₂²

F₂² = 225 - 144

F₂² = 81

F₂ = 9

The other force has a magnitude of 9 N.

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