Engineering Mechanics Test 1

Result

Engineering Mechanics Test 1

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Question 1
1 / -0

Two forces \({\vec F_1} = \hat i + 2\hat y + 3\hat x\) and \({\vec F_2} = 4\hat i + 3\hat y - \hat x\) are acting on a rigid body. The component of \({\vec F_2}\) in direction of \({\vec F_1}\) is ______ N

A
1.5-2

B
1.54-21

C
1.57-26

D
1.59-22

Solution

Concept:
Component of \({\vec F_2}\) in \({\vec F_1} = {\vec F_2}\cos \theta \)
\({\rm{Where}},\cos \theta = \frac{{{{\vec F}_1}.{{\vec F}_2}}}{{\left| {{{\vec F}_1}} \right|\left| {{{\vec F}_2}} \right|}}\)
Calculation:
\({\vec F_1}.{\vec F_2} = 4 + 6 + \left( { - 3} \right) = 7\)
\(\left| {{{\vec F}_1}} \right| = 3.74\;N;\left| {{{\vec F}_2}} \right| = 5.099\;N\)
cos θ = 0.367
∴ F₂ cos θ = 5.099 × 0.367
∴ F₂ cos θ = 1.87 N