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The magnitude of two forces, which when acting at right angles produce resultant force of √10 kg and when acting at 60 degree produce resultant force of √13 kg. These forces are?
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The magnitude of two forces, which when acting at right angles produce...
Given:
Resultant force at right angles = $\sqrt{10}$ kg
Resultant force at 60 degrees = $\sqrt{13}$ kg
To find:
Magnitude of two forces
Solution:
Let the two forces be F1 and F2.
Using Pythagoras theorem:
$F1^2 + F2^2 = (\sqrt{10})^2$
$F1^2 + F2^2 = 10$ ---(1)
Using cosine rule:
$(\sqrt{13})^2 = F1^2 + F2^2 + 2F1F2\cos 60^\circ$
$13 = F1^2 + F2^2 + F1F2$
$F1F2 = 13 - F1^2 - F2^2$ ---(2)
Substitute equation (1) in equation (2)
$F1F2 = 13 - 10$
$F1F2 = 3$
Now, solve for F1 and F2 using the following method:
$F1 = \frac{F1F2}{F2}$
$F2 = \frac{F1F2}{F1}$
Substitute F1 in the above equation to get F2 and vice versa.
Final Answer:
The two forces are:
F1 = $\sqrt{\frac{5}{2}}$ kg
F2 = $\sqrt{\frac{14}{5}}$ kg
Resultant force at right angles = $\sqrt{10}$ kg
Resultant force at 60 degrees = $\sqrt{13}$ kg
To find:
Magnitude of two forces
Solution:
Let the two forces be F1 and F2.
Using Pythagoras theorem:
$F1^2 + F2^2 = (\sqrt{10})^2$
$F1^2 + F2^2 = 10$ ---(1)
Using cosine rule:
$(\sqrt{13})^2 = F1^2 + F2^2 + 2F1F2\cos 60^\circ$
$13 = F1^2 + F2^2 + F1F2$
$F1F2 = 13 - F1^2 - F2^2$ ---(2)
Substitute equation (1) in equation (2)
$F1F2 = 13 - 10$
$F1F2 = 3$
Now, solve for F1 and F2 using the following method:
$F1 = \frac{F1F2}{F2}$
$F2 = \frac{F1F2}{F1}$
Substitute F1 in the above equation to get F2 and vice versa.
Final Answer:
The two forces are:
F1 = $\sqrt{\frac{5}{2}}$ kg
F2 = $\sqrt{\frac{14}{5}}$ kg
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The magnitude of two forces, which when acting at right angles produce resultant force of √10 kg and when acting at 60 degree produce resultant force of √13 kg. These forces are?
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The magnitude of two forces, which when acting at right angles produce resultant force of √10 kg and when acting at 60 degree produce resultant force of √13 kg. These forces are? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The magnitude of two forces, which when acting at right angles produce resultant force of √10 kg and when acting at 60 degree produce resultant force of √13 kg. These forces are? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnitude of two forces, which when acting at right angles produce resultant force of √10 kg and when acting at 60 degree produce resultant force of √13 kg. These forces are?.
The magnitude of two forces, which when acting at right angles produce resultant force of √10 kg and when acting at 60 degree produce resultant force of √13 kg. These forces are? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The magnitude of two forces, which when acting at right angles produce resultant force of √10 kg and when acting at 60 degree produce resultant force of √13 kg. These forces are? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnitude of two forces, which when acting at right angles produce resultant force of √10 kg and when acting at 60 degree produce resultant force of √13 kg. These forces are?.
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