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3 years ago

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ONLINE CALCULATOR .A force of 187 pounds makes an angle of 73 degrees 36 ' with a second force. The resultant of the two forces

makes an angle of 29 degrees 1 ' to the first force. Find the magnitudes of the second force and of the resultant.

1 answer:

saul85 [17]3 years ago

3 0

Answer:

The magnitudes of the second force is $Z = 129.9 N$

The magnitudes of the resultant force is $R = 256.047 N$

Explanation:

From the question we are told that

The force is $F = 187 \ lb$

The angle made with second force $\theta_o = 73 ^o 36' = 73 + \frac{36}{60} = 73.6^o$

The angle between the resultant force and the first force $\theta _1 = 29 ^o 1 ' = 29 + \frac{1}{60} = 29.0167^o$

For us to solve problem we are going to assume that

The magnitude of the second force is Z N

The magnitude of the resultant force is R N

According to Sine rule

$\frac{F}{sin (\theta _o - \theta_1 } = \frac{Z}{\theta _1}$

Substituting values

$\frac{187}{sin(73.3 - 29.01667)} =\frac{Z}{sin (29.01667)}$

$267.82 =\frac{Z}{0.4851}$

$Z = 129.9 N$

According to cosine rule

$R = \sqrt{F ^2 + Z^2 + 2(F) (Z) cos (\theta _o) }$

Substituting values

$R = \sqrt{187^2 + 129.9 ^2 + 2 (187 ) (129.9) cos (73.6)}$

$R = 256.047 N$

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