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Basile [38]
3 years ago
5

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.
Physics
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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