Two forces acting on an object produce the maximum net force if they are acting at an angle of:Multiple choice: a) 0 degrees b) 45 degrees c) 90 degrees d) 135 degrees e) 180 degrees

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prottoy's profile pic

prottoy | Student, Grade 10 | eNotes Newbie

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After looking at the options, and after representing it graphically (in the form of vector) I conclude that the correct answer is 0 degrees (a), because, it can't be 180 degrees(e) because then the forces will be opposite to each other and the body will be in equillibrium, so, if we see it in this way, the maximum resultant force will be produced when the ang between them is 0 degree.

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

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When two forces are acting simultaneously on an object then a single force that will produce the same effect as the two forces is known as resultant force. In the two separate forces are called component forces.

Resultant forces of any combination of two component forces can be found out using the parallelogram law of forces. As per this law when two forces acting simultaneously on a particle are represented in magnitude and direction  by the two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by the diagonal of the parallelogram passing through the point.

We observe that the magnitudes of the diagonal of a parallelograms passing through a point common to two sides increases as the angle between two sided reduces. As this angle approaches 0, the two sides tend to overlap each other and the magnitude of diagonal tends to become equal to sum of magnitudes of two sides. Thus the resultant force is maximum when the component forces are acting at an angle equal to 0, and is equal to the sum of two component forces.

Therefore, option a) in the question is the right answer.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

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The sum of two forces a and b is acting an angle x degree is also the rsultint force c and is given by:

c = sqrt(a^2+b^2+2abcosx) becomes maximum when cosx =1 or x=0

The choice is correct.


giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We have to deal with the additional vectorial structure called an inner product. In  this type of additional structure  each pair of vectors in the space is associated with a scalar quantity, called the inner product of the vectors.

In this case, the 2 forces are the 2 vectors above and if the 2 vectors are on the same dirrection and the same sense, the angle between 2 forces will be 0, so the maximum force will be reached at 0 degrees.


The inner product of the resultant force is

F1*F2=IF1I*IF2I*cos (F1,F2)

Wr know that the maximum value of the 

IF1I*IF2I*cos (F1,F2) is given by the maximum value of the cos (F1,F2)=1 when the angle between F1 and F2 is 0.

So the right answer is a) 0 degrees

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