Question

Two forces,whose resultant is 100n, are perpendicular to each other.If one of them makes an angle of 60 with the resultant,calculate its magnitude: (sin60=0.8660,cos60=0.5000)

Answer 1

50 N and 86.6 N

Step-by-step explanation:

Given that

R = 100 N

Cos 60° = 0.5

Sin 60° = 0.8660

Assume the first force is F1, so

F1 = 100 x cos 60

F1 = 100 x 0.5

F1 = 50 N

Assume that the second force is F2, so

F2 = 100 x sin 60

F2 = 100 x 0.866

F2 = 86.6 N approximately 87N

The magnitudes are 87 N and 50 N.

Check,

R = √(F1)² + (F2)²

R = √(50)² + (86.6)²

R = √2500 + 7500

R = √10000

R = 100 N

Therefore, since we checked from the gotten magnitude for our resultant, the answer is correct

Answer 2

50.00N

Step-by-step explanation:

The diagram for this question has been drawn and attached to this response.

As shown in the diagram,

Let the first vector be A

Let the second vector be B

Let the resultant vector be R

R = A + B (The resultant is the vector sum of the two vectors)

One of the vectors (B in this case) makes an angle of 60 with the resultant R.

Since the two vectors are perpendicular (90 degrees) to each other, then, the second vector A makes an angle 30 degrees with the resultant vector R

Now

Let's resolve the vectors A, B and R into the x and y components

R = (100 cos 60°) i + (100 sin 60°) j

A = 0 i + A j

B = B i + 0 j

Remember that:

R = A + B

Now substitute the values of R, A and B as follows;

(100 cos 60°) i + (100 sin 60°) j = 0 i + A j + B i + 0 j

Collect like terms

(100 cos 60°) i + (100 sin 60°) j = (0 + B)i + (A + 0) j

(100 cos 60°) i + (100 sin 60°) j = (B) i + (A) j

Compare both sides

100cos 60° = B

100 sin 60° = A

Solve for A and B

A = 100 sin 60°

B = 100 cos 60°

Substitute the values of sin 60° = 0.8660 and cos 60° = 0.5000

A = 100 x 0.86600 = 86.60N

B = 100 x 0.5000 = 50.00N

Therefore, the magnitude of the vector (B) that makes an angle of 60 with the resultant is 50.00N