Question

2 (a) The following horizontal forces act on an object: A, 6 N along the y-axis; B,
10 N along the negative y-axis; and C8 N at an angle of 45° clockwise from
the positive x-axis. Find the magnitude of A+B-C.
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Answer 1

Given info : The following horizontal forces act on an object: A, 6N along the y-axis; B, 10N along the negative y-axis; and C, 8N at an angle of 45°clockwise from the positive x-axis.

To find : the magnitude of A + B - C is ...

solution : write all forces in vector form,

A = 6N along the y - axis

so, A = 6 j ...(1)

B = 10 N along the negative y - axis

so, B = -10 j ...(2)

C = 8N at an angle of 45° clockwise from the positive x axis.

so, C = (8cos45° i - 8sin45° j)

= (4√2 i - 4√2 j) ...(3)

now A + B - C = 6j - 10j -(4√2i - 4√2j)

= - 4j - 4√2i + 4√2j

= (-4 + 4√2)j - 4√2i

now the magnitude of A + B - C = √{(-4 + 4√2)² + (-4√2)²}

= √(16 + 32 -32√2 + 32)

= √(80 - 32√2)

= 5.894 ≈ 6N

Therefore the magnitude of A + B - C = 6N