Question

Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 21.0∘ west of north, and the resultant of these two pulls is 450.0 N directly northward. Assume that the smaller pull has a component directed to the north.

Part A Use vector components to find the magnitude of the larger pull. Express your answer with the appropriate units. Flarger = Previous AnswersRequest Answer

Part BPart complete Use vector components to find the magnitude of the smaller pull. Express your answer with the appropriate units. Fsmaller = 175 N Previous Answers Correct

Part C Use vector components to find the direction of the smaller pull. ϕ = ∘ east of north

Answer 1

F₁ = larger force, directed 21 degrees west of north

F₂ = smaller force, directed d degrees east of north

F₁ = 2*F₂

F = total resultant force, 450 N, directed due north (no East-West component)

now East-West and North-South components.

The East-West equation

0 = (F₁)sin(21) + (F₂)sin(d)

substituting F₁ = 2*F₂,

we have:

(F₂)sin(d) = 2*F₂*sin(21)

Therefore,

d = arcsin( 2 sin(21)

d = 45.78 ^o

The North-South equation

450 = F₁cos(21) + F₂cos(d)

450 = 2*F₂*cos(21) + F₂*cos(d)

F₂ = 450 / ( 2cos(21) + cos(45.78) )

F₂ = 175.47 N smaller force

F₁ = 350.94 N larger force