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two men pull a boat into the space between docks by applying independent forces

ID: 1261626 • Letter: T

Question

two men pull a boat into the space between docks by applying independent forces as shown. The one man applies a froce of 40N at an angle of 44 degrees as shown. The other man applies a force at an angle of 37 degrees. Which must the magnitude of this force be in order for the boat to move straight into the space (along the dotted line) with no side to side motion? If the boat has a mass of 50kg, what is the resultant of the boat at that point?

two men pull a boat into the space between docks by applying independent forces as shown. The one man applies a froce of 40N at an angle of 44 degrees as shown. The other man applies a force at an angle of 37 degrees. Which must the magnitude of this force be in order for the boat to move straight into the space (along the dotted line) with no side to side motion? If the boat has a mass of 50kg, what is the resultant of the boat at that point?

Explanation / Answer

Component of 40 N along dotted line = 40cos44 = 28.77 N

Component of 40N perpendicular to dotted line = 40 sin44 = 27.79 N

Component of F along dotted line   = Fcos37

Component of 40N perpendicular to dotted line = Fsin37

Fnet is along dotted line . So sum of forces perpendicular to dotted line must be zero.

Fsin37 - 27.79 = 0

F = 27.79 / sin37 = 46.17 N .............Ans

So Fnet = 28.77 + Fcos37 = 28.77 + 46.17cos37 = 65.64 N

Acc. a = Fnet /m = 65.64 / 50 = 1.31 m/s^2