Thank you fo rhelping. Pleasr show work. Three forces of magnitudes F1 = 4.0 N,

Question

Thank you fo rhelping. Pleasr show work.

Three forces of magnitudes F1 = 4.0 N, F2 = 6.0 N, and F3 = 8.0 N are applied to a block of mass to = 2.0 kg, initially at rest, at angles shown on the diagram. (Figure 1) In this problem, you will determine the resultant (net) force by combining the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e.. all angles are positive). Calculate the magnitude of the resultant force Frightarrowr = Frightarrow1 + Frightarrow2 + Frightarrow3 acting on the block. Express the magnitude of the resultant force in newtons to two significant figures. What angle does Frightarrowr make with the positive x axis? Express your answer in degrees to two significant figures.

Explanation / Answer

F1 = 4 cos 25 i + 4 sin 25 j = 3.62 i + 1.69 j

F2 = 6 cos 35 i - 6 sin 35 j = 4.91 i - 3.44 j

F3 = -8 i

so Fz = F1 + F2 + F3

=> Fz = 0.53 i - 1.75 j

A) magnitude of Fz = |Fz| = sqrt (0.53^2 + 1.75^2)

so |Fz| = 1.83 N

B) angle made with +ve x axis = 360 - tan^-1 (1.75/0.53)

so angle = 286.85 degrees

C) accln = Fz/m

=> |a| = |Fz|/m = 1.8/2 = 0.914 m/s^2

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