What is the magnitude of the mass\'s acceleration vector, a? The diagram below s

Question

What is the magnitude of the mass's acceleration vector, a? The diagram below shows a block of mass m = 2.00 kg on a frictionless horizontal surface, as seen from above. Three forces of magnitudes F_1 = 4.00 N, F_2 = 6.00 N, and F_3 = 8.00 N are applied to the block, initially at rest on the surface, at angles shown on the diagram. (Figure 1) In this problem, you will determine the resultant (total) force vector from the combination of the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive). What is the direction of a? In other words, what angle does this vector make with respect to the positive x axis?

Explanation / Answer

Resolving the Vectors in X and Y directions

we get

Fresultant = F1 Cos 25 i + F1 Sin 25 j -F3 i + F2 Cos 325 i + F2 Sin 325 j

Solving We get Fresultant = 0.54 i -1.75 j

Magnitude of Resultant Force = sqrt(.54^2 + (-1.75)^2) = 1.832N

C . acceleration magnitude = F/m= 0.916 m/s2

D. Direction of a is the direction of force = tan-1 (-1.75/0.54) = 287.15 Degrees

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