Three forces acting on a spherical mass M are depicted in the diagram below. dyn

Question

Three forces acting on a spherical mass M are depicted in the diagram below. dynamically generated plot A.

Calculate the magnitude and direction (i.e., the angle with respect to the positive H-axis, measured positive as counter-clockwise) of the total force acting on M. Notice that the arrows representing the forces end on grid intersections. Magnitude: Direction: Tries 0/20 B. When a fourth force is applied to the mass, it is observed that the velocity of the mass stops changing and remains constant. What are the horizontal and vertical components of that fourth force? Horizontal: Vertical:

Explanation / Answer

Here, F1= -20i

          F2 = 70i + 40j

           F3 = 50i - 20j

So, Net Force on M = F1 + F2 + F3

                                = -20i + 70i + 40j + 50i - 20j

                                 = 100i + 20j

=> Magnitude of force on M = sqrt(1002 + 202 )

                                              = 101.98 N

Direction = tan-1(20/100)

               = tan-1(0.2)

                =11.31 degrees with respect to the positive H-axis, measured positive as counter-clockwise.

When a fourth force is applied to the mass, it is observed that the velocity of the mass stops changing and remains constant so, net force applied on mass M is zero .

=> Fourth Force applied on mass M = -100i -20j

=> Horizontal component of fourth force = -100 N     towards -ve x axis

       Vertical component of fourth force = -20 N     towards -ve y axis

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