(This contains all needed information according to my professor) A block of mass

Question

(This contains all needed information according to my professor) A block of mass m = 2.61 kg is held in equilibrium on a frictionless incline of angle = 56.7 by the horizontal force F, as shown in the figure. (a) Determine the value of F (N). (b) Determine the normal force (N) exerted by the incline on the block.

Hint: Draw a free-body diagram of the block. Choose a coordinate system with the x axis parallel to the surface of the incline and the y axis perpendicular to the surface of the incline.

Explanation / Answer

a)Force F will be given by:

R cos(theta) = mg

R sin(theta) = F

F/mg = tan(theta)

F = mg tan(theta)

F = 2.61 x 9.81 x tan56.7 = 38.98 N = 40 N(aprox)

Hence, F = 38.98 N

b)Normal force will be:

N = F sin(theta) + mg cos(theta)

N = 38.98 x sin56.7 + 2.61 x9.81 x cos56.7 = 32.58 + 14.06 = 46.64 N

Hence, N = 46.64 N

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