A mass is placed, at rest, on a horizontal, frictionless surface and three force

Question

A mass is placed, at rest, on a horizontal, frictionless surface and three forces are applied to it at once. F1 has a magnitude of 75 Newtons is directed in the positive x direction, F2 has a magnitude of 11 Newtons is directed in the negative y direction, and F3 has a unknown magnitude and is directed at an angle of 22 degrees below the negative x axis. After these forces have been applied for 7.4 seconds, the mass has moved a horizontal displacement of 24 meters in the positive x direction. If the mass is 3 kg, what is the normal force on the mass in Newtons?

Explanation / Answer

net force along X-axis Fx = F1 + F3*cos(22)

Fx = 75 + F3*cos(22) = m*ax

ax is the accealration along X-axis

apply S = 0.5*ax*t^2

24 = 0.5*ax*7.4^2

ax = 24/(0.5*7.4*7.4) = 0.876 m/s^2

then 75-F3*cos(22) = 3*0.876

F3 = 72.372/cos(22) = 78.05 N

along Y-axis

F2+F3*sin(22) = N

Normal force N = 11+(78.05*sin(22)) = 40.3 N

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