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 76 Newtons is directed in the positive x direction, F2 has a magnitude of 10 Newtons is directed in the negative y direction, and F3 has a unknown magnitude and is directed at an angle of 26 degrees below the negative x axis. After these forces have been applied for 8.9 seconds, the mass has moved a horizontal displacement of 20 meters in the positive x direction. If the mass is 2 kg, what is the normal force on the mass in Newtons?

Explanation / Answer

here,

distance travelled bby the object , d = 20 m

time taken , t = 8.9 s

let the accelration of the object be a

using seccond equation of motion

s = u*t + 0.5 * a*t^2

20 = 0 + 0.5 * a * 8.9^2

a = 0.505 m/s^2

theta = 26 degree

equating the forces horizontally

F1 - F3*cos(26) = m*a

76 - F3 *0.8988 = 2 * 0.505

F3 = 83.43 N

let the normal reaction force be N

F2 + m*g + F3*sin(theta) = N

10 + 2 * 9.8 + 83.43 * sin(26) = N

N = 66.17 N

the normal reaction on the mass is 66.17 N

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