A mass of 8 kg lies on a horizontal, frictionless floor. A force of 53 Newtons pushes to the left (negative x direction) with a force of 53 Newtons. Another force of unknown magnitude pushes the mass in a direction of 28.5 degrees above the positive x axis. The mass is originally at rest before these forces are applied and 2.9 seconds after the forces have been applied, the mass has moved to the left a distance of 11.5 meters. What is the magnitude of the unknown force in Newtons?

Question

A mass of 8 kg lies on a horizontal, frictionless floor.  A force of 53 Newtons pushes to the left (negative x direction)  with a force of 53 Newtons.  Another force of unknown magnitude pushes the mass in a direction of 28.5 degrees above the positive x axis.  The mass is originally at rest before these forces are applied and 2.9 seconds after the forces have been applied, the mass has moved to the left a distance of 11.5 meters.  What is the magnitude of the unknown force in Newtons?

Henry · Answer

V = 11.5m. / 2.9s. = 3.97m/s.

a = (Vf - Vo) / t,
a =(3.97 - 0) / 2.9 = 1.37m/s^2.

Fn = ma = 8 * 1.37 = 10.94N.

Fn = -57 + F*cos28.5 = 10.94,
-57 + 0.879F = 10.94,
0.879F = 10.94 + 57 = 67.94,
F = 77.3N