Find the magnitude of the applied force F.?

Old Science Guy

.. find force parallel to ramp from a diagram of ramp Fp = m g sin(angle) = 90.0 (9.81) sin 37.0° = 531.34 N from a 2nd diagram of applied force we get Fa = Fp / cos(angle) = 531.34 / cos 37.0° = 665 N When you get a good response, please consider giving a best answer. This is the only reward we get. When you get a good response, please consider giving a best answer. This is the only reward we get.

electron1

The force that causes the box to decelerate is the component of its weight that is parallel to the ramp. The component of the horizontal force that is parallel to the ramp causes the box to accelerate. Since the box is moving at a constant speed, these two forces are equal in magnitude. Weight = 90.0 * 9.8 = 882 N Force parallel = 882 * sin 37 This is approximately 530 N. For the horizontal force, force parallel = F * cos 37 F * cos 37 = 882 * sin 37 F = 882 * tan 37 This is approximately 665 N. I hope this is helpful for you.

RealPro

The force is acting horizontally, so its component parallel to the incline must be F * cos(37.0°) Without the force, the component of the box's weight parallel to the incline (downward) would be the only unbalanced force acting on the box, mg*sin(37.0°) So the two must cancel so all the forces become balanced and there is no acceleration Fcos(37.0°) = mgsin(37.0°) F = mg * tan(37.0°)