A 149 kg crate is pushed at constant speed up a frictionless inclined plane of theta = 51 with the horizontal. Assuming one pushes with a horizontal force, what is the magnitude of the force F (in N) required to do this?
See previous post: Mon,10-14-13,2:31 PM.
To determine the magnitude of the force required to push the crate up the inclined plane, we need to analyze the forces acting on the crate. In this case, we have two forces acting on the crate: the gravitational force and the force applied parallel to the incline.
1. Gravitational force:
The weight (gravitational force) acting on the crate can be calculated using the formula:
Weight = mass * gravitational acceleration,
where mass = 149 kg and gravitational acceleration ≈ 9.81 m/s².
Weight = 149 kg * 9.81 m/s² ≈ 1462.69 N (approximately)
2. Force parallel to the incline:
The force parallel to the incline can be determined using the formula:
Force_parallel = mass * acceleration_parallel,
where mass = 149 kg and acceleration_parallel = 0 m/s² (since it is moving at a constant speed).
Force_parallel = 149 kg * 0 m/s² = 0 N
Since the crate is moving at a constant speed up the frictionless inclined plane, the net force on the crate is zero. This means that the force applied parallel to the incline is equal in magnitude but opposite in direction to the gravitational force.
Therefore, the magnitude of the force required to push the crate up the inclined plane is equal to the weight of the crate, which is approximately 1462.69 N.