What is the effort force required to prevent a 200 N object from sliding on a 30° frictionless incline?

To determine the effort force required to prevent a 200 N object from sliding down a 30° frictionless incline, we must analyze the forces acting on the object along the incline. In a frictionless scenario, the only force that acts against the effort to keep the object at rest is the component of its weight that acts parallel to the slope.

The weight of the object can be split into two components: one acting perpendicular to the incline and the other acting parallel to the incline. The force acting parallel to the incline, which is responsible for potentially sliding down, can be calculated using the sine function of the incline angle.

The formula to find the component of the weight acting down the incline is:

Force parallel to the incline = Weight × sin(θ)

In this case, the weight of the object is 200 N, and θ is 30°:

Force parallel to the incline = 200 N × sin(30°)

The sine of 30 degrees is 0.5, so:

Force parallel to the incline = 200 N × 0.5 = 100 N

Therefore, it requires an effort force of 100 N applied up the incline to prevent the object from sliding down, as