Final answer:
To find the horizontal component of the applied force, we use the cosine of the angle times the force. Calculating this for an angle of 30 degrees and a force of 100 N, we find that the effective horizontal force on the crate is 86.6 N. The correct option is B.
Step-by-step explanation:
To find the effective force acting on the crate in the horizontal direction, we need to find the horizontal component of the applied force. We can use trigonometry to calculate this. The horizontal component of a force is given by the formula: Horizontal Force = Applied Force * cos(angle). In this case, the applied force is 100 N and the angle is 30 degrees. Plugging these values into the formula, we get: Horizontal Force = 100 N * cos(30°) = 100 N * 0.866 = 86.6 N. Therefore, the effective force acting on the crate in the horizontal direction is 86.6 N, which corresponds to option B.
The student asked: "A horizontal force of 100 N is required to push a crate across a rough surface. If the force is applied at an angle of 30 degrees to the horizontal, what is the effective force acting on the crate in the horizontal direction?" To find the effective force in the horizontal direction, we must calculate the component of the force that lies along the horizontal axis.
To calculate the horizontal force (Fhorizontal), we use the cosine component of the force:
Fhorizontal = F * cos(θ)
Where F is the applied force and θ is the angle of the force relative to the horizontal plane.
By plugging in the values:
Fhorizontal = 100 N * cos(30°) = 100 N * (√3/2) = 100 N * 0.866 = 86.6 N
Therefore, the correct answer is B. 86.6 N, which is the effective horizontal force acting on the crate.