A 200-N box is placed on an inclined plane that makes a 35.0° angle with the horizontal. Find the component of the weight force parallel to the plane's surface.
To find the component of the weight force parallel to the plane's surface, we can use trigonometry. Here's how you can calculate it:
Step 1: Draw a diagram: Draw a rough diagram of the inclined plane with the given angle and the weight force acting vertically downward.
Step 2: Identify the forces: In this situation, we have two forces acting on the box: the weight force (W) acting vertically downward and the force component parallel to the plane's surface (F_par).
Step 3: Resolve the weight force: Resolve the weight force (W) into two components: the component parallel to the plane's surface (F_par) and the component perpendicular to the plane's surface (F_perp).
Step 4: Apply trigonometry: We can use some trigonometry to find the value of the component of the weight force parallel to the plane's surface (F_par). In this case, we have the angle of the inclined plane (35.0°) and the magnitude of the weight force (200 N). We'll use the equation:
F_par = W * sin(θ)
where θ is the angle of the inclined plane.
Step 5: Calculate the component: Substituting the given values into the equation, we have:
F_par = 200 N * sin(35.0°)
Step 6: Solve for F_par: Use a calculator to evaluate the sine of 35.0 degrees and multiply it by 200 N:
F_par ≈ 200 N * 0.5736 ≈ 114.72 N
Therefore, the component of the weight force parallel to the plane's surface is approximately 114.72 N.