1. Forces Acting on the Object:
* Gravity (Fg): This acts directly downward, with a component parallel to the incline (Fg sin θ) and a component perpendicular to the incline (Fg cos θ).
* Normal Force (Fn): This acts perpendicular to the incline, balancing the component of gravity perpendicular to the incline.
* Friction (Ff): This acts parallel to the incline, opposing the motion.
* Applied Force (Fa): This is the force you apply to push the object up the incline.
2. Formula:
To move the object up the incline at a constant velocity (no acceleration), the applied force must balance the forces opposing it:
Fa = Fg sin θ + Ff
Where:
* Fa is the applied force (the pushing force).
* Fg is the force of gravity (mass x acceleration due to gravity).
* θ is the angle of the incline.
* Ff is the force of friction (coefficient of friction x normal force).
Important Notes:
* Friction: The formula assumes kinetic friction (friction during motion). If the object is at rest, you'll need to use the static friction coefficient.
* Angle: The angle of the incline is measured from the horizontal.
* Constant Velocity: The formula assumes constant velocity. If you want to accelerate the object up the incline, you'll need to add a term for the net force (mass x acceleration).
Example:
Let's say a 10 kg object is on a 30-degree incline. The coefficient of kinetic friction is 0.2.
1. Fg: 10 kg x 9.8 m/s² = 98 N
2. Fg sin θ: 98 N x sin(30°) = 49 N
3. Fn: 98 N x cos(30°) = 84.87 N
4. Ff: 0.2 x 84.87 N = 16.97 N
5. Fa: 49 N + 16.97 N = 65.97 N
Therefore, you would need to apply a force of approximately 65.97 N to push the object up the incline at a constant velocity.
