1. Understand the Forces
* Gravity (Weight): The force of gravity acts straight down on the mass. Its magnitude is (mass * acceleration due to gravity) = 20 kg * 9.8 m/s² = 196 N.
* Normal Force: The force exerted by the inclined plane perpendicular to its surface. It balances the component of gravity perpendicular to the plane.
* Friction Force: The force opposing the motion of the mass along the plane. It's proportional to the normal force and the coefficient of kinetic friction.
* Applied Force: The force you need to apply parallel to the incline to pull the mass at a constant speed.
2. Break Down Forces
* Component of Gravity Parallel to the Plane: This is the force that needs to be overcome to pull the mass upwards. It's calculated as (weight of the mass * sin(angle)).
* 196 N * sin(30°) = 98 N
* Component of Gravity Perpendicular to the Plane: This is balanced by the normal force. It's calculated as (weight of the mass * cos(angle)).
* 196 N * cos(30°) = 169.7 N (approximately)
* Friction Force: This opposes the motion and is calculated as (coefficient of kinetic friction * normal force).
* 0.20 * 169.7 N = 33.94 N (approximately)
3. Calculate the Applied Force
To pull the mass at a constant speed, the applied force must balance the forces acting against the motion:
* Applied Force = (Component of gravity parallel to the plane) + (friction force)
* Applied Force = 98 N + 33.94 N = 131.94 N (approximately)
Therefore, you need approximately 131.94 Newtons of force to pull the 20 kg mass at a uniform slow speed up the inclined plane.
