The acceleration of the cart, considering the applied force, friction, and the inclined plane, is approximately 0.314m/s^2.
In the scenario of pushing a cart of physics books up a ramp inclined at 9.000⁰, several forces are at play. The applied force, directed horizontally, is 1200 N. The gravitational force, acting vertically downward, is countered by a component along the ramp, and the normal force acts perpendicular to the ramp. Additionally, there is a kinetic friction force opposing the direction of motion.
The force diagram illustrates that the applied force overcomes the component of gravitational force along the ramp and the kinetic friction force. The net force, calculated by subtracting the frictional force from the component of the gravitational force along the ramp, is used to determine the acceleration using Newton's second law (F = ma). The acceleration is found to be approximately 0.314m/s^2, signifying the rate at which the cart accelerates up the inclined plane, accounting for the applied force, gravitational force component, and frictional resistance.