Final answer:
The acceleration of a snowboarder moving down a slope with an incline of 10.0° and a coefficient of kinetic friction of 0.20 is calculated by subtracting the force of friction from the gravitational force along the incline and then applying Newton's second law to solve for acceleration. The result is that the snowboarder's acceleration depends on the angle of the slope and the coefficient of friction, but not on the snowboarder's mass.
Step-by-step explanation:
To understand the acceleration of a snowboarder moving down an incline, we need to apply the concepts of physics, specifically Newton's second law of motion and the forces involved in motion on an incline. The forces acting on the snowboarder include gravity, normal force, and the force of friction. Given that the incline angle is 10.0° and the coefficient of kinetic friction (μ_k) is 0.20, we can calculate the acceleration.
First, we calculate the force of gravity along the incline, which is given by Fg = m * g * sin(θ), where m is the mass of the snowboarder, g is the acceleration due to gravity (9.8 m/s²), and θ is the incline angle. Second, the force of kinetic friction (μ_k) opposing the motion is given by Ff = μ_k * N, where N is the normal force, which can be found using N = m * g * cos(θ).
To find the net force acting on the snowboarder, we subtract the force of friction from the gravitational force along the incline: Fnet = Fg - Ff. Finally, we use Newton's second law (F = m * a) to solve for the acceleration a = Fnet / m. Note that the mass (m) cancels out, and the acceleration of the snowboarder only depends on the gravitational acceleration, the incline angle, the coefficient of friction, and does not depend on the mass of the snowboarder.
Therefore, the acceleration of the snowboarder is a result of these combined forces. Calculations would yield a numerical value for a based on the given angle and coefficient of friction.