Olympic Skier Tina Maze: Determining Acceleration Down a Steep Slope

Olympic skier Tina Maze skis down a steep slope that descends at an angle of 30 degrees below the horizontal.

Tina Maze, an Olympic skier, is navigating a steep slope with an angle of 30 degrees downward from the horizontal. In this scenario, we are tasked with determining Tina's acceleration as she skis down the slope. To solve this problem, we will need to consider the coefficient of sliding friction between her skis and the snow, which is 0.10.

Determine Maze's acceleration. Express your answer with the appropriate units.

Since Tina is sliding down on an inclined ramp, we can break down the forces acting on her:

1. Net Force along the Inclined Plane:

Fx = mg sinθ

2. Force Component Perpendicular to the Inclined Plane:

Fy = mg cosθ

It is important to note that the force normal to the inclined plane is counterbalanced by the normal force. Thus, we can find the normal force as:

Fn = mg cosθ

To find the friction force, we can use the formula:

Ff = µ * Fn

Ff = 0.10 * mg cosθ

Considering the net force along the inclined plane, we have:

Fnet = mgsinθ - Ff

Fnet = mgsinθ - 0.10 * mgcosθ

By applying Newton's second law, we can express the net force as:

Fnet = ma

Combining the previous equations, we arrive at the expression for acceleration:

a = gsinθ - 0.10gcosθ

a = 9.81 * sin(30) - 0.10 * 9.81 * cos(30)

a = 4.06 m/s^2

Therefore, Tina Maze's acceleration as she skis down the steep slope is 4.06 m/s^2.

What is the coefficient of sliding friction between Tina Maze's skis and the snow?

The coefficient of sliding friction between Tina Maze's skis and the snow is 0.10.