# Calculating the Resultant External Forces Acting on Billy Bob While Skiing Down a Slope

## Billy Bob's Skiing Adventure

Billy Bob is in a tuck and skiing down a 40 degree slope. Air resistance pushes backward on him with a force of 20 N. The coefficient of dynamic friction between his skis and the snow is 0.09. Billy Bob's mass is 103 kg.

## What is the magnitude of the resultant of the external forces that act on Billy Bob?

**Final answer:**

The **magnitude** of the external forces acting on Billy Bob while skiing down a 40 degree slope can be calculated by considering his weight, air resistance, and the frictional force. The **normal force** and the component of weight parallel to the slope are calculated, before these are used to determine the resultant force. The magnitude of this resultant force is 574.5 Newtons.

## Explanation:

The magnitude of the external forces acting on Billy Bob while **skiing** can be calculated by accounting for three key forces: his weight, the frictional force, and air **resistance**. His weight component parallel to the slope can be determined with the formula m*g*sin(θ), where m is Billy Bob's mass (103 kg), g is the **gravitational acceleration** (9.8 m/s²), and θ is the slope angle (40°). Thus, the parallel weight component is approximately 665.7 N.

Next, we calculate the normal force, which balances Billy Bob's weight component perpendicular to the slope. This can be obtained using the formula m*g*cos(θ), which yields about 791.4 N. We then use the frictional force formula, f_k = μ_k*N, where μ_k is the **coefficient of friction** (0.09). This calculation results in a frictional force of approximately 71.2 N.

Finally, we calculate the net force acting on Billy Bob by summing up all the forces affecting him. We add the parallel component of his weight, the frictional force and the air resistance (acting in the opposite direction), which gives us 665.7 N (downhill force) - 71.2 N (friction) - 20 N (air resistance) = 574.5 N. Thus, the magnitude of the resultant of the external forces acting on Billy Bob is 574.5 Newtons.

What are the key factors to consider when calculating the resultant external forces acting on an object on a slope? When calculating the resultant external forces acting on an object on a slope, it is crucial to consider the object's weight components parallel and perpendicular to the slope, the frictional forces, air resistance, and the angle of inclination of the slope. These factors play a significant role in determining the overall magnitude and direction of the resultant force experienced by the object.