A 63-kg
 skier speeds down a trail, as shown in the figure (Figure 1). The surface is smooth and inclined at an angle of 22 ∘
 with the horizontal.Find the magnitude of the net force acting on the skier.        

To find the magnitude of the net force acting on the skier, we can use the following physics principles. 

The force causing the skier to accelerate down the incline is the **component of the gravitational force** acting along the slope.

### Step 1: Determine the gravitational force
The gravitational force \( F_g \) acting on the skier is the skier's weight:
\[
F_g = m \cdot g
\]
where:
- \( m = 63 \, \text{kg} \) is the mass of the skier,
- \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity.

\[
F_g = 63 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 617.4 \, \text{N}
\]

### Step 2: Calculate the component of force along the incline
The net force acting on the skier is the component of the gravitational force along the incline, which is:
\[
F_{\text{net}} = F_g \cdot \sin(\theta)
\]
where:
- \( \theta = 22^\circ \) is the angle of the incline.

\[
F_{\text{net}} = 617.4 \, \text{N} \times \sin(22^\circ)
\]

### Step 3: Compute the result
Let's calculate the value of \( F_{\text{net}} \).The magnitude of the net force acting on the skier is approximately **231.28 N**.

Would you like further details or have any questions? Here are five related questions to deepen understanding:

1. How would the net force change if the angle of the incline increased?
2. What would be the skier's acceleration along the incline?
3. How does friction affect the net force if the surface is not smooth?
4. What would happen to the net force if the skier's mass were doubled?
5. How can you calculate the normal force acting on the skier in this situation?

**Tip:** When dealing with inclined planes, always break the forces into components parallel and perpendicular to the surface.

A 63-kg skier speeds down a trail. The surface is smooth and inclined at an angle of 22° with the horizontal. Find the magnitude of the net force acting on the skier.

This problem involves calculating the net force acting on a 63-kg skier descending a smooth slope inclined at 22°. Learn how to apply Newton's second law and decompose forces using trigonometry. Ideal for high school students in grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation