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When an object moves with constant velocity, it means that its speed and direction are unchanging. In physics, this indicates that the object's acceleration is zero. The key takeaway here is that the net force acting on the object must also be zero for it to maintain constant velocity.
In the context of the toboggan sliding down a hill at a constant velocity, this implies that the forces acting on the toboggan are in balance. Specifically, the gravitational force pulling it down along the hill is exactly countered by the force of kinetic friction. This balance allows the toboggan to slide steadily without speeding up or slowing down.
For students, understanding constant velocity in this example highlights the equilibrium of opposing forces and reinforces the concept of net zero force, a fundamental idea in classical mechanics.

Gravitational force is the attractive force that acts between any two masses. For the toboggan on the hill, this force acts downward, toward the center of the Earth.
When dealing with inclined planes, like our hill, gravitational force can be broken into two components:

• Parallel to the hill's surface: This component causes the toboggan to slide down the hill. It's calculated as \( mg \sin \theta \), where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( \theta \) is the angle of the hill with respect to the horizontal.
• Perpendicular to the hill's surface: This component is responsible for the normal force and is calculated as \( mg \cos \theta \). It acts as the reactive force against the hill's surface.

Breaking gravitational force into components helps us understand how the toboggan continues to move at a constant velocity.

The normal force is a key concept when analyzing objects on surfaces. It's the force exerted by a surface to support the weight of an object resting on it, acting perpendicular to the surface.
For the toboggan sliding down an inclined hill, the normal force balances the component of the gravitational force perpendicular to the hill's surface. This ensures that the toboggan doesn’t slide sideways or sink into the hill. Mathematically, it is represented as \( N = mg \cos \theta \).
Understanding the normal force helps in calculating the frictional forces, as kinetic friction is proportional to this normal force. Students can appreciate the normal force's role in the physics of motion as it interacts with other forces to sustain or resist movement.

The coefficient of kinetic friction is a dimensionless value that represents the ratio of the force of kinetic friction between two bodies and the normal force pressing them together.
In our exercise, this value is determined when the toboggan moves at constant velocity down the hill. It is calculated by the ratio \( \mu_k = \frac{\sin \theta}{\cos \theta} \) or \( \mu_k = \tan \theta \), where \( \theta \) is the angle of inclination of the hill. Inserting \( 8.00^{\circ} \) into this formula yields a coefficient of approximately 0.1405.
This coefficient helps describe how much frictional force exists between the toboggan and the hill's surface. It is crucial in problems involving motion on surfaces, helping students understand how friction influences movement and speed.