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When pulling an object like a suitcase with a strap, the force you apply can be broken down into two components: horizontal and vertical.
This means any force that's not acting directly along the x or y axis can be split into parts that do.
Here's how that works:

• Horizontal Component: This is the part of the force parallel to the ground, responsible for overcoming the frictional force. In our example, this component is calculated as the force exerted by the student times the cosine of the angle of pull, which is given by the formula: \( F\cos(50^{\circ}) \).


• Vertical Component: This part acts perpendicular to the ground and assists or opposes gravity. It's calculated using the sine of the angle: \( F\sin(50^{\circ}) \).

Each of these components plays a crucial role in determining whether the suitcase moves, and how fast it does so.
If the horizontal component equals the frictional force, the suitcase moves at a constant velocity.

Friction is a force that resists motion, and it depends on two main factors: how hard the surfaces are pressed together, and the nature of the surfaces.
The latter is quantified by the coefficient of friction, which is a dimensionless number.
The coefficient of friction \( \mu \) is defined as the ratio of the frictional force \( F_f \) to the normal force \( N \):

• Formula: \( \mu = \frac{F_f}{N} \).

This means if you divide the frictional force by the normal force, you'll get \( \mu \).
In our suitcase example, the frictional force is given as \( 75 \text{ N} \), and after calculating the normal force, \( N \approx 126.2 \text{ N} \).
Using these values, the coefficient of friction is approximately \( 0.595 \).
It means for every unit of force pressing the surfaces together, about 0.595 units of force resist sliding.

The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it.
In this physics scenario, since the suitcase is being pulled at an angle, the normal force doesn't just equal the weight of the suitcase.In fact, the vertical component of the pulling force reduces the normal force, as part of the force counteracts gravity:

• Weight of the Suitcase: The force due to gravity, calculated by mass times gravitational acceleration: \( mg \).
• Reduction by Vertical Component: This force component works against the pull of gravity, making the net gravitational force less: \( F\sin(50^{\circ}) \).
• Resulting Normal Force: Given by the equation: \( N = mg - F\sin(50^{\circ}) \).

So, with our values: \( \approx 215.6 \text{ N} \) gravitational force minus \( 89.4 \text{ N} \) vertical component results in \( N \approx 126.2 \text{ N} \).
The normal force is crucial for calculating other forces such as friction.

Equilibrium occurs in mechanical systems when all the forces balance out such that there is no net force or acceleration.
This is vital in interpreting motion scenarios, as it indicates a constant speed or stationary condition.In this suitcase problem, the student moves it across the floor at constant velocity.
Because there is no acceleration, the forces at play must be in equilibrium:

• Horizontal Equilibrium: The pulling force horizontally \( F\cos(50^{\circ}) \) equals the frictional force. This prevents the suitcase from either speeding up or slowing down as they cancel each other out.
• Vertical Equilibrium: The gravitational force is balanced by the normal force and the vertical component of the pulling force, indicating no vertical movement.

Understanding these equilibrium conditions helps us calculate forces effectively.
They assure us that the calculations of horizontal and vertical components, forces like friction and normal force, are consistent and explain why the suitcase travels at a constant speed.