Physics: Forces and Friction Practice Flashcards

Gravitational Force

Gravitational force, also identified as weight ($F_g$ or $w$), is defined as a force of attraction that the earth exerts on an object. This force is always acting downwards towards the center of the Earth. The magnitude of this force can be related to the net force ($F_{net} = ma$) but specifically refers to the calculation involving mass and the acceleration due to gravity, expressed by the formula $w = mg$.

In these equations, $m$ represents mass, which remains always constant regardless of location. The acceleration due to gravity on Earth is denoted as $g$, which is equal to $9.8\,m/s^2$. Weight is directly proportional to the net force acting upon an object in free-fall scenarios.

Normal Force

The normal force ($F_N$ or $N$) is defined as a contact force exerted by a surface on an object. Alternatively, it is described as the perpendicular force exerted by a surface on an object in contact with it. The term "normal" indicates that the force acts at a $90^{\circ}$ angle relative to the surface.

When an object is placed on a flat, straight-line surface, the normal force is equal in magnitude and opposite in direction to the weight, represented as $N = -mg$. However, when an object is positioned on a slope, the normal force corresponds to the perpendicular component of the gravitational force ($F_{g\perp}$). In such cases, the calculation for the normal force is $N = mg\cos(\theta)$.

Frictional Force

Frictional force is a force that opposes the motion of an object and acts parallel to the surface. There are two distinct types of frictional force. The first is static frictional force ($f_s$), which is a force that opposes the motion of an object at rest. Its maximum value is calculated using the formula $f_{s,max} = \mu_s N$. The second type is kinetic frictional force ($f_k$), which opposes the motion of a moving object and acts parallel to the surface. It is calculated using the formula $f_{fk} = \mu_k N$.

In these formulas, $f_{max}$ refers to the maximum static frictional force, $\mu$ represents the coefficient of friction, and $N$ is the normal force. General principles regarding friction state that the rougher the surface, the higher the frictional force, whereas a smoother surface results in less frictional force. Frictional force is directly proportional to the normal force; thus, a higher normal force results in higher friction. This is evidenced when grinding an object: the harder you press down, the higher the normal force and the higher the resulting frictional force.

Coefficient of Friction

The coefficient of friction ($\mu$) is a ratio between the frictional force and the normal force, derived from the formula $f = \mu N$, which rearranges to $\mu = \frac{f}{N}$. Because it is a ratio of two forces, $\mu$ is dimensionless and does not have units. The value of the coefficient depends entirely on the materials of the two surfaces that are in contact. For example, steel on wet ice has a low coefficient of friction, while rubber on tarmac has a higher coefficient of friction, providing more grip and less sliding. The coefficient only changes if the surfaces themselves are changed; otherwise, it remains the same.

Dynamics of Static and Kinetic Friction

When an object is at rest and no horizontal force is applied, there is no frictional force. When a small amount of force is applied to a static object, it begins to experience static friction. As the applied force increases, the static friction increases until it reaches its maximum value ($f_{s,max}$). Eventually, the applied force overcomes the maximum static frictional force, and the object starts to move. At this point, the resistance transitions to kinetic friction. Kinetic friction remains constant while the object moves at a constant speed and is generally smaller than the maximum static friction, such that $f_k < \mu_s N$, while $f_k = \mu_k N$.

Angle, Normal Force, and Slope Calculations

The steepness of a slope significantly affects the normal force and, consequently, the frictional force. As the angle of the slope increases, the normal force decreases, leading to a decrease in frictional force ($N \propto f$). This relationship is governed by the formula $N = mg \cos(\theta)$.

Consider an example of a $2\,kg$ mass on two different slopes. In the first scenario with a $30^{\circ}$ slope, the normal force is calculated as $N = 2 \times 9.8 \times \cos(30^{\circ})$, which equals $19.6 \times 0.866 = 16.97\,N$. In the second scenario with a steeper $60^{\circ}$ slope, the normal force is $N = 2 \times 9.8 \times \cos(60^{\circ})$, which equals $19.6 \times 0.5 = 9.8\,N$. This demonstrates that the sharper the angle, the lower the normal force and friction.

Summary of Force Dynamics

Increasing the mass of an object will increase the frictional force but will not change the coefficient of friction. The coefficient of friction only changes if the surface materials change. Rougher surfaces result in higher coefficients, while smoother surfaces result in lower coefficients. Additionally, increasing the angle of a slope decreases the normal force and the frictional force.

Applied force is defined as a force that a person or another apparatus exerts on an object. Tension force ($T$ or $F_T$) is the force experienced by a rope, string, or cable, such as when an object is hanging from a ceiling. The rope applies force to the object in a direction that is always along the rope (usually upwards). Tension complies with Newton's Third Law as an action-reation pair.

Using the formula $F_{net} = ma$, tension in a vertical system can be modeled as $T - w = ma$. The greater the applied pulling force, the greater the tension. When an object is at rest, $T = w$, meaning $T = mg$. Tension is directly proportional to mass; more mass results in greater tension. On a slope with an angle (e.g., $30^{\circ}$), forces can be broken into components: the horizontal component is $T \cos(30^{\circ})$ and the vertical component is $T \sin(30^{\circ}) = mg$.