AP Physics 1 inclined planes with friction cheat sheet

What is the force of friction?

Frictional force opposes motion. It is calculated as: $\displaystyle F_f = \mu F_n$, where $\displaystyle \mu$ is the coefficient of friction, $\displaystyle F_n$ is the normal force.

True or False: Inclined planes reduce the weight of an object.

False - Inclined planes do not reduce weight; they change the direction of the force.

What affects the normal force on an inclined plane?

Normal force $\displaystyle F_n = mg \cos \theta$, where $\displaystyle m$ is mass, $\displaystyle g$ is gravity, $\displaystyle \theta$ is the incline angle.

Fill in the blank: The angle of inclination, $\displaystyle \theta$, affects ____.

the component of gravitational force acting parallel and perpendicular to the incline.

How to calculate net force on an inclined plane with friction?

$\displaystyle F_{net} = mg \sin \theta - F_f$, where $\displaystyle F_f = \mu F_n$.

Difference between static and kinetic friction.

Static friction ($\displaystyle \mu_s$) prevents motion, while kinetic friction ($\displaystyle \mu_k$) acts when two surfaces slide past each other.

What is the formula for gravitational force on an incline?

$\displaystyle F_g = mg$, where $\displaystyle m$ is mass, $\displaystyle g$ is acceleration due to gravity (9.8 m/s²).

True or False: Friction is independent of surface area.

True - Friction depends on the materials and normal force, not surface area.

Calculate $\displaystyle F_f$ if $\displaystyle \mu = 0.3$ and $\displaystyle F_n = 50N$.

$\displaystyle F_f = \mu F_n = 0.3 \times 50N = 15N$.

How does increasing the incline angle affect friction?

As angle increases, $\displaystyle F_n$ decreases, reducing friction, but $\displaystyle F_g$ parallel increases.

What is the maximum angle of incline for static equilibrium?

$\displaystyle \tan \theta_{max} = \mu_s$, thus $\displaystyle \theta_{max} = \tan^{-1}(\mu_s)$.

Cause → Effect: Increase in mass on an incline.

Increases gravitational force and normal force, increasing frictional force.

What happens when an object slides down an incline?

It accelerates due to net force: $\displaystyle F_{net} = mg \sin \theta - F_f$.

Determine $\displaystyle F_f$ if $\displaystyle \mu_k = 0.2$ and $\displaystyle F_n = 30N$.

$\displaystyle F_f = \mu_k F_n = 0.2 \times 30N = 6N.$

Frictional Force Equation

$\displaystyle f_f = \beta N$, where $\displaystyle \beta$ is the coefficient of friction, $\displaystyle N$ is the normal force.

Incline Angle Impact

As incline angle increases, normal force decreases, leading to increased acceleration.

True or False: Friction always opposes motion.

True - Friction acts opposite to the direction of motion.

Components of Weight on Incline

Weight components: $\displaystyle W_ ext{parallel} = mg imes ext{sin}( heta)$, $\displaystyle W_ ext{perpendicular} = mg imes ext{cos}( heta)$.

Calculate Normal Force

For a block on a 30° incline: $\displaystyle N = mg imes ext{cos}(30°)$. Use $\displaystyle g = 9.8 ext{ m/s}^2$.

Static vs. Kinetic Friction

Static: prevents motion. Kinetic: acts during motion. $\displaystyle \beta_s > \beta_k$ usually.

Force of Gravity on Incline

$\displaystyle F_g = mg$ acts downwards, split into parallel and perpendicular components.

Find Acceleration on Incline

$\displaystyle a = g ( ext{sin}( heta) - \beta imes ext{cos}( heta))$.

Incline With Friction Example

Mass = 5 kg, $\displaystyle heta = 30°$, $\displaystyle \beta = 0.2$. Calculate acceleration.

Coefficient of Friction Definition

Ratio of frictional force to normal force. $\displaystyle \beta = f_f/N$.

Incline Effect on Friction

Higher incline angles reduce normal force and thus frictional force.

Work Done Against Friction

$\displaystyle W = f_f imes d$, where $\displaystyle d$ is the distance moved along the incline.

True or False: Normal force is equal to weight on a flat surface.

True - on flat surfaces, $\displaystyle N = mg$.

Work-Energy Principle on an Incline

Total work done equals change in kinetic energy: $\displaystyle W = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$.