Inclined Plane

The inclined plane is a classic experimental device consisting of a flat surface forming an angle with the horizontal. It allows the study of force decomposition, accelerated motion and friction. This concept is part of the middle and high school curriculum.

Discover FizziQ

How to measure it in class

With the FizziQ app, the accelerometer and the inclinometer allow you to study the inclined plane.

Steps:

Place the smartphone on an inclined board
Measure the angle α with the FizziQ inclinometer
Let the smartphone slide and record the acceleration
Verify that a = g × sin(α) (without friction)
Measure the actual acceleration and deduce the friction coefficient
Repeat for different angles and materials

Scientific activities on this topic

Possible extensions with FizziQ: measurement of the friction coefficient and determination of the critical angle of sliding.

Learn more

Force decomposition:

On an inclined plane at angle α, the weight P = mg decomposes into:

Component parallel to the plane: P_// = mg × sin(α) → causes acceleration
Perpendicular component: P_⊥ = mg × cos(α) → balanced by the normal reaction

Motion without friction:

The acceleration is: a = g × sin(α)

This is uniformly accelerated linear motion with constant acceleration, less than g.

Motion with friction:

The friction force opposes the motion: f = μ × N = μ × mg × cos(α)

The acceleration becomes: a = g × (sin(α) - μ × cos(α))

Critical angle:

For α < arctan(μ), the object remains stationary. For α = arctan(μ), the object is on the verge of sliding.

Formula

Acceleration without friction: a = g × sin(α)

Acceleration with friction (sliding): a = g × (sin(α) - μ × cos(α))

Critical angle of sliding: α_lim = arctan(μ)

Velocity at the bottom of a plane of length L (starting from v₀ = 0): v = √(2 × a × L)

where:

α: angle of the plane with the horizontal
μ: kinetic friction coefficient
g: gravitational acceleration (9.81 m/s²)

Application examples

Galileo used inclined planes to slow down the fall and measure g
Wheelchair access ramps limit the incline to make climbing easier
Ski slopes have inclines from 15° (blue) to 45° (black)
Sloped roofs allow rainwater to drain

FAQ

Q: How to measure μ with FizziQ? A: Gradually incline the plane until sliding occurs. At the critical angle: μ = tan(α_lim). Or measure a on a known slope and calculate μ.

Q: Why did Galileo use inclined planes? A: To “dilute gravity”: the acceleration g×sin(α) is lower than g, which made measurements easier with the clocks of that era.

Q: Does the acceleration depend on mass? A: No (without friction). As with free fall, all objects have the same acceleration g×sin(α) on a given plane.

Q: How to verify the formula a = g×sin(α) with FizziQ? A: Measure the angle α with the inclinometer, calculate g×sin(α), and compare with the acceleration measured by the accelerometer. The difference comes from friction.

Friction Force - Uniformly Accelerated Linear Motion - Linear Acceleration - Inclinometer