Enter the mass, the angle, and the coefficient of friction into the calculator to determine the Incline Plane Acceleration. 

Incline Plane Acceleration Formula

The following equation is used to calculate the Incline Plane Acceleration.

A = (m*g*sin(a) - m*g*cos(a)*CF) / m
  • Where A is the Incline Plane Acceleration (m/s^2)
  • m is the mass (kg)
  • a is the angle (degrees)
  • CF is the coefficient of friction (none)

What are the units for Incline Plane Acceleration?

The most common units for Incline Plane Acceleration are m/s^2.

How to Calculate Incline Plane Acceleration?

Example Problem:

The following example problem outlines the steps and information required to calculate the Incline Plane Acceleration.

First, determine the mass. In this example, the mass is measured to be 50 (kg).

Next, determine the angle. For this problem, the angle is calculated to be 45 (degrees).

Next, determine the coefficient of friction. In this case, the coefficient of friction is found to be .75 (none).

Finally, calculate the Incline Plane Acceleration using the formula above: 

A = (m*g*sin(a) – m*g*cos(a)*CF) / m

Inserting the values from above and solving the equation gives us: 

A = (50*9.81*sin(45deg) – 50*9.81*cos(45deg)*.75) / 50 = 1.734 (m/s^2)


What factors affect the Incline Plane Acceleration?

The Incline Plane Acceleration is affected by several factors including the mass of the object, the angle of the incline, and the coefficient of friction between the object and the surface. Changes in any of these variables can significantly alter the acceleration of the object.

How does the angle of incline impact the acceleration?

The angle of the incline plays a crucial role in determining the acceleration. A steeper angle increases the component of gravitational force acting down the slope, thus increasing the acceleration, assuming all other factors remain constant. Conversely, a shallower angle reduces this component, leading to a decrease in acceleration.

Can the Incline Plane Acceleration be negative?

Incline Plane Acceleration can be negative if the force of friction opposing the motion down the slope is greater than the component of gravitational force driving the motion. This scenario typically occurs when the coefficient of friction is high and/or the angle of incline is shallow. A negative acceleration indicates that the object is decelerating or accelerating in the opposite direction of the initial motion.