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How to Calculate the Acceleration of an Object on an Inclined Plane

When you were a kid, you probably slid down slides at the school playground. You wouldn't have thought of it then, but the acceleration of gravity determined your acceleration down those slides. The acceleration of gravity varies depending on your distance from the earth, but near the earth's surface it is approximately 9.806 meters per second squared, which is the same as 32.174 feet per second squared. An inclined plane is not much different from a playground slide.

Things You'll Need

Measuring stick
Scientific calculator

Instructions

- 1
  Measure the length of the base of your inclined plane using a measuring stick. The base of the inclined plane is the part of the plane touching the floor. For example, say your inclined plane is 3 meters (9.84 feet) long.
- 2
  Measure the height of your inclined plane at its highest point using a measuring stick. For example, say the highest point is 1.5 meters (4.92 feet) high.
- 3
  Divide the height of your inclined plane by its length, using a scientific calculator. For example, 3/1.5 = 2. The tangent of the angle of your plane is 2.
- 4
  Find the arc tangent of the tangent of your plane using a scientific calculator. The arc tangent button on your scientific calculator will be marked "ARCTAN" or "TAN^-1." For example, using a Texas Instruments TI-83-Plus scientific calculator, press the yellow "2nd" button, then the "TAN^-1" button, enter 2, then press the "ENTER" button. Your screen shows 63.43494882. The angle of the slope of your inclined plane is approximately 63.4 degrees.
- 5
  Find the sine of the angle you have calculated, using a scientific calculator. The sine button on your scientific calculator will be marked "SINE" or "SIN." For example, using the same Texas Instruments calculator, press the "SIN" button, enter 63.43494882, then press the "ENTER" button. Your screen shows 0.894427191. The sine of the angle of the slope of your inclined plane is approximately 0.8944.
- 6
  Multiply the sine of the angle of the slope of your inclined plane by the acceleration of gravity in meters per second squared (m/s^2), which is 9.806 m/s^2 (32.174 feet per second squared). For example, 0.894427191 x 9.806 = 8.770753035. The acceleration of the object on this inclined place is approximately 8.77 meters per second squared (28.77 feet per second squared).

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