Tutoring physics, gravity is perennial. The tutor explains the dilution of gravity that occurs on a slope.

Everyone knows that a ball rolls more slowly down a slope than if it falls straight down. The gentler the slope, the more slowly the ball rolls.

Yet, a physicist would never be comfortable with just that knowledge. “How fast does it accelerate at a given steepness?” the physicist would ask. They always need a number.

Well, in this case, coming up with the number is relatively easy. First of all, we need to agree that the straight-down acceleration due to gravity on Earth, called g, has the following value:

g=-9.8m/s²

where the negative sign just means “down” (positive means up).

Now, let’s examine this slope:

The acceleration due to gravity, down this slope, will be

a=g(h/L) = -9.8*(h/L)m/s²

Example 1: Imagine a slope 7m long that rises 3m. What is the acceleration due to gravity down this slope?

Solution: First, we draw a diagram, as below:

Now we invoke the dilution formula:

a=g(h/L)=-9.8*3/7=-4.2m/s²

Of course, the dilution formula doesn’t consider friction; the actual acceleration will be slower with the effect of friction.

Hope this helps:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.