Shop / engineering: inclined plane (length ÷ height)
Inclinedplane.
A ramp for shop and engineering class. The load stays 10 lb. Change the angle or the length of the slope and read the effort.
Slope lengthHeight Ideal mechanical advantage. The same number is 1 / sin θ. A longer ramp for the same rise needs less push.
Setting the ramp on the bench…
Lesson Shop / engineering: inclined plane (length ÷ height)
Load10 lb
Effort—
Angle—
Slope—
Height—
Run—
Drag to look around the ramp. The arrow along the slope is the effort. The arrow straight down is the 10 lb load.
Change the ramp.
The load stays 10 lb. Move the angle or the slope length beside the ramp. Ideal mechanical advantage is slope length divided by height. The angle stays between 8° and 60°.
What a ramp is for
Less force, longer push
Ideal mechanical advantage is the length of the slope divided by the height. The same number is 1 / sin θ. Use the slope, not the flat run.
A gentler ramp needs less effort and a longer push. A steeper ramp needs more effort over a shorter slope.
You push 2.50 lb along 8.00 ft. The load rises 2.00 ft. Ideal work matches either way: 20.0 ft·lb.
Set the height to 2 ft and the angle to 30°. Predict the effort before you look: half of 10 lb, because sin 30° is 1/2. Then stretch the slope to 8 ft and leave the height at 2 ft. The advantage should read 4.00 and the effort 2.50 lb. Stretch it again to 12 ft: 12 ÷ 2 = 6, so the effort falls to 1.67 lb.
Lengthover height.
Use this page next to a board, a stack of blocks, and a 10 lb weight. The classroom use is ideal mechanical advantage: slope length divided by height.
06.1
Learning objectives
- Compute ideal mechanical advantage as slope length ÷ height.
- Compute the same advantage as 1 / sin θ.
- Find the effort for a 10 lb load: effort = load ÷ advantage.
- State the tradeoff: less effort means a longer push along the slope.
06.2
Classroom loop
- Cover the readout. Height 2 ft, slope 4 ft. Students compute 4 ÷ 2 and the effort for 10 lb.
- Uncover 2.00 : 1 and 5.00 lb. Check that the angle is 30° and that sin 30° is 1/2.
- Lengthen the slope to 8 ft and keep the height at 2 ft. Students predict 4.00 and 2.50 lb.
- Raise the angle toward 60°. The effort climbs toward the load. A steep ramp barely helps.
06.3
Shop examples
A loading ramp, a wheelchair ramp, a switchback trail, a screw (an inclined plane wrapped around a cylinder). This model leaves out friction. On a real ramp you also push against friction, so the effort is higher than the ideal.