Forces on an inclined plane and Tippy the tip truck

Forces on an inclined plane and Tippy the tip truck

How do you figure out the forces is a common question I get when teaching a particular subject. None more so than those on an inclined plane (or slope). Rather than getting onto the whiteboard to explain, from time to time, I bring out Tippy the tip truck.

A few years ago, in the middle of winter, right before teaching a slope lowering course, I had an idea of how to explain the forces on a slope. I walked into a toy store and bought a toy tip truck (Tippy) and then onto a sports store for a fish scale.

It’s a quick and dirty method. With Tippy, we can demonstrate the principle of what’s happening. It’s not going to be super accurate but enough to show what’s going on – a trend. In a classroom setting, it’s interactive, and everyone gets it. 

The testing equipment

  • Something on wheels. I used a toy truck. 
  • iPhone with an App that can measure slope angle – Angle Pro App (iPhone) is free, and you can lay your phone flat on the inclined surface.
  • Some tape to stick your phone to the liftable surface.
  • Some weight (20 carabiners).
  • You need a flat liftable surface, such as a plank of wood (or could be a bench or small table).
  • You also need some cord, an overhead anchor and a progress capture.

The setup

  • I attached the carabiners to the tip truck.
  • Then weighed the truck and carabiners (2.4kg).
  • I rigged up a plank of wood with one end of the cord.
  • I then attached the cord to an overhead anchor and progress capture.
  • Attached Tippy to the fish scales and the cord
  • Stuck the iPhone to the plank
  • Lifted the plank of wood in 15-degree increments and recorded the results (see below)

The results

InclineMeasuredMeasured / 2.4
factor*
Predicted
factor*
Difference
00.00.00.00.0
150.50.20.30.1
301.10.50.50.0
451.60.70.70.0
602.00.80.90.1
752.31.01.00.0
902.41.01.00.0

* Definition of factor (and examples)

The factor, defined as ‘numbers we can multiply together to get another number’.

In the results above, the factor is a decimal representation of the % of the force on the system. For example, a factor of .5 means 50% of the force applied to the rope system and anchors.

Why don’t we use % – wouldn’t that be easier? If all the loads were 1kN, then that would be, but they may not be. The second number we need to multiply could be 2, 3, or 4kN.

A rescue example is:

  • If we have 4 people on a stretcher, i.e., 3 people and a patient with a mass of 400kg applying around 4kN of force,
  • on a 30-degree slope with a factor of 0.5,
  • 4kN x 0.5 = 2kN (on the ropes and anchors).

An abseiling/rappelling example is:

  • if we have a person with a mass of 100kg abseiling/rappelling applying around 1kN of force,
  • on a 45-degree slope with a factor of 0.7,
  • 1kN x 0.7 = .7kN (on the ropes and anchors).

Conclusions

  • With simple tools, you can show what’s happening with forces without having to go into any math equations.
  • Accuracy to one decimal place is enough to show a trend.
  • For an inclined plane (slope), as the angle increases the amount of force on the system (ropes and anchors) becomes greater.

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