Suggestion for teaching force components on ramps

[ScienceNostalgia101]

Wasn't sure whether this was better for science education or here, but when in doubt, I go with "here."

 

When I was a physics student, I always found it confusing that on ramps, the usual force components (cosine of angle off the ground for horizontal, sine of angle off the ground for vertical) were flipped for ramps. I get the reasoning for it, and I'm sure there are a bunch of mnemonics various teachers use for it, but I found that after I was no longer a physics student, and before I became a physics teacher, I spent so much time playing with programs like Paint Shop Pro that I found an even better way to remember it.

 

First, you draw the ramp with the components into and along the ramp drawn...

...then, you rotate the image until the ramp looks like it's flat and gravity is at an angle...

...and that way, you know that whatever angle the ramp makes with the ground is the angle the force "into" the ramp makes with gravity, making the other angle the difference between that angle and 90.

 

What do you think? Would this be a good way to simplify it for high school and/or introductory college physics students? (I know at later physics courses it gets more complicated and requires a more sophisticated understanding of geometry, but at earlier levels, I would think this kind of reasoning would be better than nothing.)

Edited March 30, 2021 by ScienceNostalgia101

[ScienceNostalgia101]

For the record, I'm fully aware that ideally vectors should be scaled and these vectors are obviously not. This was just meant to illustrate the point from an angle perspective, not a scaled magnitude one in and of itself.

[Country Boy]

Wouldn't it be simpler just to tilt your head?

Edited April 25, 2021 by Country Boy

[swansont]

2 hours ago, Country Boy said:

Wouldn't it be simpler just to tilt your head?

How would that help you remember which angle is which?

[Bufofrog]

On 3/30/2021 at 4:33 PM, ScienceNostalgia101 said:

What do you think?

I think everyone has there own way of thinking about and remembering things.

I use to remember trig by just knowing sine.  Sine A = opp/hyp, the other one is the other hyp. one and the weird one doesn't have a hyp. in it but it is kinda like sine. 

Not really useful to anyone but me and why that sticks in my mind, I don't know....

[exchemist]

On 3/30/2021 at 9:33 PM, ScienceNostalgia101 said:

Wasn't sure whether this was better for science education or here, but when in doubt, I go with "here."

 

When I was a physics student, I always found it confusing that on ramps, the usual force components (cosine of angle off the ground for horizontal, sine of angle off the ground for vertical) were flipped for ramps. I get the reasoning for it, and I'm sure there are a bunch of mnemonics various teachers use for it, but I found that after I was no longer a physics student, and before I became a physics teacher, I spent so much time playing with programs like Paint Shop Pro that I found an even better way to remember it.

 

First, you draw the ramp with the components into and along the ramp drawn...

...then, you rotate the image until the ramp looks like it's flat and gravity is at an angle...

...and that way, you know that whatever angle the ramp makes with the ground is the angle the force "into" the ramp makes with gravity, making the other angle the difference between that angle and 90.

 

What do you think? Would this be a good way to simplify it for high school and/or introductory college physics students? (I know at later physics courses it gets more complicated and requires a more sophisticated understanding of geometry, but at earlier levels, I would think this kind of reasoning would be better than nothing.)

I don't find this especially simple to grasp, actually. Though maybe it is if you stand in front of a class explaining it as you go. 

What I always used to do is consider what would happen if the angle went to zero. The Cos component is the one that goes to full value and the Sin component is the one that goes to zero.  

[studiot]

On 3/30/2021 at 9:33 PM, ScienceNostalgia101 said:

Wasn't sure whether this was better for science education or here, but when in doubt, I go with "here."

 

When I was a physics student, I always found it confusing that on ramps, the usual force components (cosine of angle off the ground for horizontal, sine of angle off the ground for vertical) were flipped for ramps. I get the reasoning for it, and I'm sure there are a bunch of mnemonics various teachers use for it, but I found that after I was no longer a physics student, and before I became a physics teacher, I spent so much time playing with programs like Paint Shop Pro that I found an even better way to remember it.

 

First, you draw the ramp with the components into and along the ramp drawn...

...then, you rotate the image until the ramp looks like it's flat and gravity is at an angle...

...and that way, you know that whatever angle the ramp makes with the ground is the angle the force "into" the ramp makes with gravity, making the other angle the difference between that angle and 90.

 

What do you think? Would this be a good way to simplify it for high school and/or introductory college physics students? (I know at later physics courses it gets more complicated and requires a more sophisticated understanding of geometry, but at earlier levels, I would think this kind of reasoning would be better than nothing.)

 

 

I do hope that no teacher of Physics, Mechanics or Engineering Science would ever show such a diagram to the class, whatever the angle of the ramp.

Understanding of Forces means understanding where to properly place them on diagrams.