Find the speed of the biker at the bottom of the hill

[paulimerci]

I get it now. Yes, I see that a single problem can be approached in many different ways and ultimately give the same result. I can now understand more clearly. Was my approach to post #32 right?

 

[PeroK]

I get it now. Yes, I see that a single problem can be approached in many different ways and ultimately give the same result. I can now understand more clearly. Was my approach to post #32 right?

It looks right, but a bit overcomplicated IMO. One good thing about a free-body diagram is that you can label the forces with an arrow showing the direction of each force. This allows you to jump in with the algebra already simplified somewhat. If $f$ is the friction force acting up the slope and $l$ is the length of the slope, then you can simply write$$F_{net} = mg \sin \theta - f$$or$$W_{net} = (mg \sin \theta - f)l$$You don't have to invoke angles of $\phi =0$ and $\phi = \pi$ etc.

There's something to be said for keeping things simply initially until you develop some intuition for these problems.

 

[paulimerci]

It looks right, but a bit overcomplicated IMO. One good thing about a free-body diagram is that you can label the forces with an arrow showing the direction of each force. This allows you to jump in with the algebra already simplified somewhat. If $f$ is the friction force acting up the slope and $l$ is the length of the slope, then you can simply write$$F_{net} = mg \sin \theta - f$$or$$W_{net} = (mg \sin \theta - f)l$$You don't have to invoke angles of $\phi =0$ and $\phi = \pi$ etc.

There's something to be said for keeping things simply initially until you develop some intuition for these problems.

Thank you; your approach looks simple and easy to understand.

 

[paulimerci]

I appreciate @kuruman @PeroK @erobz @jbriggs444 taking the time to thoroughly explain this idea. I'm incredibly grateful for that.