Sure, the technical name used in most textbooks is a Free Body Diagram, although in my circles most people generally just called it a dot model or dot diagram, since free body diagram can be a bit of a mouthful. It’s frequently used to simplify down models of forces. As I mentioned, it’s typically introduced in intro physics courses to help students not get caught up in the weeds of information/details of the system that aren’t as important as you might initially think, but I’ve had professors use them all up through my advanced mechanics/modeling courses, so their usefulness is certainly scaleable, although depending on the complexity of the system it may make more sense to break it into smaller parts. For now I’ll try to stick to as simple a model as I can.
In short, pick any object, stationary or moving - it becomes a dot on your page. Then you start adding in all the different forces acting on that object. For a glass sitting on your table, you’d have one arrow pointing downwards from the dot to represent the force caused by gravity (m*g), and another arrow pointing upwards of the exact length and opposite direction, representing the normal force of the table “pushing” upwards on the glass. Because the forces are equal in opposite directions, the object is stationary, if the forces were unequal, the object would be accelerating (reminder that acceleration is a change in direction OR velocity. If the glass were sliding across the table at a steady rate, it would not be accelerating). For added complexity, you can begin imagining what the system will look like over time.
In your weight lifter scenario, you can consider the forces acting on the weight - force from gravity downwards, and the force from the lifter keeping the weight either stationary or in controlled motion. Again, these forces are in balance and in opposite directions. Throughout the motion of the squat, the magnitude of these forces will change, but there really isn’t much force to speak of acting in any of the other directions. The bar isn’t magnetized to the wall, and you probably don’t have a strong crosswind acting on the weight in any direction, you’re not standing on a slanted floor where your normal force would no longer be directly opposite the direction of gravity, etc. At the end of the day, gravity pulls down, you push up.
Maybe this is example is a bit oversimplified for everything that goes on when riding a horse, but we’ll stick with it for now. The way I would describe it in this scenario is you have the force from gravity acting down on your body, which you (and by proxy, the horse) are counteracting. If your horse is standing still, your dot diagram is the same as your weightlifter squat. At takeoff to a fence however, there is significant acceleration forwards from the horse. In order to stay with the horse, you’ll need to exert an equivalent force in the opposite direction, which in horseback riding comes from your contact. Since we don’t sit in the saddle when we jump, that contact comes through our legs via friction against the saddle and/or the horse’s side. If you don’t have enough friction, you slip backwards. Too much friction and your horse’s eyes might be bugging out of their head lol. At the top of the jump, the model looks more like the weightlifter scenario, and at the end of the jump, there’s what I’ll call a “braking force” from the horse as they land causing acceleration towards the rear. Again, the rider must counteract this largely via frictional forces, otherwise they’ll end up on the horse’s neck. Now, friction isn’t the ONLY way to counteract these forces, but is preferable, as the alternative is allowing your leg to swing so that you can rely on your stirrups to counteract the additional forces.
In short, the difference between a squat in a gym and jumping on a horse is that weightlifting doesn’t require you to squeeze your legs together to generate friction in order to create stability throughout the duration of the movement. Being able to create said friction may require less than perfect position from a weight-lifter’s perspective, but for a rider, it’s necessary to sacrifice some of that efficiency to effectively stay secure in the saddle. As for exactly how much of an angle is necessary, I think we’ve beaten that dead horse long enough to say “it depends”.
Tbh, I don’t even know what a smith machine is.
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