>have zero understanding of Newtonian mechanics, kinematics etc.
If I shoot an arrow horizontally, is it "easier" than shooting it straight up? My brain says there's extra shit hindering its flight when you shoot it straight up.
Also how do I calculate initial velocity needed if I want to shoot an arrow to some place (x,y).
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What do you mean by "easier"? The factors influencing the arrow's motion should be its speed and acceleration, gravity, air friction and wind
Also, the required speed to make it reach a certain place also depends on the angle formed by the direction with the ground and the initial height
if the potential energy of the bow with the string pulled back is constant it's equally difficult to shoot in any direction
Shooting it horizontally will cause it to move away from you faster, but it will start to fall downwards the moment it is fired because the vertical component of the velocity is zero at that moment and gravity causes it to accelerate downwards
>depends on the angle formed by the direction with the ground and the initial height
Well this is exactly why I said it's easier to make it go far if you shoot it horizontally.
I don't understand why but the steeper the angle, the less far it will go
Shooting an arrow up means that you fight gravity and air residence. Shooting it horizontal is air residence and a small fraction of gravity (not as much)
Isn't gravity always the same? But when you shoot an arrow horizontally it just meets the ground faster and stops flying.
Your arrow always flies the same distance in the direction it's shot. This is my theory.
That's because the angle influences the projection of both speed and acceleration along both the axis. In the 2-dimensional example in pic, we can split the vector v along the x and y axis. From trigonometry theorems, we know that the projection vector along x is v*cos(b) in modulus and is parallel to the x axis. Similarly, the projection vector along y is v*sin(b) in modulus and parallel to the y axis. From this we get that, the bigger the angle b is, the smaller the modulus of the projection on x is, while the opposite happens for the other projection
>and a small fraction of gravity (not as much)
What are you talking about? Gravity affects in the same way regardless of direction
The distance a projectile will reach depends on its initial velocity and the angle its being shot from. An angle of 45 degrees, which is halfway between horizontal and vertical, wil reach the farthest with the least effort. Look up projectile angles to see what I'm talking about
Let's make this a thread for asking babby physics things you never understood.
First, why do things fall at the same speed even if the other one was twice as heavy?
Makes no sense.
If I understand this correctly, being heavy truly gives it a greater gravitational force, but it's mass is bigger and takes away the force's effectivity. For a lighter object it can change its speed much faster because it has less mass, but consequently the gravitational force pulling it down is smaller. The ratio of F/m is always the same, so everything falls down equally fast, if air resistance isn't taken into account.
>The distance a projectile will reach depends on its initial velocity and the angle its being shot from
If I know the distance and the angle, how do I get the initial velocity?
Using derivatives, not a formula straight from Wikipedia.
To be honest I'm not really sure how to do it with calculus, I'm just remembering what I saw in hs a while back. But you could do it like in pic related, provided you know the angle, distance and also the time it took for the arrow to fall. Vx is horizontal velocity, which is constant since gravity only affects the vertical component.
>What are you talking about? Gravity affects in the same way regardless of direction
Okay, I get this, but why is walking uphill more tiresome than walking on flat terrain? Is it just because you have to lift your muscles further upwards than on flat terrain, because of the upwards incline, so you spend more time and therefore energy lifting yourself?
Another physics question..
Imagine a carriage being pulled by a horse. The carriage exerts a force to the horse, but according to Newton the horse exerts a force of the same magnitude but opposite direction to the carriage. The forces cancel each other out.
How the fuck does anything ever move?
Or does the answer lie in friction of the ground?
It's because to just walk normally the force you exert on the ground must barely surpass gravity to lift you to your next step. Going up a hill, you have to raise your whole body way more than before, which means you exert a lot more force and surpass gravity by a lot more, proportional to your mass, according to newton's second law, force = mass x acceleration. This is also why fatter people have a harder time going up stairs and other places, they need to use more force to achieve the same acceleration (which gets you up) than skinny people.
Wait, what? Haven't you literally put the cart before the horse? The horse should exert a force to the carriage because it's pulling it, and the carriage exerts one back. I'm not a physics master, but I think the thing here is that the force that the carriage exerts on the horse in equal magnitude is no match for the strength of the horse. Like, the forces are the same, but the horse is not affected by it as much as the carriage would be. Like if you tried to push a pebble and a boulder with the same strength.
Definitely because of the friction of the ground. The forces exerted between the horse and the carriage are internal forces that manage to balance each other to a certain extent, but the reason of the movement is the force exerted by the horse's legs on the ground. Without friction, the horse would have no way to move the carriage
The forces don't cancel out because they're not acting on the same body. You're right, for every force there is an equal, opposite one. The thing is, the force used by the horse to move forward is the force he uses to push the ground, and therefore the equal, opposite force happens on the ground, not the carriage. So the carriage is pulled along by the horse without any pushback, besides friction. I like these questions, it's nice to be able to answer some simple stuff like this
This is wrong, the opposite of what would happen if for example the horse and the carriage collided, considering force=mass x acceleration. The lighter object would move a lot more given the same force. That's why, for example, when a truck crashes into a motorcycle, the truck barely moves while the bike goes flying, because it weighs a lot less.
But, like, isn't that what I said? That the horse isn't affected as much by the same force.
Yeah, but that would be if they collided or actually exerted the same force on each other. The way the horse, or anything really, walks is by pushing the ground and getting the same force pushing you back. So the carriage doesn't actually push the horse in any direction, its just also pushed forward by the ground. Sorry if I seemed rude btw
Oh, sorry. No, you're not being rude, you're being quite polite actually. And yeah, I understand that that's how horses and other things walk; that's the interaction between the horse and the ground, though, right? I'm talking about the interaction between the horse and the cart, because if the horse is pulling the cart, the cart must be pushing the horse, right? And then what I said about exerting forces on each other would make sense. I'm not a physics expert or anything, but that's what my thoughts were.
Yeah, you're pretty much right. As a lot of things in physics it depends on the reference point, so to the carriage there is only the traction, and to the horse there is the force he uses to move and the traction pulling him back. I was only thinking from an outsider's point of view, which would be that it's basically a big horse (with their combined mass) being moved by just the force F. The thing to note is that the traction T is weaker than F, otherwise the system wouldn't move. That's what tripped me up a bit, I thought you meant they had the same value but the horse would still be able to move due to its weight, which would be impossible since the T and F affecting the horse would cancel out if they had the same value. Open to more discussion if my explanation is weird or something
No, I think that makes sense, thank you. I'm not the guy who originally asked the question, but it helps to get a little more insight into how this whole thing works, so thanks.
here I'm showing that you can use the kinematic equation to solve for initial velocity given distance (x_f) and angle (theta). I believe the kinematic equation is derived from the kinetic energy equation using calculus. I could do that if you're really interested, but you could probably google it and find a neater explanation. here's a video about it: youtube.com
Why does physics seem harder than math even?
Math is supposed to be the most abstract and hardest subject but it's clearer and more straight forward than physics.
Like, I'm doing university math and I still can't wrap my head around shit like a horse pulling a weight
took a shot at this because I also enjoy these kinds of questions. in pic related all the paired red arrows are of equal force. notice that the harder the horse pushes the ground, the harder it will push the horse--and it is pushing the horse up and to the right. (the Earth is also pushed down and to the left, infinitesimally). the rightward force from the horse pushing the ground is what moves the horse+carriage.
>why do things fall at the same speed even if the other one was twice as heavy?
your explanation is basically correct.
the force of gravity is proportional to the mass of the object (F = m * GM/R^2), and acceleration is inversely proportional to the mass of the object (a = F/m). so you need more force to move a more massive object, but gravity also exerts a larger force on the object. they cancel perfectly.
when you move uphill, some of your kinetic energy is transformed into potential energy, instead of being used to move you forward. basically, moving uphill opposes gravity and moving downhill is aided by gravity.
physical systems are large, complex, and confusing. theoretical math is usually working with basic ingredients.
I'm trying to understand kinematics through calculus.
Did I do this right? I have no idea. I was just guessing that the constant that appears in stead of 0 should be initial velocity but I don't know why.
your intuition was correct. when you integrate the acceleration equation, you get a constant C, which is also a vector. because we know that at time=0 the velocity is equal to the initial velocity, we can solve for C to find that it indeed equals the initial velocity.
your equation for V is missing the y-component of the initial velocity, but is otherwise correct. hopefully this will make the next step of the integration make more sense as well. (hint: there's another +C vector that you can solve using X(0) = X_i).
Thank you vector man. I started reading a book "Matter and Interactions" to make sense of physics.
The directions on the wheel are the opposite of what they should be. Since the carriage is moving forward, the wheel that we see from that pic should move clockwise and the ground friction should oppose the rotation. The rest seems right.
Incorrect, an angle of close to 45 degrees is optimal for distance.
if you're implying that the rolling resistance will actually make the cart go faster, then you're wrong
Here's a brain teaser for you OP, how do you construct a triangle of which the inside angles add up to more than 180 degrees? (It also has to do with gravity)
On a second thought, you're right. The horse pulling is applying a force, not a momentum on the wheel, so yeah the directions in the pic were right. Sorry about that. Studying the whole theory covered by the upcoming exam in a week has fried my brain.
I should have put the arrows at the axle, really
Write vectors using round brackets, < , > denotes an inner product which is a completely different thing.
I used to denote vectors all through engineering school along with i,j,k. might be dependent on the discipline, or the area of the world.