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### Course: High school physics - NGSS>Unit 1

Lesson 1: Force, mass, and acceleration

# More on Newton's second law

Newton's second law can be used to solve two-dimensional motion problems. If any force vectors are acting at an angle, they can be broken into their horizontal and vertical components using trigonometry. Then, the net force in each dimension and the object's mass are entered into Newton's second law (F=ma) to determine the resulting acceleration in each dimension. Created by David SantoPietro.

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• Do all these forces happen at the same time any any given moment?

Also, do the same principles of acceleration apply here? For example, if the meteorite was going in the forward direction (positive) and the overall acceleration turned out to be negative, would this then become negative acceleration (i.e. slowing down)?

Thanks in advance for any help given! :)
• Suppose there is a meteor traveling with a constant velocity of 1000 km/h and there is no force acted on it. As it enters the gravity field of Earth, earth will start pulling the meteor with a constant force of 100 N resulting in 10 km/h^2 constant acceleration. Now there is only one force acted on meteor.

When meteor's velocity reaches 1500 km/h, we send a rocket to save the earth. The rocket starts pulling the meteor in the opposite direction with 50 N. Now there is two forces acting on meteor at the same time. The net force on meteor is 100-50=50 N towards the earth and it still accelerates but now its acceleration decreases to 5 km/h^2.

When meteor's velocity reaches 1750, we send a second rocket pulling the meteor with the same 50 N. Now net force on meteor is 100-50*2= 0 N. Since net force is 0, meteor stops accelerating but it continues with a constant velocity of 1750 towards earth.

Now we have to send a third rocket. Net force on the meteor becomes 100 - 3*50= - 50 in the opposite direction from earth, and the meteor; first starts to slow down from 1750, then stop completely, and eventually start moving in the opposite direction.
From first rocket onwards there are allways 2 or more forces acted on the meteor. Even when the meteor moves away from earth after third rocket, the force of earth's gravity continues to act on it.
• READ BEFORE CONTINUING: I think i solved this but I thought I'd share it cause if i had to go through the trouble of going through this you should too. plus it's probably wrong so check it out if you want to

I have a question, when I find the acceleration for the forces at , Do I use the acceleration I get for x and y forces in the pythagoras theorem? Or do I use the total net of the x and y forces for the pythagorean theorem?

Heres my work if it sounds confusing:

Horizontal forces:
1) +50N - 30N + 25N - 40N = +5N
2) +5N / 10kg = 0.5 m/s^2 (force/mass = acceleration)
3) acceleration of horizontal forces: 0.5 m/s^2

Vertical forces:
1) +48N - 28N = +20N
2) +20N / 10kg = 2 m/s^2 (F/m = a)
3) acceleration of vertical forces: 2 m/s^2

So do I now use the acceleration of the vertical and horizontal forces in the pythagorean theorem, like this?

a^2 + b^2 = c^2
0.5^2 + 2^2 = c^2
and then this would be my total acceleration?

OR

Do I use the total net force of the horizontal and vertical forces in the pythagorean theorem:

Horizontal force total: +5N
vertical force total: +20N

a^2 + b^2 = c^2
+5N^2 + 20N^2 = c^2

Cause if I use the total acceleration of the horizontal and vertical forces in the pythagorean theorem, how do I find the one total net force of the asteroid?

SOLVED: I realised that either method of first figuring out the total acceleration, or figuring out the total net force, would both result in the same answer. For some reason I never got far enough to realise in the end, as long as I have two of three factors in "F = m * a" I'll always find the third factor.

The total net force would be the square root of 425, or sqrt425. To make sure the answers were the same to that solving the total net force w/ acceleration first, I first figured out what the square root of 425.

(sqrt will mean square root here)

sqrt425 = 20.61552813
Then, you divide by the mass to find acceleration.
sqrt425/10kg = 10kg/10kg * acceleration
this leaves us with 2.061552813 = acceleration

2.061552813 is an important number because if we now solve this problem using the total acceleration first

(meaning we now find "F" or force instead of finding "a" or acceleration like we just did previously),

we'll see that at the end of our pythagorean theorem process of finding the total acceleration (which looks like this: 0.5^2 + 2^2 = sqrt4.25) will get us the square root of 4.25, which is also equal to 2.061552813. And the square root of 4.25 when multiplied by the mass, 10kg, will also equal the square root of 425 (sqrt425 = 20.61552813)

Here's what I mean if I didn't express my thoughts properly:

TOTAL NET FORCE: sqrt425
sqrt425 = 20.61552813
TOTAL acceleration: sqrt4.25
sqrt4.25 = 2.061552813

NET FORCE TO acceleration:
sqrt425/10kg = 2.061552813 (which is also sqrt4.25)

acceleration TO NET FORCE:
sqrt4.25 * 10kg = 20.61552813 (which is also sqrt425)

So the point of me showing this is that my thoughts are that if the answers I get are identical to each other and identical to the answers I get from the pythagorean theorem process to find either total net force or total acceleration, then that means these must be the right calculations for acceleration and net force in the end. It's like checking to see if your answer is right by solving it the other way around. is this right
• Great work solving problem this by yourself! You are correct that both methods yield the same solution—they are in fact the same solution! Have you learned about vector notation yet? If so, I recommend you trying to work through the example symbolicly with vector operations :)
• When a body is floating on water, what are the net forces acting on it?
• While a body is in water or in any other fluid(regardless of whether it is floating or sinking), 2 forces act on the body, First is it's weight acting downwards, and second is the upward force exerted by water or fluid on the body in the upward direction, this force is known as upthrust. Now, for a body to float, the upthrust must be equal to the weight of the body. Hence, the net force would be zero.

• What is Newton's second law
• It is a statement of this equation: F = ma
• When a body is floating on water, what are the net forces acting on it?
• When a body is floating in water, it is not acceleration vertically (Lets assume that it floats and is still). The force of the weight pulls it down and force of buoyancy pushes upwards with an equal magnitude.
• What is pythagoreas theoreom?
• In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":

a^2 + b^2 = c^2 ,
where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.

Although it is often argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras (c. 570 – c. 495 BC) as it is he who, by tradition, is credited with its first recorded proof. There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework. Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.

The theorem has been given numerous proofs – possibly the most for any mathematical theorem. They are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed, to objects that are not triangles at all, but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps and cartoons abound.
• How we know the angle if we're only know the magnitude for horizontal and vertical direction?
• angle = arctangent(magnitude of vertical force/magnitude of horizontal force)

Note: You may have to change the sign and/or add Pi radians (180 degrees) to get the correct angle depending on the signs of the force vectors. If the vertical force is negative, multiply the angle by -1. If the horizontal force is negative, multiply the angle by -1 and add Pi radians.
• My textbook states that Newton’s II law as “ The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.” Here it is different. So which one is correct?
• Both are correct, here is how it works:

F = ma
F = m( delta v/delta t) (acceleration is velocity divided by time)
F = (delta p)/(delta t) (mass times velocity is momentum, which is denoted by p).

F = ma and F = (delta p)/(delta t) are two different ways of stating the exact same thing. Hope this helps!
• Sin30x45N gives me a negative answer but the force is horizontal, up and positive. What do I do in this case? Thanks in advance.
• What are you getting for sin(30)? Are you getting -0.9880? If so then you are calculating the sine of 30 radians not 30 degrees. The sine of 30 degrees is 0.5.
• When calculating the net force, why are things like normal force and weight included?
• The net force is equal to the vector sum of ALL the forces acting on an object.