11/15/2023 0 Comments 2nd law of motion![]() You can verify it by taking the second derivative of this equation and working to get step 7. There is even an equation that says Force mass x acceleration or Fma. The second law states that the greater the mass of an object, the more force it will take to accelerate the object. θ(t) = θ maxcos (t (L/g) 2): The equation of motion has this solution. Gravity pulls the ball down to the ground and the air resistance slows it down. d 2θ/dt 2 + (g/L)θ = 0: You can approximate sin(θ) as θ for the purposes of a simple pendulum at very small angles of oscillation. d 2θ/dt 2 + (g/L)sinθ = 0: You can obtain this from rearranging both sides of the equation. -Mg sin(θ)L = -ML 2 d 2θ/dt: Account for the angular acceleration by substituting the second derivative of the angle with respect to time for α. This step requires calculus and differential equations. -Mg sin(θ)L = ML 2 α: You substitute the equation for moment of inertia of a rotating body using string length L as radius. -Mg sin(θ)L = I α: You can obtain the direction for the vertical force due to gravity ( -Mg) by calculating the acceleration as sin(θ)L if sin(θ) = d/L for some horizontal displacement d and angle θ to account for the direction. Ma = I α: This lets you set the force of gravitational acceleration ( -Mg sin(θ)L) equal to the force of the rotation. ΣF = Ma : Newton's second law states that the net force ΣF on an object is equal to the object's mass multiplied by acceleration.This also means that the harder you kick a ball the farther it will go. And that's one of the reasons rockets do accelerate in space because they're losing mass that loss of mass conversely increases their acceleration okay? So this is a good practice problem that kind of demonstrates Newton's second law of motion. Second Law of Motion The second law states that the greater the mass of an object, the more force it will take to accelerate the object. So 6 times 40 meters per second is 240 meters per second squared which is the acceleration at that point and time. Well if I say this increase is by 3 and this decrease is by one half then our acceleration must increase by 6 times. Well if we say that force is mass times acceleration and we say that the force the thrust is tripled during this time but the mass is decreased by one half then what happens to the acceleration okay, so we're going to say x is the change in acceleration okay. The fuel is actually becoming a thrust that's causing it to accelerate so at point where it burns up half its mass due to fuel loss and the thrust is tripled what is the acceleration going to be at that point okay? Let's say we have a rocket in space so there's no air resistance or anything, it's accelerating at 40 meters per second but while it's accelerating it's losing mass because it's burning fuel. ![]() So let's do a practice problem that you might see which is a good application of Newton's second law of motion okay. ![]() ![]() Okay, so it makes sense and we can show this relationship by Newton's formula over here, force equals mass times acceleration okay. The third is this acceleration is inversely proportional to the mass of the object so if I'm pushing an empty shopping cart I'm going to be able to get it to go a lot faster than if I'm pushing a shopping cart that's full of groceries. The first one is that a force on an object will cause that other to accelerate, the second is this acceleration is directly proportional to the force so the harder I push, the harder it accelerates okay. There's 3 components to Newton's second law. Law of force and acceleration this is also known as Newton's second law of motion. ![]()
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