If every force has an equally strong opposite force how can anything move?
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If you push on an object you are applying a force to it, but the object is also applying a force to you. What happens next depends on the relative mass of each object.
Force = Mass * acceleration.
For a given force, as mass goes up, acceleration goes down, and as mass goes down, acceleration goes up.
Lets say you try pushing against something incredibly massive, like say the Great Pyramid. Whatever force you are applying, the pyramid is also applying back at you. Its mass is far larger than yours so its acceleration is going to be far smaller, likely so small it gets wiped out by other forces acting on it. Likewise you just kind of stand there because other forces acting on you prevent you from moving (friction of your feet on the ground, air pressure, etc.).
So lets take those forces out of the equation. Lets put you in outer space. Don’t worry you have a suit on. You are deep in space, nowhere near any other stars or planets, or any other object. We can more or less ignore all the forces except the one you apply. Lets say you weigh 100kg. Lets say there is a small asteroid next to you that weighs 100kg. If you push on that asteroid, since your weight is the same, you will accelerate away from the asteroid and it will accelerate away from you at the same rate. Lets make the asteroid much bigger, say 100,000kg. You decide to push on that asteroid with a force of 100 Newtons. F=MA so you will experience an acceleration of 1m/s2 for however long you applied that force to the asteroid. Lets say you pushed for 1 second. You are now moving away from your original position at a rate of 1m per second or 3.6 km an hour. What about the asteroid? Its moving away from you at 1/1000 mps or 0.0036, aka 1000x slower than you are moving.
So how can you move something heavier than yourself, like say pushing a car? The average mid size sedan weighs 1500 kg, 15 times our theoretical person. Shouldn’t that mean we can’t push the car and keep moving forward with it? In space, we couldn’t, but on land we can due to gravity and friction. Friction ALSO applies force and that prevents us from moving backward in these situations, but what about the car? Well wheels help reduce friction. Once we put enough force into it, we overcome the friction force of the wheels and the car starts rolling (assuming we can apply enough force to begin with). The net forces combine, its not just you pushing on the car and the car pushing on you.
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