Hippocampus Physics: Forces in Balance

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In the examples we saw before, a man was pushing a crate. His push applied a force on the crate, which started the crate in motion. When we push against a heavy object, it often feels like that object is pushing back and resisting our effort. This is, in essence, Newton's Third Law. In other words, if you push against a crate with a force of 100 Newtons, the crate pushes back with an equal and opposite force of 100 Newtons. Remember the jet taking off? We asked which of Newton's laws can explain the motion of the jet. The answer is that all of Newton's laws come into play. First the jet is not moving and will not move until a force acts on it. This is Newton's First Law. Then the thrust of the jet engine starts exerting a force. By Newton's Third Law, for every force there is an equal and opposite force, and thus the jet feels this reaction causing it to move forward. The jet then accelerates due to this force according to Newton's second law that states force is equal to mass times acceleration. Then the pilot flies off into the wild blue yonder! Before applying Newton's Laws to problem solving, we need to define several forces that we experience in our everyday lives. The first of these forces is the force of gravity. When the famous apple hit Newton on the head, he realized that the same force that keeps the moon in orbit around Earth is responsible for objects falling down on Earth. That force is the force of gravity. Gravity is one of the most basic forces and affects all objects that have mass. The acceleration due to gravity on the surface of the Earth is denoted by g, and points towards the surface fo the Earth. The acceleration due to gravity on the surface of the Earth is denoted by g, and points towards the surface fo the Earth. Using Newton's second law, we can define the weight of an object as the force due to gravity on that object, which is equal to its mass times the acceleration due to gravity. Since weight is a force, its units are that of a force, or Newtons. In SI units, g is 9.8 meters per second squared. Thus, an object with a mass of 10 kg weighs 98 Newtons. The value of g we use here is that for the surface of the Earth. On the surface of the moon, the force of gravity is approximately 6 times smaller than that on Earth, or 1.7 meters per second squared. It's your turn to answer a question. ... The correct answer is 17 Newtons, since the force of gravity is given by mass times the acceleration due to gravity. Let's get back to Earth now, shall we? We know that gravity exerts a force on all objects, giving them their "weight." We learned from Newton's Third law that objects in contact with each other exert equal and opposite forces on each other. So if the crate is being pushed down against the ground with a force equal to its weight, does that mean that the ground is pushing back? The answer is yes! We call this contact force the normal force. In case of an object resting on flat ground, the magnitude of the normal force is equal to the weight of the object. In fact, scales that measure weight are actually measuring the normal force exerted by the scale on the object. What would happen to the normal force if we pulled upward on the object with a force of 50 N without lifting the object off the floor? Since the crate is stationary, its acceleration must be zero, which means that all the forces acting on the crate are in balance. We'll choose the upward direction as positive. What are the forces acting on the crate? To help us solve this and other Newton's Laws problems, we use what are called force diagrams. To construct a force diagram, we begin by marking all the forces acting on the object, in our case the crate. There are three forces acting on the crate. The force of gravity pointing downward with a magnitude of 100 Newtons, the normal force upward, and the force of the rope upward at 50 Newtons. To construct our force diagram, start with a circle representing our object as a point mass, then move the forces so that they are acting through the center of this mass. To solve for the normal force, we write Newton's Second Law as the net force equals mass times acceleration, equals the normal force in the positive direction, plus our force upward minus the force of gravity. Since the acceleration of the crate is zero, the net force must be zero. We can solve for the normal force by taking the force of gravity and the force we exerted to the other side of the equation. Next, we plug in 50 Newtons for our force and 100 Newtons for gravity, which gives us a normal force of 50 Newtons. Thus, pulling upward on the crate has reduced the contact force between the crate and the ground. Your turn to try this. If the force we provide is now pushing downward, the normal force is the sum of our push, which is 50 Newtons, plus the force of gravity, which is 100 Newtons, giving us 150 Newtons