Newton’s Laws of Motion

Dynamics

After studying Kinematics, we know how to describe motion in two and three dimensions. But what causes this motion? Dynamics is the study of the relationship between motion of objects and the cause of the motion (forces). We will use kinematics' quantities such as displacement, velocity, and acceleration. Two new concepts: force and mass. The material in this section will be covered on Exam 2.

Forces A force is a push or pull on an object. The concept of force gives us a quantitative description of the interaction between two bodies or between a body and its environment. Some types of forces include: Contact forces Long-Range Forces (gravitational attraction, electrostatic force,...) Forces are vectors - they have magnitude and direction. Forces obey the superposition principle: the effect of any number of forces applied to a point on an object is the same as the effect of a single force equal to the vector sum of the forces applied at that point.

Forces in Nature

Forces

Forces are vectors - they have magnitude and direction. Forces obey the superposition principle: the effect of any number of forces applied to a point on an object is the same as the effect of a single force equal to the vector sum of the forces applied at that point.

Newton’s First Law Newton's First Law (Law of Inertia) An object at rest will remain at rest unless it is acted upon by a net external force. An object in motion with constant velocity will continue to move with constant velocity unless it is acted upon by a net external force. Inertia The tendency of a body to keep moving once it is set in motion. Equilibrium If the net external force on a body is zero it is said to be in equilibrium. An object in equilibrium will either be at rest or in motion in a straight line with constant velocity.

Inertial Frame of Reference Newton’s First Law is valid in some frames of reference, in some it is not valid! Inertial frame of reference: where NFL is valid. Any frame of reference, which moves with a constant velocity relative to inertial frame of reference, is also inertial.

Newton’s Second Law What happens if the net force is not zero?

Newton’s Second Law Experiments show that for any given body the magnitude of the acceleration is directly proportional to the magnitude of the net force acting on the body. m is inertial mass of a body

Newton’s Second Law Can you think of a force that is equal to 1 Newton? Hint: Consider the “weight” of a common object

Newton’s Second Law If a net external force acts on the body, the body accelerates. The direction of acceleration is the same as the direction of the net force. The net force vector is equal to the mass of the body times the acceleration of the body.

Newton’s Second Law The design of high- performance motorcycles is based on Newton’s Second Law To maximize the forward acceleration, motorcycles are made as light as possible (minimum mass!) and have the most powerful engine possible (maximum forward force!) Powerful engine Large F Lightweight body Small m MAX MIN

Unit of Force SI unit of the magnitude of force: Newton [N], unit of force that gives acceleration of 1 m/s 2 to a body with a mass of 1 kg.

Types of Forces Contact force: Two objects pushing against each other F a,b = “force acting on a due to b” F head,thumb = “force on head due to thumb” r m1m1 m2m2 F 12 F 21 Action at a distance: Gravitational force, Electromagnetic force

Weight of a body: the force of Earth’s gravitational attraction to a body. Weight is a vector! Weight acts on bodies all the time, whether they are in free fall or not. Mass characterizes inertial properties of a body. Large stone Hard to throw because of its large mass Hard to lift because of its large weight Mass and Weight

Newton’s Third Law

Warm-Up: Projectile Motion A 76.0-kg boulder is rolling horizontally at the top of a vertical cliff that is 20 m above the surface of a lake, as shown in the Figure below. The top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the dam level with the surface of the water in the lake. A level plane is 25 m below the top of the dam. A. What must the minimum speed of the rock be just as it leaves the cliff so it will travel to the plain without striking the dam? B. How far from the foot of the dam does the rock hit the plain?

Warm-Up: Newton’s Laws N1L: An object at rest will remain at rest unless it is acted upon by a net external force. An object in motion with constant velocity will continue to move with constant velocity unless it is acted upon by a net external force. N2L: If a net external force acts on the body, the body accelerates. The direction of acceleration is the same as the direction of the net force. The net force vector is equal to the mass of the body times the acceleration of the body. N3L: For every action there is an equal and opposite reaction.

Warm-Up: Newton’s Laws N1L and N2L apply to a specific body. Decide to which body you are referring! It is not trivial sometimes. Only forces acting on the body matter. To analyze person walking, include the force that the ground exerts on the person as he walks, but NOT the force that the person exerts on the ground. Free-body diagrams are essential to help identify the relevant forces. Action-reaction pair NEVER appear in the same free-body diagram. When a problem involves more than one body: take this problem apart and draw a separate free-body diagram for each body.

Newton’s Third Law Newton's Third Law Forces always occur in equal and opposite pairs. If object A exerts a force on object B, then object B will exert an equal and opposite force on object A. Newton's Third Law is often commonly stated "For every action there is an equal and opposite reaction." The Action and Reaction forces in Newton's Third Law act on different objects, never on the same object.

Free-Body Diagrams

Force Diagrams

F R on M = F M on R

Free Body Diagrams Free-Body Force Diagram is a diagram that shows a single object (as a point) by itself, free of its surroundings, with vectors drawn to show the magnitudes and directions of all forces exerted ON the object by other objects. Be careful to include only the forces acting ON the object. Do not include any forces exerted BY the object on other objects or on itself. Two forces which constitute a Newton's Third Law Action-Reaction Pair NEVER appear on the same force diagram since these forces always act on different objects. When the problem involves more than one object you should draw separate force diagrams for each object.

Free Body Diagrams In some circumstances when objects that are in physical contact are moving as one unit (both have the same acceleration) it is acceptable, and in fact useful, to draw a composite force diagram for the objects. In this case the forces exerted on one object by the other do not appear on the diagram because the forces would occur in equal and opposite pairs by Newton's Third Law and would thus cancel each other. You should be able to answer the question "What other body is applying this force?" for every force on your force diagram. If you can't answer that question you may be dealing with a non-existent force. Never include non-existent forces such as "the force of acceleration (the "ma" force)"

Free Body Diagrams Tension in a rope at any point is the force that the rope exerts at that point. For a rope that can be considered as massless (its mass is small compared to the other objects in the problem) the tension at every point in the rope is the same. Ropes and Pulleys: Later in the semester when we study rotational motion, we will see that the tension in a rope actually does have to be different on each side of a real pulley (one whose mass cannot be ignored, i.e. one that has inertia). For now we are not equipped to handle that situation and will only study situations where a rope passes over a pulley that can be considered to be massless. In this case the magnitude of the tension will be the same on both sides of the pulley. The effect of a massless pulley is only to change the direction of the tension.

Newton’s 2 nd Law says that for an object: F = ma. We must isolate the forces acting only on the object and draw the Free Body Diagram. THEN, solve for the net force on the object to find its acceleration. B = board F = floor W = wall E = earth F W,B F B,W F B,F F B,E F F,B F E,B All Force Pairs F B,W + F B,F + F B,E = 0 F B,W F B,F F B,E Free Body Diagram Free Body Diagrams