Translational motion, forces, work, energy, and equilibrium in living systems

Force-Newton's First Law, inertia

Experience suggests that an object at rest will remain at rest if left alone, and that an object in motion tends to slow down and stop unless some effort is made to keep it moving. NEWTON'S FIRST LAW OF MOTION-A body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. Note the repeated use of the verb "remains." We can think of this law as preserving the status quo of motion. Rather than contradicting our experience, Newton's first law of motion states that there must be a cause (which is a net external force) for there to be any change in velocity (either a change in magnitude or direction).

Newton's Second Law (F=ma)

Fnet = ma is used to define the units of force in terms of the three basic units for mass, length, and time. The SI unit of force is called the newton (abbreviated N) and is the force needed to accelerate a 1-kg system at the rate of 1 m/s2. That is, since Fnet = ma, 1 N = 1 kg ⋅ m/s2. While almost the entire world uses the newton for the unit of force, in the United States the most familiar unit of force is the pound (lb), where 1 N = 0.225 lb.

Force-Friction, static, and kinetic

Friction is a force that opposes relative motion between systems in contact and its magnitude has two forms: static friction and kinetic friction.

Force-Friction, static, and kinetic-Key Terms

Friction: The resistance to motion of one object moving relative to another. Kinetic friction: Also known as sliding friction or moving friction, is the amount of retarding force between two objects that are moving relative to each other. Static friction: The friction that exists between a stationary object and the surface on which it's resting. Normal force: Contact or support force exerted upon an object that is in contact with another stable object. The component of a contact force that is perpendicular to the surface that an object contacts. Magnitude of static friction fs: fs ≤ μsN Magnitude of kinetic friction fk: fk = μkN Coefficient of friction: A value that shows the relationship between two objects and the normal reaction between the objects that are involved. Its value is dependent on both of the materials involved.

Forces

Gravity is an attractive force that is felt by all forms of matter. All objects exert gravitational forces on each other. The magnitude of the gravitational force between two objects is Fg = Gm1m2/r^2 where G is the universal gravitational constant (6.67 X 10 -11 N*m^2/kg^2, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass. This equation is commonly tested in the context of proportionalities. For example, the magnitude of the gravitational force is inversely related to the square of the distance (that is r is halved, then Fg will quadruple). The magnitude of the gravitational force is also directly related to the masses of the objects (that is, if m1 is tripled, the Fg will triple).

Newton's Second Law (F=ma)-Key Points

If the only force acting on an object is due to gravity, the object is in free fall. Friction is a force that opposes the motion past each other of objects that are touching.

Newton's Second Law (F=ma)-Key Points

In equation form, Newton's second law of motion is: a= Fnet/m This is often written in the more familiar form: Fnet = ma. The weight w of an object is defined as the force of gravity acting on an object of mass m. The object experiences an acceleration due to gravity g: w = mg.

Force-Newton's First Law, inertia-Key Terms

Inertia: the tendency of an object to remain at rest or remain in motion. Mass: the quantity of matter in a substance; measured in kilograms. Newton's first law of motion/Law of Inertia: A body at rest remains at rest or, if in motion, remains in motion at a constant velocity unless acted on by a net external force; also known as the law of inertia. Force: Any interaction that, when unopposed, will change the motion of an object.

Newton's Second Law (F=ma)

Newton's Second Law states that when a net force acts on an object, the change in the object's state of motion will be inversely proportional to the mass of the object and directly proportional to the net force acting on the object.

Newton's Third Law, forces equal and opposite

Newton's Third Law of Motion states whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts.

Force-Newton's First Law, inertia

Newton's first law of motion, also known as the law of inertia, states that a body at rest remains at rest or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. Fnet = ma Newton's laws, which are expressed as equations, describe the effects forces have on objects that have mass.

Newton's Third Law, forces equal and opposite-Key Terms

Newton's third law of motion: Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts. Thrust: The reaction force that pushes a body forward in response to a backward force.

Newton's Second Law (F=ma)-Key Points

Acceleration (a) is defined as a change in velocity, meaning a change in its magnitude or direction, or both. An external force is one acting on a system from outside the system, as opposed to internal forces, which act between components within the system. Newton's second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.

Forces

Acceleration due to gravity g, decreases with height above the Earth and increases the closer one gets to the Earth's center of mass. Near the Earth's surface, use g = 10 m/s^2.

Forces-Center of mass-Key Terms

Center of mass: A point representing the mean position of the matter in a body or system. Vector addition: The operation of adding two or more vectors together into a vector sum. Mass: The physical property of matter that depends on size and shape of matter, and is expressed as kilograms by the SI system. Center of gravity: A point from which the weight of a body or system may be considered to act. Table edge: A method used to find the center of mass of small rigid objects with at least one flat

Forces-Center of mass

Complex objects can often be represented as collections of simple shapes, each with uniform mass. We can then represent each component shape as a point mass located at the centroid. Voids within objects can even be accounted for by representing them as shapes with negative mass.

Forces

Every change in velocity is motivated by a push or pull- a force. Force is a vector quantity that is experienced as pushing or pulling on objects. Force can exist between objects that aren't even touching such as gravity or electrostatic force between point charges. The SI Unit for force is the Newton (N) which is equivalent to one kg*m/s^2.

Newton's Second Law (F=ma)-Key Terms

Free-fall: A situation in which the only force acting on an object is the force due to gravity friction: a force past each other of objects that are touching; examples include rough surfaces and air resistance. Gravity: The natural force that causes things to fall toward the earth; is written as g in equations (g = 9.8 m/s2). Mass: The measure of the amount of matter in a substance or an object. Weight: The weight of an object is related to the force acting on the object, either due to gravity or to a reaction force that holds it in place.

Force-Friction, static, and kinetic-Key Points

Friction is a contact force between systems that opposes the motion or attempted motion between them. Simple friction is proportional to the normal force N pushing the systems together. (A normal force is always perpendicular to the contact surface between systems.) Friction depends on both of the materials involved. The magnitude of static friction fs between systems stationary relative to one another is given by fs ≤ μsN where μs is the coefficient of static friction, which depends on both of the materials. The kinetic friction force fk between systems moving relative to one another is given by fk = μkN where μk is the coefficient of kinetic friction, which depends on both of the materials.

Force-Friction, static, and kinetic

Friction is a force that is around us all the time that opposes relative motion between systems in contact but also allows us to move. One of the simpler characteristics of friction is that it is parallel to the contact surface between systems and always in a direction that opposes motion or attempted motion of the systems relative to each other. If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction. Kinetic friction converts kinetic energy to thermal energy by generating heat. When objects are stationary, static friction can act between them; the static friction is usually greater than the kinetic friction between the objects.

Force-Friction, static, and kinetic

Frictional forces, such as f, always oppose motion or attempted motion between objects in contact. Much of the friction is actually due to attractive forces between molecules making up the two objects (even perfectly smooth surfaces are not friction-free). The direction of friction is always opposite that of motion, parallel to the surface between objects, and perpendicular to the normal force. The magnitude of the frictional force has two forms: one for static situations (static friction), the other for when there is motion (kinetic friction).

Newton's Second Law (F=ma)-Key Terms

Net external force: The vector sum of all external forces acting on an object or system; causes a mass to accelerate. Acceleration: The rate at which an object's velocity changes over a period of time. Newton: A newton (N) is the international unit of measure for force. One newton is equal to 1 kg*m/s^2

Force-Newton's First Law, inertia-Key Points

Newton's first law of motion states that a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. This is also known as the law of inertia. Inertia is the tendency of an object to remain at rest or remain in motion. Inertia is related to an object's mass. Mass is the quantity of matter in a substance.

Newton's Second Law (F=ma)

Newton's second law of motion is closely related to Newton's first law of motion. It mathematically states the cause and effect relationship between force and changes in motion. Newton's second law of motion is more quantitative and is used extensively to calculate what happens in situations involving a force. It states that when a net force acts on an object, the change in the object's state of motion will be inversely proportional to the mass (m) of the object and directly proportional to the net force (Fnet) acting on the object. It can be written as: Fnet = ma

Newton's Second Law (F=ma)-Key Terms

Newton's second law of motion: States when a net force acts on an object, the change in that object's state of motion will be inversely proportional to the mass (m) of the object and directly proportional to the net force (F) acting on the object. It can be written as F = ma. Force: A force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. System: A portion of the physical universe chosen for analysis. Everything outside the system is known as the environment. The environment is ignored except for its effects on the system.

Newton's Third Law, forces equal and opposite-Key Points

Newton's third law of motion represents a basic symmetry in nature, with an experienced force equal in magnitude and opposite in direction to an exerted force. Two equal and opposite forces do not cancel because they act on different systems. Action-reaction pairs include a swimmer pushing off a wall, helicopters creating lift by pushing air down, and an octopus propelling itself forward by ejecting water from its body. Rockets, airplanes, and cars are pushed forward by a thrust reaction force. Choosing a system is an important analytical step in understanding the physics of a problem and solving it.

Newton's Third Law, forces equal and opposite

Newton's third law of motion represents a certain symmetry in nature: Forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself. Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts. Mathematically, if a body A exerts a force F on body B, then B simultaneously exerts a force -F on A. In vector equation form: FAB = −FBA

Forces-Center of mass

One useful application of the center of mass is determining the maximum angle that an object can be tilted before it will topple over. The figure below shows a cross-section of a truck. The truck has been poorly loaded with many heavy items loaded on the left-hand side. The center of mass is shown as a red dot. A red line extends down from the center of mass, representing the force of gravity. Gravity acts on all the weight of the truck through this line. If the truck is tipped at an θt, then all the weight of the truck will be supported by the left-most edge of the left wheel. Should the angle be further increased then the point of support will move outside of any point of contact with the road and the truck is guaranteed to topple over. The angle θt is the topple limit.

Forces-Center of mass

One very useful property of the center of mass is that it can be used to define the origin of a moving reference frame for a system. This reference frame is sometimes called the COM frame. The COM frame is particularly useful in collision problems. It turns out that the momentum of a fully-defined system measured in the COM frame is always zero. This means that calculations can often be much simpler when done in the COM frame compared to the laboratory reference frame.

Forces-Center of mass-Key Terms

Plumb line: A method useful for determining the center of mass for a complex planar shape with unknown dimensions. It relies on finding the center of mass of a thin body of homogeneous density having the same shape as the complex planar shape. Topple limit (θt): The maximum angle that an object can be tilted before it will topple over. Reference frame: A frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements within that frame. Laboratory reference frame: A frame of reference centered on the laboratory in which the experiment is done. This is the reference frame in which the laboratory is at rest. Momentum: The quantity of motion of a moving body, measured as a product of its mass and velocity.

Newton's Second Law (F=ma)

Remember, it is important to be aware that weight and mass are very different physical quantities. Mass is a scalar measurement, the quantity of matter (how much "stuff",) and does not vary in classical physics. Meanwhile, weight is a vector measurement, the gravitational force, and varies depending on gravity. The SI Unit for mass is the kilogram which is independent of gravity. One kilogram of material on Earth will have the same mass as one kilogram of material on the Moon. Although, weight and mass are not the same thing, they are related using the equation Fg = mg where Fg is the weight of the object, m is the mass, and g is the acceleration due to gravity or 9.8 m/s^2.

Forces-Center of mass-Key Points

The center of gravity is the point through which the force of gravity acts on an object or system. The table edge method can be used to find the center of mass of small rigid objects with at least one flat side. One useful application of the center of mass is determining the topple limit, the maximum angle that an object can be tilted before it will topple over. Another useful property of the center of mass is that it can be used to define the origin of a moving reference frame for a system.

Forces-Center of mass

The center of gravity is the point through which the force of gravity acts on an object or system. In most mechanics problems the gravitational field is assumed to be uniform. The center of gravity is then in exactly the same position as the center of mass. The terms center of gravity and center of mass tend to often be used interchangeably since they are often at the same location. There are a couple of useful experimental tests that can be done to determine the center of mass of rigid physical objects.

Forces-Center of mass-Key Points

The center of mass (COM) is a statement of spatial arrangement of mass (i.e. distribution of mass within the system). The experimental determination of the center of mass of a body uses gravity forces on the body and relies on the fact that in the parallel gravity field near the surface of the earth the center of mass is the same as the center of gravity. For a 2D object, an experimental method for locating the center of mass is to suspend the object from two locations and to drop plumb lines from the suspension points. The intersection of the two lines is the center of mass.

Forces-Center of mass

The center of mass can be found by vector addition of the weighted position vectors which point to the center of mass of each object in a system. One quick technique which lets us avoid the use of vector arithmetic is finding the center of mass separately for components along each axis: See Notecard. Together, these give the full coordinates (COMx​, COMy​) of the center of mass of the system.

Newton's Second Law (F=ma)

The equation illustrates that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. The effect of the force, acceleration, is a change in the object's velocity (in magnitude, direction, or both). The smaller the mass experiences a given force, the greater its acceleration. The greater a mass experiences a given force, the smaller its resulting acceleration or effect of that force. The direct proportionality between F and a demonstrates that for a given mass, the greater the force, the greater the acceleration.

Force-Newton's First Law, inertia

The idea of cause and effect is crucial in accurately describing what happens in various situations. For example, consider an air hockey table. When the air is turned off, the puck slides only a short distance before friction slows it to a stop. However, when the air is turned on, it creates a nearly frictionless surface, and the puck glides long distances without slowing down. Additionally, if we know enough about the friction, we can accurately predict how quickly the object will slow down. Friction is an external force.

Forces-Center of mass

The plumb line method is also useful for objects which can be suspended freely about a point of rotation. An irregularly shaped piece of cardboard suspended on a pin-board is a good example of this. The cardboard pivots freely around the pin under gravity and reaches a stable point. A plumb line is hung from the pin and used to mark a line on the object. The pin is moved to another location and the procedure repeated. The center of mass then lies beneath the intersection point of the two lines.

Force-Newton's First Law, inertia

The property of a body to remain at rest or to remain in motion with constant velocity is called inertia. Newton's first law is often called the law of inertia. As we know from experience, some objects have more inertia than others. It is obviously more difficult to change the motion of a large boulder than that of a basketball, for example. The inertia of an object is measured by its mass. Roughly speaking, mass is a measure of the amount of "stuff" (or matter) in something. The quantity or amount of matter in an object is determined by the numbers of atoms and molecules of various types it contains. Unlike weight, mass does not vary with location. The mass of an object is the same on Earth, in orbit, or on the surface of the Moon. n practice, it is very difficult to count and identify all of the atoms and molecules in an object, so masses are not often determined in this manner. Operationally, the masses of objects are determined by comparison with the standard kilogram.

Forces-Center of mass

The table edge method can be used to find the center of mass of small rigid objects with at least one flat side. The object is pushed slowly without rotating along the surface of a table towards an edge. At the point where the object is just about to fall, a line is drawn parallel to the table edge. The procedure is repeated with the object rotated 90°. The intersection point of the two lines gives the location of the center of mass in the plane of the table.

Forces-Center of mass

The weight of an object can be thought of as being applied at a single point in that object called the center of mass or gravity. The center of gravity is related and corresponds to the single point at which one can conceptualize gravity acting on an object. Only for a homogenous body (with symmetrical shape and uniform density) should one expect the center of gravity to be located at its geometric center. For example, we can approximate the center of gravity for a metal ball as the geometric center of the sphere. The same cannot be said for a human body, television, or any asymmetrical non-uniform object. The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.

Newton's Third Law, forces equal and opposite

There are two important features of Newton's third law. First, the forces exerted (the action and reaction) are always equal in magnitude but opposite in direction. Second, these forces are acting on different bodies or systems: A's force acts on B and B's force acts on A. In other words, the two forces are distinct forces that do not act on the same body. Thus, they do not cancel each other. Physical contact is not necessary for Newton's third law; the mutual gravitational pull between the Earth and the Moon traverses hundreds of thousands of kilometers of space.

Newton's Third Law, forces equal and opposite

We sometimes refer to this law loosely as "action-reaction," where the force exerted is the action and the force experienced as a consequence is the reaction. Newton's third law has practical uses in analyzing the origin of forces and understanding which forces are external to a system. For example, rake a swimmer who uses her feet to push off the wall in order to gain speed. The more force she exerts on the wall, the harder she pushes off. This is because the wall exerts the same force on her that she forces on it. She pushes the wall in the direction behind her, therefore the wall will exert a force on her that is in the direction in front of her and propel her forward. This reaction force, which pushes a body forward in response to a backward force, is called thrust.

Newton's Second Law (F=ma)

When an object is dropped, it accelerates toward the center of Earth. Newton's second law states that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its weight w. Weight can be denoted as a vector w because it has a direction; down is, by definition, the direction of gravity, and hence weight is a downward force. The magnitude of weight is denoted as w. In the absence of air resistance, all objects fall with the same acceleration g. The equation for weight—the gravitational force on a mass m: w = mgg = 9.80 m/s2 (on Earth)

Newton's Second Law (F=ma)

When the net external force on an object is its weight, we say that it is in free-fall. That is, the only force acting on the object is the force of gravity. In the real world, when objects fall downward toward Earth, they are never truly in free-fall because there is always some upward force from the air acting on the object.

Forces-Center of mass

When the term reference frame is used in physics it refers to the coordinate system used for calculations. A reference frame has a set of axes and an origin (zero point). In most problems, the reference frame is fixed relative to the laboratory and a convenient (but arbitrary) origin point is chosen. This is known as the laboratory reference frame. However, in classical physics, it is also possible to use any other reference frame and expect the laws of physics to hold within it. This includes reference frames which are moving relative to the laboratory.

Force-Friction, static, and kinetic

When there is no motion between the objects, the magnitude of static friction fs is: fs ≤ μsN where μs is the coefficient of static friction and N is the magnitude of the normal force (the force perpendicular to the surface). Once an object is moving, the magnitude of kinetic friction (fk) is: fk = μkN where μk is the coefficient of kinetic friction. A system in which fk = μkN is described as a system in which friction behaves simply. For both static and kinetic friction, the coefficient of friction depends on the two surfaces that are in contact. Kinetic friction dissipates energy (in the form of heat) that is proportional to the force times the distance over which the force acts.