Which law of motion that when body A exerts a force body B will exert but oppositely directed force on body?

1. An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.
2. The acceleration of an object depends on the mass of the object and the amount of force applied.
3. Whenever one object exerts a force on another object, the second object exerts an equal and opposite on the first.

Sir Isaac Newton worked in many areas of mathematics and physics. He developed the theories of gravitation in 1666 when he was only 23 years old. In 1686, he presented his three laws of motion in the “Principia Mathematica Philosophiae Naturalis.”

By developing his three laws of motion, Newton revolutionized science. Newton’s laws together with Kepler’s Laws explained why planets move in elliptical orbits rather than in circles.

Below is a short movie featuring Orville and Wilbur Wright and a discussion about how Newton’s Laws of Motion applied to the flight of their aircraft.

Newton’s First Law: Inertia

An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.

Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This tendency to resist changes in a state of motion is inertia. If all the external forces cancel each other out, then there is no net force acting on the object.  If there is no net force acting on the object, then the object will maintain a constant velocity.

Examples of inertia involving aerodynamics:

• The motion of an airplane when a pilot changes the throttle setting of an engine.
• The motion of a ball falling down through the atmosphere.
• A model rocket being launched up into the atmosphere.
• The motion of a kite when the wind changes.

Newton’s Second Law: Force

The acceleration of an object depends on the mass of the object and the amount of force applied.

His second law defines a force to be equal to change in momentum (mass times velocity) per change in time. Momentum is defined to be the mass m of an object times its velocity V.

Let us assume that we have an airplane at a point “0” defined by its location X0 and time t0. The airplane has a mass m0 and travels at velocity V0. An external force F to the airplane shown above moves it to point “1”. The airplane’s new location is X1 and time t1.

The mass and velocity of the airplane change during the flight to values m1 and V1. Newton’s second law can help us determine the new values of V1 and m1, if we know how big the force F is. Let us just take the difference between the conditions at point “1” and the conditions at point “0”.

F = (m1 * V1 – m0 * V0) / (t1 – t0)

Newton’s second law talks about changes in momentum (m * V). So at this point, we can’t separate out how much the mass changed and how much the velocity changed. We only know how much product (m * V) changed.

Let us assume that the mass stays at a constant value equal to m. This assumption is rather good for an airplane because the only change in mass would be for the fuel burned between point “1” and point “0”. The weight of the fuel is probably small relative to the weight of the rest of the airplane, especially if we only look at small changes in time. If we were discussing the flight of a baseball,  then certainly the mass remains a constant. But if we were discussing the flight of a bottle rocket, then the mass does not remain a constant and we can only look at changes in momentum. For a constant mass m, Newton’s second law looks like:

F = m * (V1 – V0) / (t1 – t0)

The change in velocity divided by the change in time is the definition of the acceleration a. The second law then reduces to the more familiar product of a mass and an acceleration:

F = m * a

Remember that this relation is only good for objects that have a constant mass. This equation tells us that an object subjected to an external force will accelerate and that the amount of the acceleration is proportional to the size of the force. The amount of acceleration is also inversely proportional to the mass of the object; for equal forces, a heavier object will experience less acceleration than a lighter object. Considering the momentum equation, a force causes a change in velocity; and likewise, a change in velocity generates a force. The equation works both ways.

The velocity, force, acceleration, and momentum have both a magnitude and a direction associated with them. Scientists and mathematicians call this a vector quantity. The equations shown here are actually vector equations and can be applied in each of the component directions. We have only looked at one direction, and, in general, an object moves in all three directions (up-down, left-right, forward-back).

Example of force involving aerodynamics:

• An aircraft’s motion resulting from aerodynamic forces, aircraft weight, and thrust.

Newton’s Third Law: Action & Reaction

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

His third law states that for every action (force) in nature there is an equal and opposite reaction. If object A exerts a force on object B, object B also exerts an equal and opposite force on object A. In other words, forces result from interactions.

Examples of action and reaction involving aerodynamics:

• The motion of lift from an airfoil, the air is deflected downward by the airfoil’s action, and in reaction, the wing is pushed upward.
• The motion of a spinning ball, the air is deflected to one side, and the ball reacts by moving in the opposite
• The motion of a jet engine produces thrust and hot exhaust gases flow out the back of the engine, and a thrusting force is produced in the opposite direction.

Review Newton’s Laws of Motion

Forces Due to Friction (and Newton's Third Law)

There are two forms of force due to friction, static friction and sliding friction. When you push a heavy box, it pushes back at you with an equal and opposite force (Third Law) so that the harder the force of your action, the greater the force of reaction until you apply a force great enough to cause the box to begin sliding. You then notice that it requires less force to cause the box to continue to slide.

The force of static friction is what pushes your car forward. The engine provides the force to turn the tires which, in turn, pushes backwards against the road surface. By Newton's Third Law, the "reaction" of the surface to the turning wheel is to provide a forward force of equal magnitude to the force of the wheel pushing backwards against the road surface. This is a force of static friction as long as the wheel is not slipping.

The size of the friction force depends on the weight of the object. In the case of static friction, the maximum friction force occurs just before slipping. Its magnitude is the weight of the object times the coefficient of static friction. We will do exercises only for cases with sliding friction. In that case, the force of sliding friction is given by the coefficient of sliding friction times the weight of the object. The coefficients of static and sliding friction depend on the properties of the object's surface, as well as the property of the surface on which it is resting. Clearly, resting on sandpaper would be expected to give a different answer than resting on ice.

For those who are following this closely, consider how anti-lock brakes work. When you apply your car brakes, you want the greatest possible friction force to oppose the car's motion. This occurs when the wheels are in contact with the surface, rather when they are skidding, or sliding. So you want the wheels to keeps spinning and not to lock...i.e., to stop turning at the rate the car is moving forward. With computer controls, anti-lock breaks are designed to keep the wheels rolling while still applying braking force needed to slow down the car.

A Closer Look at Newton's Third Law

The Third Law says that forces come in pairs. When an object A exerts a force on object B, object B exerts an equal and opposite force on object A. For example, when an object is attracted by the earth's gravitational force, the object attracts the earth with an equal an opposite force. According to Newton's second law, an object's weight (W) causes it to accelerate towards the earth at the rate given by g = W/m = 9.8 meters / s2, where m is the object's mass. However, what is not readily realized is that the earth is also accelerating toward the object at a rate given by W/Me, where Me is the earth's mass. Since Me is so incredibly large compared with the mass of an ordinary object, the earth's acceleration toward the object is negligible for all practical considerations.

The Third Law if often stated by saying the for every "action" there is an equal and opposite "reaction."

Falling objects accelerate toward the earth, but what about objects at rest on the earth, what prevents them from moving? The net force must be zero if they don't move, but how is the force of gravity counterbalanced? See Figure 2-16 of page 45 in the text.

The person in the figure is standing at rest on a platform. He experiences a force Wep (earth-on-person) and the earth experiences a force Wpe (person-on-earth). Wep and Wpe are a pair of Third Law forces. They act on different bodies. The earth attracts the person, and the person attracts the earth.

The person also presses against the floor with a force equal to Wep, his weight. We call this force, Fpf (person-on-floor). But now the Third Law enters again. The reaction to this force is Ffp (floor-on-person).

Now consider Newton's Second Law as it applies to the motion of the person. The net force acting on the person is his weight, Wep pointing downward, counterbalanced by the force Ffp of the floor acting upward. The two cancel, so the net force is zero and his acceleration is zero...i.e.,.he remains at rest.

A rocket is propelled in accordance with Newton's Third Law. A force is required to eject the rocket gas, Frg (rocket-on-gas). This is counterbalanced by the force of the gas on the rocket, Fgr (gas-on-rocket). In empty space, Fgr is the net force acting on the rocket and it is accelerated at the rate Ar (acceleration of rocket) where Fgr = Mr x Ar (2nd Law), where Mr is the mass of the rocket.

Another Third Law example is that of a bullet fired out of a rifle. The force exerted by the expanding gas in the rifle on the bullet is equal and opposite to the force exerted by the bullet back on the rifle. The bullet is much less massive than the rifle, and the person holding the rifle, so it accelerates very rapidly. The rifle and the person are also accelerated by the recoil force, but much less so because of their much greater mass.

Newton's Laws for Circular Motion

• Newton's Third Law explains force of moon on earth is equal and opposite to the force of earth on moon. Likewise, force of sun on earth-moon system is equal and opposite to force of earth-moon system on sun.
• Newton's Second Law relates the force directed toward the center of the circle to the acceleration of the rotating object whose direction also points to the center.
• The attactive force acting between an satellite orbiting the earth in a circular path causes the object to accelerate toward the earth, but as it keeps its circular orbit, it never gets closer to the earth! This is because the satellite has a velocity tangent to its circular orbit which tends to cause it to move away from the earth. If gravity were suddenly turned off, like the knife cutting the string in the example discussed in class, the satellite would maintain a straight line motion (Newton's First Law) and travel away from the earth. The gravitational pull keeps the satellite in orbit, causing it to fall by just the right amount in each instant of time. Note that a circular orbit is achieved if the tangential velocity is exactly the right amount for the satellite's distance above the earth. If the tangential velocity were greater than this amount, it would not maintain a circular orbit ... it would form an elliptic orbit if the velocity were not too great. For great enough velocity, the object would move an ever increasing distance away from the earth. Likewise, for a tangential velocity below the critical value, the object would fall increasingly closer to the earth.