Newton’s Laws of Motion

Newton’s Laws of Motion www.assignmentpoint.com

Newton’s laws of motion • Net force • Action/reaction • Inertial Reference frame • Non-inertial Ref frame • Mass • Acceleration • Friction • Inertial Force • Non-inertial Force • Q: Define as many of these concepts as you can? www.assignmentpoint.com

First Law: Law of Inertia Q: How does this animation relate to first law? Q: What is state of motion? Q: Where is unbalanced force applied ? An object at rest (v=0) remains at rest AND an object at constant velocity (v=c) remains at constant velocity UNLESS acted upon by an unbalanced force (Fnet not equal zero). www.assignmentpoint.com

Second Law: force definition Acceleration is produced when a unbalanced force acts on a mass. The greater the mass of the object being accelerated the greater the amount of force needed to accelerate the object. www.assignmentpoint.com

Third law: action/reaction For every action, there is an equal and opposite reaction. Force is always an interaction between two objects that occurs and an action/reaction force pair. No one object applies a force, both apply equal and opposite force on each other. If force was not always an action reaction pair, momentum would NOT be conserved. The rocket's action is to push down on the ground with the force of its powerful engines, and the reaction is that the ground pushes the rocket upwards with an equal force. www.assignmentpoint.com

Three Laws of classical mechanics • In the absence of a net force, a body either is at rest or moves in a straight line with constant speed. • 2. A body experiencing a force F experiences an accelerationa related to F by F = ma, where m is the mass of the body. Alternatively, force is equal to the time derivative of momentum. • 3. Whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction. www.assignmentpoint.com

First Law Redux Newton's first law is also called the law of inertia. It states that if the vector sum of all forces (that is, the net force) acting on an object is zero, then the acceleration of the object is zero and its velocity is constant. The first point needs no comment, but the second seems to violate everyday experience. For example, a hockey puck sliding along ice does not move forever; rather, it slows and eventually comes to a stop. According to Newton's first law, the puck comes to a stop because of a net external force applied in the direction opposite to its motion. This net external force is due to a frictional force between the puck and the ice, as well as a frictional force between the puck and the air. If the ice were frictionless and the puck were traveling in a vacuum, the net external force on the puck would be zero and it would travel with constant velocity so long as its path were unobstructed. Implicit in the discussion of Newton's first law is the concept of an inertial reference frame, which for the purposes of Newtonian mechanics is defined to be a reference frame in which Newton's first law holds true. There is a class of frames of reference (called inertial frames) relative to which the motion of a particle not subject to forces is a straight line.Newton placed the law of inertia first to establish frames of reference for which the other laws are applicable.To understand why the laws are restricted to inertial frames, consider a ball at rest inside an airplane on a runway. From the perspective of an observer within the airplane (that is, from the airplane's frame of reference) the ball will appear to move backward as the plane accelerates forward. This motion appears to contradict Newton's second law (F = ma), since, from the point of view of the passengers, there appears to be no force acting on the ball that would cause it to move. However, Newton's first law does not apply: the stationary ball does not remain stationary in the absence of external force. Thus the reference frame of the airplane is not inertial, and Newton's second law does not hold in the form F = ma. www.assignmentpoint.com

Second law redux • Newton's second law states that the force applied to a body produces a proportional acceleration; the relationship between the two is • where F is the force applied, m is the mass of the body, and a is the body's acceleration. If the body is subject to multiple forces at the same time, then the acceleration is proportional to the vector sum (that is, the net force): • The second law can also be shown to relate the net force and the momentump of the body: • Therefore, Newton's second law also states that the net force is equal to the time derivative of the body's momentum: www.assignmentpoint.com

Second Law redux: Impulse An impulseI occurs when a force F acts over an interval of time Δt, and it is given by Since force is the time derivative of momentum, it follows that This relation between impulse and momentum is closer to Newton's wording of the second law. Impulse is a concept frequently used in the analysis of collisions and impacts. www.assignmentpoint.com

The laws: relationship to the conservation laws In modern physics, the laws of conservation of momentum, energy, and angular momentum are of more general validity than Newton's laws, since they apply to both light and matter, and to both classical and non-classical physics. This can be stated simply, "Momentum, energy and angular momentum cannot be created or destroyed.“ Because force is the time derivative of momentum, the concept of force is redundant and subordinate to the conservation of momentum, and is not used in fundamental theories (e.g. quantum mechanics, quantum electrodynamics, general relativity, etc.). www.assignmentpoint.com

Analysis of ball and feather fall in vacuum • A vacuum is required to prove gravitational acceleration of an object is independent of its mass. The vacuum means that no air molecules are present to create friction on the falling object. • This friction would resists the objects acceleration (greater velocity). • Thus, any friction means that an object cannot be in a free-fall state. • The vacuum is NOT why the feather and ball fall at same rate: i.e., hit the bottom at same time with same velocity. • The fact that gravity would be very constant over a few 10’s of meters is also NOT why the masses fall at same rate. • So, why does the feather and ball fall at same rate in a frictionless (airless) environment? www.assignmentpoint.com

Why acceleration is independent of mass (without friction)Larger Mass = Larger gravity force Larger Mass = Larger inertial forceSo, Larger gravity force is resisted by larger inertial force This means acceleration is independent of mass www.assignmentpoint.com

Position, velocity and acceleration 1-D kinematic equations of motion Projectile velocity along path x: position (m) v: velocity (m/s) a: acceleration (m/s2) a = ∆v/ ∆t (m/s/s = m/s*1/s = m/s2 ) v = ∆x/ ∆t (m/s = m/s) What is relation between x and t? What is acceleration at vy = 0 point? www.assignmentpoint.com

acceleration In physics, and more specifically kinematics, acceleration is the change in velocity over time.[1] Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows down. However, as a vector quantity, acceleration is also the rate at which direction changes.[2][3] Acceleration has the dimensionsLT−2. In SI units, acceleration is measured in metres per second squared (m/s2). In common speech, the term acceleration commonly is used for an increase in speed (the magnitude of velocity); a decrease in speed is called deceleration. In physics, a change in the direction of velocity also is an acceleration: for rotary motion, the change in direction of velocity results in centripetal (toward the center) acceleration; where as the rate of change of speed is a tangential acceleration. Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time t is found in the limit as time interval Δt → 0. www.assignmentpoint.com

Linear free-fall: Zero to 30 m/s (60 mph) in 3 seconds! www.assignmentpoint.com

Orbital free-fall • If initial ball velocity this is slow (A,B) , the ball falls back to earth tracing out a parabolic path. Called ballistic trajectory. • If initial ball velocity is too fast (E) (>escape velocity) , the ball leaves earth traveling outward towards infinity and never comes back. • Given correct initial ball velocity (C), the ball will go into orbit which means it is in continual free-fall as pull of gravity acts perpendicular to velocity vector to accelerate ball towards earth by the same amount that the earth’s surface curves away. • Question: what would happen if you were placed at 1000 km above the earth and let go with no initial velocity ? www.assignmentpoint.com

Centripetal acceleration Why if string breaks does ball moves off in a straight line? www.assignmentpoint.com

Gravity field in Space shuttle The gravity field strength diminishes as 1/r2 where r is reckoned with respect to center of the earth. At earth’s surface 6400 km from center of earth, the gravity field strength is 9.8 m/s2. So what is gravity field strength at 380 km above the earth’s surface which is the normal height that the space shuttle orbits. Orbital velocity at 380 km height is about 17,400 miles per hour (7800 m/s). The Orbital period at 380 km height is about 92 minutes. Centripetal acceleration for stable orbit must be: a = v2/r = 78002 / 6.75e6 =9.01 m/s2 . Does 8.74 = 9.01 m/s2 , it is close. I used approximate numbers from the web. The gravity field is 88% of the gravity at the surface. So, why are the people weightless? www.assignmentpoint.com

Weightlessness in orbit Weightlessness in an orbiting spacecraft is physically identical to free-fall, with the difference that gravitational acceleration causes a net change in the direction, rather than the magnitude, of the spacecraft's velocity. This is because the acceleration vector is perpendicular to the velocity vector. In typical free-fall, the acceleration of gravity acts along the direction of an object's velocity, linearly increasing its speed as it falls toward the Earth, or slowing it down if it is moving away from the Earth. In the case of an orbiting spacecraft, which has a velocity vector largely perpendicular to the force of gravity, gravitational acceleration does not produce a net change in the object's speed, but instead acts centripetally, to constantly "turn" the spacecraft's velocity as it moves around the Earth. Because the acceleration vector turns along with the velocity vector, they remain perpendicular to each other. Without this change in the direction of its velocity vector, the spacecraft would move in a straight line, leaving the Earth altogether. www.assignmentpoint.com

Terminal velocity (falling through fluid) In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the air, water or other fluid through which it is moving. A free-falling object achieves its terminal velocity when the downward force of gravity (Fg) equals the upward force of drag (Fd). This causes the net force on the object to be zero, resulting in an acceleration of zero.[1] When a falling object has reached terminal velocity, is it still in free-fall state ? www.assignmentpoint.com

Fields extend or propagate to infinite • Gravity field from mass • Electric field from charge • Sound source wave field • Electro-magnetic wave field For r=0, f(r) is undefined (infinite). For limit as r →∞, f(r) = 0. For all other r values (domain), f(r) is finite. Moral of story: Fields never die. The gravitational effects of you, me, the planet, anything, extends to infinity! Although at far distances, the effects becomes so small as to not be measurable. www.assignmentpoint.com

Newton’s Laws of Motion