Patterns of Motion

In a moving airplane, you feel forces in many directions when the plane changes its motion. You cannot help but notice the forces involved when there is a change of motion.

Laws of Motion

Among other accomplishments, Sir Isaac Newton invented calculus, developed the laws of motion, and developed the law of gravitational attraction.

Newton's First Law of Motion –Every object remains in its state of rest or motion unless acted upon by an unbalanced force. –Objects tend to remain either at rest or in straight line motion. –This tendency to resist changes in motion is inertia. –Mass is a measure of the amount of inertia an object has.

Top view of a person standing in the aisle of a bus. (A) The bus is at rest, and then starts to move forward. Inertia causes the person to remain in the original position, appearing to fall backward.

(B) The bus turns to the right, but inertia causes the person to retain the original straight line motion until forced in a new direction by the side of the bus.

This marble can be used to demonstrate inertia.

Newton's Second Law of Motion –The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to the mass of the object. –This law describes the relationship between net force, acceleration, and mass

This bicycle rider knows about the relationship between force, acceleration, and mass.

At a constant velocity the force of tire friction (F 1 ) and the force of air resistance (F 2 ) have a vector sum that equals the force applied (Fa). The net force is therefore 0.

More mass results in less acceleration when the same force is applied. With the same force applied, the riders and the bike with twice as much mass will have half the acceleration, with all other factors constant. Note that the second rider is not pedaling.

–The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to the mass of the object. –The unit of force used in the SI system is the Newton (N) –N= kg  m/s 2 –Force is equal to mass times acceleration F=ma –Weight is equal to the mass of an object times the force of gravity w=mg

Newton's Third Law of Motion. –Whenever two objects interact, the force exerted on one object is equal in size and opposite in direction to the force exerted on the other object. F A due to B = F B due to A

Forces occur in matched pairs that are equal in magnitude and opposite in direction.

The football player's foot is pushing against the ground, but it is the ground pushing against the foot that accelerates the player forward to catch a pass.

Both the astronaut and the satellite received a force of 30.0 N for 1.50 s when they pushed on each other. Both then have a momentum of 45.0 kg m/s in the opposite direction. This is an example of the law of conservation of momentum.

Momentum

Momentum (  ) is the product of the mass of an object (m) and its velocity (v). –  = mv The law of conservation of momentum –The total amount of momentum remains constant in the absence of some force applied to the system.

Two unusual aspects of momentum –The symbol for momentum does not indicate what the quantity if measures is. –The units for momentum (kg  m/s) has no name.

According to the law of conservation of momentum, the momentum of the expelled gases in one direction equals the momentum of the rocket in the other direction in the absence of external forces.

Forces and Circular Motion.

Centripetal force. –This is the force that keeps an object in its straight line path Centrifugal force. –The imaginary force that is thought to force objects toward the outside of an object moving in a circular pattern. –Actually the force is simply the tendency of the object to move in a straight line.

The acceleration of an object moving in a circular path (a c ) is –a c = v 2 /r m = mass v = velocity r = the radius of the circular path. –This can be substituted into the Force equation F = ma F = mv 2 /r

Centripetal force on the ball causes it to change direction continuously, or accelerate into as circular path. Without the unbalanced force acting on it, the ball would continue in a straight line.

Newton's Law of Gravitation.

Objects fall due to the force of gravity (g) on them. –This force is 9.8 m/s 2 –It is this force that gives objects weight w = mg

Universal Law of Gravitation –Every object in the universe is attracted to every other object in the universe by a force that is directly proportional to the product of their masses and inversely proportional to the square of the distances between them. F = G(m 1 m 2 )/d 2 G is a proportionality constant and is equal to 6.67 X N  m 2 /kg 2 –Usually the objects in our environment that we interact with on an everyday basis are so small that the force is not noticed due to the large force of attraction due to gravity.

The variables involved in gravitational attraction. The force of attraction (F) is proportional to the product of the masses (m1, m2) and inversely proportional to the square of the distance (d) between the centers of the two masses.

The force of gravitational attraction decreases inversely with the square of the distance from the earth's center. Note the weight of a 70.0 kg person at various distances above the earth's surface.

Gravitational attraction acts as a centripetal force that keeps the Moon from following the straight-line path shown by the dashed line to position A. It was pulled to position B by gravity ( m/s2) and thus "fell" toward Earth the distance from the dashed line to B, resulting in a somewhat circular path.