Newton’s Second Law of Motion

Mass the quantity of matter in an object the measurement of the inertia measured in kilograms (kg)

Weight the force upon an object due to gravity Weight = Mass  Acceleration of gravity W = mg measured in Newtons (N) in the metric system or pounds (lb) in the British system

The weight of a 10 kg brick is... A) 98 N B) 10 kg C) 9.8 kg D) 10 N E) 98 kg

Mass and Weight should not be confused with... Volume the quantity of space an object occupies Density the quantity mass per unit volume

Mass and Weight On the Moon the gravitational force is only 1/6 as strong as on the Earth. In space you are “weightless” but not “massless”. Your mass does not depend on where your are. (e.g. Earth, Moon, or space).

WeightLocationMass Earth Moon Space 18.4 kg 180 N 30 N 0 N

NEWTON'S 2 nd LAW OF MOTION F a m Fa mm F a m m m Fa Fa Fa M MM

Newtons’ Second Law  F = m a The acceleration of an object is directly proportional to the net force acting on the object… …and inversely proportional to the mass of the object.

Example Questions How much acceleration does a 747 jumbo jet of mass 30,000kg experience in takeoff when the thrust of all of the engines is 120,000N? A) 747 N B) 4 kg C) 1/4 kg D) 4 m/s 2 E) 30,000 kg times 9.8 m/s 2

Example Questions How much acceleration does a 747 jumbo jet of mass 30,000kg experience in takeoff when the thrust of all of the engines is 120,000N? A) 747 N B) 4 kg C) 1/4 kg D) 4 m/s 2 E) 30,000 kg times 9.8 m/s 2

Example Questions The same net force is applied to two blocks. If the blue one has a smaller mass than the yellow one, which one will have the larger acceleration? F F

Example Questions The same net force is applied to two blocks. If the blue one has a smaller mass than the yellow one, which one will have the larger acceleration? A) Blue B) Yellow F F

If the net force is parallel to the velocity, then the speed of the object increases. If the net force is anti-parallel to the velocity, then the speed of the object decreases.

If the net force is perpendicular to the velocity, the direction of the velocity changes.

Force and acceleration are vector quantities. If v is parallel to F, speed increases. If v is antiparallel to F, speed decreases. If v perpendicular to F, direction of v changes. See Check Yourself questions page 59, 61, 63 & 65.

Freely Falling Objects Free fall is the motion of an object subject only to the influence of gravity. The acceleration due to gravity is a constant, g.

Freely Falling Objects Free fall from rest:

When the Acceleration is g... …the object is in Free Fall. Consider a 1kg rock and a 1gram feather. –Which object weighs more? A. Rock B. Feather C. Neither

Freely Falling Objects An object falling in air is subject to air resistance (and therefore is not freely falling).

When the Acceleration is g... …the object is in Free Fall. Consider a 1kg rock and a 1gram feather. –On which is the gravitation force stronger? A. Rock B. Feather C. Neither

When the Acceleration is g... …the object is in Free Fall. Consider a 1kg rock and a 1gram feather. –Which object has more mass? A. Rock B. Feather C. Neither

When the Acceleration is g... …the object is in Free Fall. Consider a 1kg rock and a 1gram feather. –Which has a greater acceleration when dropped from rest? A. Rock B. Feather C. Neither

When the Acceleration Is Less Than g... …the object is not in Free Fall. In this case there is a force other than gravity. That force is air resistance. Air resistance depends on size, shape, air density, and speed.

When Acceleration Is Zero... …we say the object is in Mechanical Equilibrium. …the net force is zero. For Static Equilibrium the velocity is zero. For Dynamic Equilibrium the velocity is constant.

Important Equations: When the Acceleration is g... –  F=ma mg=ma a=g When the Acceleration Is Less Than g... –  F=ma mg-R=ma a=g-R/m When Acceleration Is Zero... –  F=ma mg-R= a=0

After jumping from an airplane a skydiver will fall until the air resistance equals her weight. At that point... –A) she opens her parachute –B) she will fall no farther –C) she will fall faster –D) she will fall with constant speed –E) she will hit the ground

Equations v = d / t a =  v / t W = m g  F = ma Note: Bring a calculator to class for the remainder of the semester.

Real World Forces: Gravity Support (normal force) Tension Friction (static vs. kinetic)

When Acceleration Is Zero - Equilibrium Static Equilibrium Velocity is zero Examples: Hanging from a tree Weighing yourself on a set of scales Computer setting on a table Car parked on an incline Normal up Weight down Scales pushing up Tree pulling up Normal Friction

Dynamic Equilibrium Velocity is nonzero and constant Examples: Driving at constant velocity Force from road Weight down Friction Normal up Weight down Air resistance Terminal velocity in parachuting