Chapter 6 Newtons Second Law of Motion: Force and Acceleration
6.1 Force Causes Acceleration
Unbalanced forces acting on an object cause the object to accelerate.
Most often, the force we apply is not the only force acting on an object.
Ex. after a boy kicks the football, both gravity and air resistance are acting on the football.
The combination of forces acting on an object is the net force. Acceleration depends on the net force. To increase the acceleration of an object, you must increase the net force acting on it. Double the force and the acceleration doubles, triple the force and the acceleration triples. An objects acceleration is directly proportional to the net force acting on it.
acceleration ~ net force
6.2 Mass Resists Acceleration
Ex. push on an empty cart, now push equally hard on a heavily loaded cart. The loaded cart will accelerate much less than the empty cart.
Acceleration depends on the mass being pushed.
For a constant force, an increase in the mass will result in a decrease in the acceleration.
The same force applied to twice as much mass results in only half the acceleration. For three times the mass, one-third the acceleration results. In other words, for a given force, the acceleration produced inversely proportional to the mass.
Acceleration ~ 1/mass
Inversely means that the two values change in opposite directions.
6.3 Newton’s Second Law
Newtons second law describes the relationship among an objects mass, an objects acceleration, and the net force on an object.
Newtons second law states that the acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.
Acceleration = net force/mass
a = F/m
6.4 Friction
Friction acts on materials that are in contact with each other, and it always acts in a direction to oppose relative motion.
The force of friction between the surfaces depends on the kinds of material in contact and how much the surfaces are pressed together.
Friction is not restricted to solids sliding or tending to slide over one another. Friction also occurs in liquids and gases. Both liquids and gases are called fluids because they flow. Fluid friction occurs as an object pushes aside the fluid it is moving through.
Ex. Running a 100-m dash through waist deep water
Air resistance is the friction acting on something moving through air. Air resistance is a very common form of fluid friction.
Ex. Walking, jogging, riding a bike, or skiing
When friction is present, an object may move with a constant velocity even when an outside force is applied to it. In such case, the friction force just balances the applied force.
6.5 Applying Force—Pressure
Balance a book in different positions on the palm of your hand. Although the force is always the same, you’ll notice differences are due to differences in the area of contact for each case.
For a constant force, an increase in the area of contact will result in a decrease in the pressure.
The amount of force pre unit is called pressure.
P = force/application
P=F/A
You exert more pressure against the ground when you stand on on one foot than when you stand on both feet. This is due to the decreased area of contact. The smaller the area supporting a given force, the greater the pressure on that surface.
6.6 Free Fall Explained
Free fall occurs when a falling object encounters no air resistance. Galileo showed falling objects accelerate equally, regardless of their masses. This is strictly true if air resistance is negligible, that is, if the objects are in free fall.
All free falling objects fall with the same acceleration because the net force on an object is only its weight, and the ratio of weight to mass is the same for all objects.
6.7 Falling and Air Resistance
The feather and coin fall with equal accelerations in a vacuum, but very unequally in the presence of air. The force due to air resistance diminishes the net force action on the falling objects.
Speed and Area
The force due to air resistance is experienced when you stick your hand out of a window of a moving car. If the car moves faster, the force on your hand increases, indicating that air resistance force depends on speed. Instead of your hand, you hold your textbook out the window with the large side facing forward, exposing maximum frontal area for the book, the air resistance force is much larger than it was on your hand at the same speed.
The air resistance force an object experiences depends on the object’s speed and area.
Air resistance force ~ speed x frontal area
Terminal Speed
When the air resistance force on a falling object builds up to the point where it equals the weight of the object, then the net force on the object is zero and the object stops accelerating. We say that the object has terminal speed.
Terminal speed is the speed at which the acceleration of a falling object is zero because friction balances the weight. If we are concerned with direction, which is down for falling objects, we say t has reached its terminal velocity.
Terminal velocity is terminal speed together with the direction of motion.