6. SAMPLE PROBLEMS AND HELPFUL LINKS
In real life situations, objects do not move in straight lines. This is because there are many factors involved in movements -- friction, air resistance, gravity, and others. For this reason we will examine motion in two dimensions. This will encompass allowing for friction, examining projectile (objects shot or thrown into the air) motion, and circular motion.
Newton's three Laws of Motion give some interesting findings. The inertia law -- Newton's first -- states that objects tend to stay in their state of motion unless an outside force acts on the system. Why does a rolling ball stop if it indeed does tend to stay in the same state of motion ? This is because an outside force -- friction -- is acting.
The "law of interaction"-- Newton's third Law of Motion -- says that for every action there is an equal and opposite reaction. This means that for every force there is an equal and opposite reaction force. If a man jumps from a row boat, the boat accelerates backwards. This is because the action force of the man jumping from the boat is equal and opposite to the force pushing the boat backwards.
In first half of chapter seven of our textbook, forces are examined in their two dimensions. If an object is placed on an incline, it is easier to move up the incline than it would be to lift it straight up. Why ? Because the weight (a type of force) is acting in two directions. Part of the weight is working against your push but the remainder is simply holding the object to the ramp.
Another interesting find is that all objects have gravitational pulls
toward other objects. This -- along with the action/reaction law
-- leads to the fact that if an apple is falling toward the Earth, there
must be an equal and opposite force pulling the Earth toward the apple.
Students will discover why this does not appear to occur in the reading
of the book.
BACK TO THE TOP
An object that is dropped will hit the ground at the same time that an object thrown horizontally if they are dropped from the same height. Why ? Because the force of gravity affects the vertical, but not the horizontal. If, for example, a diver fell from a high dive as another diver ran straight off of a high dive of the same height, both divers would hit the ground at the same time.
Another way to examine projectiles is to show what happens to an object shot or thrown at an angle. For instance, if a golf ball is hit on a flat stretch of ground on a calm day, it will take the same time to rise as it does to fall. The distance it travels will be determined by the angle that it was hit at and the velocity that it left at. With mathematical understanding, we can show that the golf ball that travels the farthest is the one that leaves the club at a 45 degree angle.
Ever wonder what happens to a racecar as it travels around a curve ? Or why astronauts are put into a gravitron and spun around at fast speeds ? Both topics deal with centripetal force, which is the force that pulls an object out of its straight line travel into a circular motion.
Why is it then that you feel an outward pull when you travel in a circle ? This is the centrifugal force pushing you outward. It occurs because of Newton's inertial law of motion -- the tendency of an object to stay in its state of motion unless acted upon by an outside force. In this case, the outside force is the centripetal force which is changing the direction of your motion.
Why do planets move around the Sun ? Why does the moon circle the Earth ? This is due to the pull of gravity, a force which exists between any two objects. Kepler's laws supply us with the knowledge of how planets travel around the Sun, including the fact that the orbital paths are elliptical, the fact that a planet moves at a faster rate when closer to the sun, and the reasoning for the fact that we may calculate the period of a cycle of a planet circling the Sun by simply knowing its distance from the Sun.
SAMPLE PROBLEMS AND HELPFUL LINKS
| TOPIC | SAMPLE PROBLEMS | HELPFUL LINKS |
| TWO DIMENSIONAL MOTION | Chapter | AMUSEMENT PARK PHYSICS |
| TWO DIMENSIONAL FORCES | Chapter 6: page145 questions 1-10, 12-13, 20-24, 26-30, 34,35,37
Chapter 7: page 171, questions 14-17, 30-35. Gravitational forces:
|
CHAPTER 6 REVIEW WORKSHEET |
| PROJECTILES | Chapter 7: pages 169-172, questions 1-9, 39-45. | AMUSEMENT PARK PHYSICS LINK #2 |
| CIRCULAR MOTION | Chapter 7: pages 169-173, questions 10-13, 49-53. | . |
| PLANETARY MOTION | Chapter 8: pages 193-5, questions 1-3, 9-13, 41-44. | KEPLER'S LAWS |