3/9/15 Gravity and Newton Gravity What really happened? Probably the more correct version of the story is that Newton, upon observing an apple fall from a tree, began to think along the following lines: The apple is accelerated, since its velocity changes from zero as it is hanging on the tree and moves toward the ground. Thus, by Newton's 2nd Law there must be a force that acts on the apple to cause this acceleration. Let's call this force "gravity", and the associated acceleration the "acceleration due to gravity". Then imagine the apple tree is twice as high. Again, we expect the apple to be accelerated toward the ground, so this suggests that this force that we call gravity reaches to the top of the tallest apple tree. The story goes that Newton was sitting under an apple tree and an apple fell on his head. This event caused him to suddenly think of the Universal Law of Gravitation. The history of Gravity Sir Isaac Newton theorized the Law of Gravitation in 1687 1
3/9/15 GRAVITY DEFINED UNIVERSAL LAW OF GRAVITATION The tendency of objects with mass to accelerate towards each other One of the four fundamental forces (interactions) in nature. There is an apple on my head Newton's law of universal gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Simplified: Gravity is greater when mass is larger and distance is shorter. Gravity and our Solar System Planets and Gravity Since Jupiter is the largest planet, it has the most gravity. The Sun s gravity is what holds our solar system together. Pluto has the least amount of gravity of all the planets 2
3/9/15 MICROGRAVITY Mass and Weight are two different Properties of Matter MASS The further an object is away from another object, the force of gravity is weaker. The further an object moves from the surface of the Earth, the less gravity it feels from the Earth. Scientists on the Space Shuttle experience microgravity MASS If you pulled a mouse and an elephant with the same amount of force, the elephant would respond less to pulling even if he didn t pull back at all. This is because an elephant has more mass than a mouse. Which Law of Newton s does this relate to? v Mass is a physical property of matter that explains how much matter is in an object v Mass does not change when gravity changes WEIGHT v Weight is a force which is calculated by multiplying the acceleration of gravity times mass. v Weight can change when gravity changes WEIGHT An elephant on the Earth would weigh less on the Moon, because gravity is less on the moon. An elephant s mass would not change if he went to the moon 3
Free-body diagrams Free-body diagrams are used to show the relative magnitude and direction of all forces acting on an object. This diagram shows four forces acting upon an object. There aren t always four forces, For example, there could be one, two, or three forces. Problem 1 A book is at rest on a table top. Diagram the forces acting on the book. In this diagram, there are normal and gravitational forces on the book. 4
Problem 2 An egg is free-falling from a nest in a tree. Neglect air resistance. Draw a free-body diagram showing the forces involved. Gravity is the only force acting on the egg as it falls. Problem 3 A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. A free body diagram for this situation looks like Gravity pulls down on the squirrel while air resistance keeps the squirrel in the air for a while. 5
Problem 4 A rightward force is applied to a book in order to move it across a desk. Consider frictional forces. Neglect air resistance. Construct a free-body diagram. Let s see what this one looks like. Note the applied force arrow pointing to the right. Notice how friction force points in the opposite direction. Finally, there is still gravity and normal forces involved. When an object moves in a circle at constant speed, we describe it as undergoing uniform circular motion. Its speed is constant, but its velocity is not because velocity includes direction and the object s direction is clearly changing. Circular Motion Circular Motion A changing velocity means acceleration. The pull on the string is always directed perpendicular to the velocity. The pull accelerates the ball into a circular path, even though the ball does not speed up or slow down. The pull changes only the direction of the velocity, not the magnitude. 6
Centripetal Force The centripetal force always points toward the center of the circle about which the object moves with uniform speed. Circular Motion If the string breaks, the ball flies off in a straight line. It is the force of the string that causes the acceleration in this example of uniform circular motion. Centripetal Force Centripetal force is the name given to any force that is directed at right angles to the path of a moving object and that tends to produce circular motion. Examples: the gravitational force directed toward the center of the Earth holds the Moon in an almost circular orbit about the Earth; an electromagnetic force that is directed toward the nucleus holds the electrons that revolve about the nucleus of the atom. Directions in centripetal force problems: Positive direction is inwards toward center of circle. Negative direction is outward away from center of circle. 7
The forces acting on a person sitting in a roller coaster car are shown. The person s weight F W is present and so is the normal force F N that the seat exerts on him (this is your apparent weight). Vertical Circles Vertical Circles The normal force F N, the force you feel on the seat of your pants, can be positive, negative, or zero. A negative value for F N means the passenger has to be strapped in, with the straps exerting an upward force. Such a situation would be dangerous, and roller coaster designers avoid this. If F N = 0 N, the person seems to be weightless as well as upside down. Vertical Circles Experiencing a significant number of g s makes the work of the heart more difficult. Accelerations of eight to ten g s make it difficult for the circulatory system to get enough blood to the brain and may result in blackouts. Pressure suits that squeeze on the legs push blood back into the rest of the body, including the brain, and help prevent blackouts. For an object attached to a string and moving in a vertical circle, the centripetal force is at a minimum at the top of its vertical path and at a maximum at the bottom of its vertical path. Tension 8