Monday, June 13, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 1 PHYS 1443 – Section 001 Lecture #5 Monday, June 13, 2011 Dr. Jaehoon Yu • Newton’s Laws of Motion – Force – Newton’s Law of Inertia – Mass and Newton’s second law of motion – Newton’s third law of motion – Categories of Forces • Free Body Diagram Today’s homework is homework #3, due 10pm, Thursday, June 16!!Monday, June 13, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 2 Announcements • Quiz #2 tomorrow, Tuesday, June 14 – Beginning of the class – Covers: CH 1.1 – what we finish today (CH4.5)Monday, June 13, 2011 3 Reminder: Special Project for Extra Credit • Show that the trajectory of a projectile motion is a parabola!! – 20 points – Due: tomorrow, Tuesday, June 14 – You MUST show full details of your OWN computations to obtain any credit • Much beyond what was covered in page 21 of this lecture note!! PHYS 1443-001, Spring 2011 Dr. Jaehoon YuMonday, June 13, 2011 4 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 4 Example for a Projectile Motion • A stone was thrown upward from the top of a cliff at an angle of 37o to horizontal with initial speed of 65.0m/s. If the height of the cliff is 125.0m, how long is it before the stone hits the ground? Since negative time represents the time with the stone on the ground if it were thrown from the ground. BecomesMonday, June 13, 2011 5 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 5 Example cont’d • What is the speed of the stone just before it hits the ground? • What are the height and the range of the stone? Do these yourselves!!!Monday, June 13, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 6 Force We’ve been learning kinematics; describing motion without understanding what the cause of the motion is. Now we are going to learn dynamics!! Can someone tell me what FORCE is? FORCE is what causes an object to move. FORCE is what causes changes to the velocity of an object!! The above statement is not entirely correct. Why? Because when an object is moving with a constant velocity no force is exerted on the object!!! What does this statement mean? When there is force, there is change of velocity!! What happens if there are several forces exert on an object? Forces are vector quantities, so vector sum of all forces, the NET FORCE, determines the direction of the resulting acceleration of the object. F1 F2 NET FORCE, F= F1+F2 When the net force on an object is 0, it has constant velocity and is at its equilibrium!! What does force cause? It causes an acceleration.!!Monday, June 13, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 7 More Forces There are various classes of forces Contact Forces: Forces exerted by physical contact of objects Examples of Contact Forces: Baseball hit by a bat, Car collisions Field Forces: Forces exerted without physical contact of objects Examples of Field Forces: Gravitational Force, Electro-magnetic force What are possible ways to measure the strength of a force? A calibrated spring whose length changes linearly with the force exerted . Forces are vector quantities, so the addition of multiple forces must be done following the rules of vector additions.Monday, June 13, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 8 Newton’s First Law and Inertial Frames Aristotle (384-322BC): The natural state of a body is rest. Thus force is required to move an object. To move faster, ones needs larger forces. Galileo’s statement is formulated by Newton into the 1st law of motion (Law of Inertia): In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity. A frame of reference that is moving at a constant velocity is called the Inertial Frame What does this statement tell us? • When no net force is exerted on an object, the acceleration of the object is 0. • Any isolated object, the object that does not interact with its surroundings, is either at rest or moving at a constant velocity. • Objects would like to keep its current state of motion, as long as there are no net force that interferes with the motion. This tendency is called the Inertia. Galileo’s statement on natural states of matter: Any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of retardation are removed!! Is a frame of reference with an acceleration an Inertial Frame? NO!Monday, June 13, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 9 Mass Mass: A measure of the inertia of an object or the quantity of matter • Independent of the object’s surroundings: The same no matter where you go. • Independent of the method of measurement: The same no matter how you measure it. The same forces applied to two different masses result in different acceleration depending on the mass. The heavier the object, the bigger the inertia !! It is harder to make changes of motion of a heavier object than a lighter one. Note that the mass and the weight of an object are two different quantities!! Weight of an object is the magnitude of the gravitational force exerted on the object. Not an inherent property of an object!!! Weight will change if you measure on the Earth or on the moon but the mass won’t!! Unit of mass?Monday, June 13, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 10 Newton’s Second Law of Motion The acceleration of an object is directly proportional to the net force exerted on it and is inversely proportional to the object’s mass. How do we write the above statement in a mathematical expression? Since it’s a vector expression, each component must also satisfy: Newton’s 2nd Law of Motion Fii∑ mFrom this we obtainMonday, June 13, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 11 Unit of the Force From the vector expression in the previous page, what do you conclude the dimension and the unit of the force are? The dimension of force is The unit of force in SI is For ease of use, we define a new derived unit called, Newton (N)Monday, June 13, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu 12 Acceleration Example 4.3 What constant net force is required to bring a 1500kg car to rest from a speed of 100km/h within a distance of 55m? This is a one dimensional motion. Which kinetic formula do we use to find acceleration? What are given? Thus, the force needed to stop the car is What do we need to
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