1. Tuesday June 7, 2005 1 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt PHYS 1443 – Section 001 Lecture #5 Tuesday June 67 2005 Dr. Andrew Brandt Reference Frames Short Review Newton’s Laws/Force

2. Tuesday June 7, 2005 2 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Announcements Homework+tests: –First homework attempted by 11/12, most people did well –Second HW on ch3 due today 5pm (ch4 HW due 6/13 at 2pm, but start it early) – First test on Ch 1-3 Weds June 8 at 8:30 am

3. Tuesday June 7, 2005 3 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Maximum Range and Height What are the conditions that give maximum height and range of a projectile motion? This formula tells us that the maximum height can be achieved when  i =90 o !!! This formula tells us that the maximum range can be achieved when 2  i =90 o, i.e.,  i =45 o !!!

4. Tuesday June 7, 2005 4 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Observations in Different Reference Frames Results of physical measurements in different reference frames could be different Observations of the same motion in a stationary frame would be different than the ones made in the frame moving together with the moving object. Consider that you are driving a car. To you, the objects in the car do not move while to the person outside the car they are moving with the same speed and direction as your car. O Frame S r’ O’ Frame S’ The position vector r’ is still r’ in the moving frame S’.no matter how much time has passed!! v0v0 The position vector r is no longer r in the stationary frame S when time t has passed. v0tv0t r How are these position vectors related to each other?

5. Tuesday June 7, 2005 5 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Relative Velocity and Acceleration The velocity and acceleration in two different frames of references can be denoted, using the formula in the previous slide: O Frame S r’ O’ Frame S’ v0v0 v0tv0t r Galilean transformation equation What does this tell you? The acceleration measured in two frames are the same when the frames move at a constant velocity with respect to each other!!! The earth’s gravitational acceleration is the same in a frame moving at a constant velocity wrt the earth.

6. Tuesday June 7, 2005 6 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Review: Ch 1-2 Velocity as a function of time Displacement as a function of velocity and time Displacement as a function of time, velocity, and acceleration Velocity as a function of displacement and acceleration Significant figures, displacement, velocity, acceleration, 1-D motion, free fall, constant acceleration equations:

7. Tuesday June 7, 2005 7 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Chapter 3 Coordinate systems, vectors (defn., operations, components unit vectors), 2-D motion, projectile motion, reference frames Range+Max height

8. Tuesday June 7, 2005 8 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Force (Ch 4) We’ve been learning kinematics; describing motion without understanding the cause of the motion. Now we are going to learn dynamics!! What is FORCE? FORCEs are what cause an object to move FORCEs cause a change in 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. Forces cause acceleration. What happens there are several forces being exerted on an object? Forces are vector quantities, so vector sum of all forces, the NET FORCE, determines the motion of the object. F1F1 F2F2 NET FORCE, F= F 1 +F 2 When net force on an object is 0, it has constant velocity and is at its equilibrium!!

9. Tuesday June 7, 2005 9 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt More Force There are various classes of forces Contact Forces: Forces exerted by physical contact with 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, Electromagnetic force What are possible ways to measure strength of Force? A calibrated spring whose length changes linearly with the force exerted. Forces are vector quantities, so addition of multiple forces must be done following the rules of vector addition.

10. Tuesday June 7, 2005 10 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Newton’s First Law and Inertial Frames Aristotle (384-322BC): A natural state of a body is rest. Thus force is required to move an object. To move faster, ones needs higher force. 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!! Galileo’s statement is formulated by Newton into the 1 st 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 constant velocity is called an Inertial Frame What does this statement tell us? When no force is exerted on an object, the acceleration of the object is 0. Any isolated object, an object that does not interact with its surrounding, is either at rest or moving at a constant velocity. An object maintains its current state of motion, as long as there is no force that interferes with the motion. This tendency is called the Inertia.

11. Tuesday June 7, 2005 11 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Mass Mass: A quantity of matter, or, more usefully, a measure of the inertia of a body 1.Independent of the object’s surroundings: The same no “matter” where you go. 2.Independent of the method of measurement: The same forces applied to two different masses result in different acceleration depending on the mass. The heavier (more massive) an object, the bigger the inertia. It is harder to change the motion of a heavier object than a lighter one. Note that mass and weight of an object are two different quantities! Weight of an object is the magnitude of 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.

12. Tuesday June 7, 2005 12 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt 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 should also satisfy it: From the above vector expression, what do you conclude the dimension and unit of force are? The dimension of force is The unit of force in SI is For simplicity, we define a new derived unit called, a Newton (N)

13. Tuesday June 7, 2005 13 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Acceleration Example of Newton’s 2 nd Law of Motion 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 is given? Thus, the force needed to stop the car is What do we need to know to figure out the force? Acceleration!! Initial speed: Displacement: Final speed: How are stopping distance and force related? Linearly proportional to the mass of the car Squarely proportional to the speed of the car Inversely proportional to the force by the brake

14. Tuesday June 7, 2005 14 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Acceleration Vector a FF FF Example for Newton’s 2 nd Law of Motion Determine the magnitude and direction of acceleration of a hockey puck with a mass of 0.30kg, being pulled by two forces, F1 and F2, with magnitudes of 8.0 N and 5.0 N, respectively, as shown in the picture.         Components of F 1 Components of F 2 Components of total force F Magnitude and direction of acceleration a

15. Tuesday June 7, 2005 15 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Gravitational Force and Weight Since weight depends on the magnitude of gravitational acceleration, g, it varies depending on geographical location. The attractive force exerted on an object by the Earth Gravitational Force, FgFg Weight of an object with mass M is By measuring the forces one can determine masses.

16. Tuesday June 7, 2005 16 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Some Basic Information Normal Force, n: When Newton’s laws are applied, external forces only are of interest!! Why? Because, as described in Newton’s first law, an object will keep its current motion unless a net non-zero external force is applied. Tension, T: Reaction force that reacts to gravitational force due to the surface structure of an object. Its direction is perpendicular to the surface. The reactionary force by a stringy object against an external force exerted on it. A graphical tool which is a diagram of external forces on an object object and is extremely useful in analyzing forces and motion!! Drawn only on an object. Free-body diagram assume massless taut strings

17. Tuesday June 7, 2005 17 PHYS 1443-001, Summer I 2005 Dr. Andrew Brandt Free Body Diagrams and Solving Problems Free-body diagram: A diagram of vector forces acting on an object  A great tool to solve a problem using forces or using dynamics 1.Select a point on an object in the problem 2.Identify all the forces acting only on the selected object 3.Define a reference frame with positive and negative axes specified 4.Draw arrows to represent the force vectors on the selected point 5.Write down the net force vector equation 6.Write down the forces in components to solve the problem(s)  No matter for which object we choose to draw the diagram, the results should be the same, as long as they are from the same motion M Which one would you like to select to draw the FBD? What do you think are the forces acting on this object? Gravitational force A force supporting the object exerted by the floor MeMe Which one would you like to select to draw theFBD? What do you think are the forces acting on this elevator? Gravitational forceThe force pulling the elevator (Tension) m What about the box in the elevator? Gravitational force Normal force