PHYS 1443 Section 001 Lecture 6 Thursday June

PHYS 1443 – Section 001 Lecture #6 Thursday June 9, 2005 Dr. Nurcan Ozturk for Dr. Brandt • • • Newton’s Laws/Force Friction Circular Motion Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 1

Announcements • Homework: – HW 3 on ch 4 due Monday 6/13 at 2 pm – HW 4 on ch 5 due Tuesday 6/14 at 8 pm Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 2

Newton’s Laws of Motion Newton’s 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. Newton’s 2 nd 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. Newton’s 3 rd law of motion: Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first. since Force is a vector… For simplicity, we define a new derived unit called, a Newton (N) Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 3

Some Basic Information When Newton’s laws are applied, external forces only are of inte Gravitational Force (Weight) Reaction force that reacts to Normal Force, n: gravitational force due to the surface structure of an object. Its direction is perpendicular to the surface. The reactionary force by a stringy Tension, T: object against an external force exerted on it. A graphical tool which is a diagram of external forces on an object and is extremely useful in Free-body analyzing forces and motion!! Drawn only on an diagram object. Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 4

Applications of Newton’s Laws Suppose you are pulling a box on frictionless ice, using a rope M Freebody diagram n= -Fg T Fg=Mg What are the forces being exerted on the box? T Gravitational force: Fg n= -Fg Normal force: n T Tension force: T Total force: Fg=Mg F=Fg+n+T=T If T is a constant force, ax, is constant Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 in the Is there motion Dr. Andrew Brandt y-direction? 5

Example Using Newton’s Laws A traffic light weighing 125 N hangs from a cable tied to two other cables fastened to a support. The upper cables make angles of 37. 0 o and 53. 0 o with the horizontal. Find the tension in the three cables. y 37 o 53 o Free-body Diagram T 1 T 2 37 o 53 o T 3 x Newton’s 2 nd law x-comp. of net force y-comp. of net force Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 6

Example without Friction A crate of mass M is placed on a frictionless inclined plane of angle q. ya) Determine the acceleration of the crate after it is released. y M y n q n Free-body Diagram q Fg a x xd x F= -Mg b) Supposed the crate was released at the top of the incline, and the length of the incline is d. How long does it take for the crate to reach the bottom and what is its speed at the bottom? Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 7

Forces of Friction Resistive force exerted on a moving object due to viscosity or other types of frictional properties of the medium in, or surface on, which the object moves. These forces are either proportional to the velocity or the normal force. The resistive force exerted on the object Force of static until just before the beginning of its friction, fs: movement Empiric al Formul a What does this Frictional force is variable and formula tell will increase until it reaches you? the limit Beyond the limit, the object moves, and there is NO MORE static friction but kinetic friction takes over. Force of kinetic friction, The fk resistive force exerted on the object during its movement Opposite to the motion Which direction does kinetic friction apply? Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 8

Example w/ Friction q Suppose a block is placed on a rough surface inclined relative to the horizontal. The inclination angle is increased till the block starts to move. Show that by measuring this critical angle, qc, one can determine coefficient of static friction, ms. y y n M a n Free-body fs=msn Diagram x x Fg q F= -Mg Net force On the verge of sliding, block is stationary, acceleration is zero, friction is static friction. x comp. y comp. If block moves at constant speed, acceleration is zero, friction is kinetic friction. Coefficient of kinetic friction can be calculated as Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 9

Newton’s Second Law & Uniform Circular Motion The centripetal acceleration is always perpendicular to the velocity vector, v, for uniform circular motion. Are there forces in this motion? If so, what do do? The force that causesthey the centripetal acceleration acts toward the center of the circular path and causes a change in the direction of the velocity vector. This forcedoisyou called centripetal force. What think will happen to the ball if the string that holds the ball breaks? Why? Based on Newton’s 1 st law, since the external force no longer exist, the ball will continue its motion without change and will fly away following the tangential direction to the circle. Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 10 Dr. Andrew Brandt

Example of Uniform Circular Motion A ball of mass 0. 500 kg is attached to the end of a 1. 50 m long cord. The ball is moving in a horizontal circle. If the string can withstand a maximum tension of 50. 0 N, what is the maximum speed the ball can attain before the cord Centripetal breaks? Fr m acceleratio n: When does the string break? when the centripetal force is greater than the sustainable tension. Calculate the tension of the cord when speed of the ball is 5. 00 m/s. Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 11

Example of Banked Highway (a) For a car traveling with speed v around a curve of radius r, determine a formula for the angle at which a road should be banked so that no friction is required to keep the car from skidding. y x comp. x y comp. (b) What is this angle for an expressway off-ramp curve of radius 50 m at a design speed of 50 km/h? Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 12

Forces in Non-uniform Circular Motion The object has both tangential and radial accelerations. Fr F What does this statement mean? The object is moving under both tangential and radial forces. Ft These forces cause not only the velocity but also the speed of the ball to change. The object undergoes a curved motion under the absence of constraints, such as a string. How does the acceleration Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 look? Dr. Andrew Brandt 13

Example for Non-Uniform Circular Motion A ball of mass m is attached to the end of a cord of length R. The ball is moving in a vertical circle. Determine the tension of the cord at any instant when the speed of the ball is v and the cord makes an angle q with vertical. What are the forces involved in this m motion? • The gravitational force Fg T q • The radial force, T, providing Fg=mg R tension. tangentia l comp. Radial comp. At what angles does the tension become maximum and minimum. What are the max and min tensions? Thursday June 9, 2005 PHYS 1443 -001, Summer I 2005 Dr. Andrew Brandt 14