PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 2 PHYSICS 231 INTRODUCTORY PHYSICS I Lecturer Carl Schmidt Sec 001 schmidt pa msu edu 517 355 9200 ext 2128 Office Hours Friday 1 2 30 pm in 1248 BPS or by appointment Main points of last lecture SI units Mass kilograms kg Length meters m Time seconds s Unit conversion Dimensional analysis Unit consistency Scientific Notation and Significant figures Displacement x xf xi x v Average Velocity t Graphical Representation of Average Velocity 40m v 13 3m s etween A and D v is slope of blue line 3 0s Instantaneous velocity basic formula x xf xi v t t Let time interval approach zero Defined for every instance in time Equals average velocity if v constant SPEED is absolute value of velocity Graphical Representation of Average Velocity Between A and D v is slope of blue line Graphical Representation of Instantaneous Velocity x t x v lim t 0 t Slope of tangent at that point Graphical Representation of Instantaneous Velocity v t 3 0 is slope of tangent green line Example 2 2a The instantaneous velocity is zero at A a B b d C c e Example 2 2b The instantaneous velocity is negative at A B C D E a b c d e Example 2 2c The average velocity is zero in the interval A B C D E a c b d c d c e d e Example 2 2d The average velocity is negative in the interval s A B C D a b a c c e d e SPEED Speed is v and is always positive Average speed is sum over x elements divided by elapsed time Example 2 3 x m a What is the average velocity between B and E 8 D 6 4 b What is the average speed between B and E B 2 C A 0 0 a 0 2 m s b 1 2 m s E 2 4 6 8 10 12 t s Acceleration The rate of change of the velocity a vf vi t Average acceleration measured over finite time interval Instantaneous acceleration measured over infinitesimal interval t 0 Accelerometer Demo Example 2 4 A speed boat starts from rest and reaches 3 2 m s in 2 s 1 What is its average acceleration a 16 m s2 2 Assuming acceleration is constant what is its velocity after 5 s vf v0 at 8 m s Graphical Description of Acceleration Acceleration is slope of tangent line in v vs t graph Graphical Description of Acceleration a is positive negative when v vs t is rising falling or when x vs t curves upwards downwards a 0 a 0 Example 2 5a e b c a d At which segment s is the acceleration negative A B C D a c c d c e d e Example 2 5b e b c a d A At which point s does the B acceleration equal zero C D E none of the below b c d e Constant Acceleration v v f v 0 at Recall v vs t is a straight line 1 v v 0 v f 2 x v t Also t v f v 12 v 0 v f 0 v 0 x 12 v 0 v f t Combining at t x 12 v 0 v 0 x v 0 t 12 at 2 x vs t is a parabola t Example 2 6 A speed boat starts from rest and accelerates at a rate of 1 6 m s2 far does it go after 5 s x 20 m How Solving Problems with Eq s of Motion 5 variables x t v0 vf a v f v 0 at 3 equations so far x 12 v 0 v f t x v 0 t 12 at 2 Must be 2 more equations Other Forms of Eq s of Motion v f v0 at 1 x v0 vf t 2 Substitute to eliminate v0 x v f at v f 2 1 2 x v f t at 2 t Other Forms of Eq s of Motion v f v0 at 1 x v0 vf t 2 Substitute to eliminate t x v0 v f v f v0 2 v2f v02 a x 2 2 a Final List of 1 d Equations basic equations 1 v v0 at 1 2 x v0 v t 2 1 2 3 x v0t at 2 1 2 4 x vf t at 2 v2f v20 5 a x 2 2 Which equation to use Each has 4 of the 5 variables x t v0 v a Ask yourself Which variable am I not given and not interested in Example 2 7 Crash Houlihan speeds down the interstate at 44 m s 100 mph when she slams on the brakes and slides into a concrete barrier The police measure skid marks to be 60 m long and estimate that her Mercedes would decelerate at 11 m s2 while skidding What was Crash s speed when she hit the barrier 25 m s Free Fall Special case of constant acceleration Objects near Earth s surface falling under the influence of gravity neglecting air resistance Acceleration g 9 81 m s2 a g Use the usual equations with with convention up is Galileo ather was a musician experimented with musi nitially was a professor teaching pre meds eveloped telescope 1610 Milky Way stars Moons of Jupiter Phases of Venus easured g uantified mechanics n 1632 published Dialogue concerning the two greatest world systems as found guilty of heresy Example 2 8a A man drops a brick off the top of a 50 m building The brick has zero initial velocity a How much time is required for the brick to a 3 19 s hit the ground b What is the velocity of the b 31 3 brick when it hits the m s ground A B c Example 2 8b A man throws a brick upward from the top of a 50 m building The brick has an initial upward velocity of 20 m s A B a How high above the building does the brick get before it falls b How much time does the brick spend going upwards c What is the velocity of the brick when it passes the man going downwards d What is the velocity of the brick when it hits the ground e At what time does the brick hit c Example 2 8b A man throws a brick upward from the top of a 50 m building The brick has an initial upward velocity of 20 m s a How high above the building does the brick get before it falls b How much time does the brick spend going upwards c What is the velocity of the brick when it passes the man going downwards d What is the velocity of the brick when it hits the ground e At what time does the brick hit a b c d e 20 4 m 2 04 s 20 m s 37 2 m s 5 83 …
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