Physics 231 Lecture 6 Main points of today s lecture Newton s second law F ma Gravitational and tension forces Normal force Pulleys and Atwood s machine Normal force Newton ss 3d Law Foff 2on1 Newton 2 1 Foff 11on 2 When a body exerts a force on another the second body exerts an equal oppositely directed force on the first body Conceptual question A ball b ll iis th thrown vertically ti ll up itits speed d slowing l i under d th the influence of gravity Suppose 1 we film this motion and play the tape backward so the tape begins with the ball at its highest point and ends with it reaching the point from which it was released and 2 we observe the motion of the ball from a frame of reference moving up at the initial speed of the ball The ball has a downward acceleration g in a 1 and 2 b only 1 c only l 2 2 d neither 1 nor 2 1 In the movie of the ball run in reverse the ball would look like it is falling downward from rest 2 IIn th the moving i frame f the th ball b ll would ld look like it is falling downward from rest Newton s second Law Newton s N 2ndd law l F ma a is the acceleration m is the mass of the object j It is proportional p p to the number of nucleons neutrons and protons in an object F is the net total force acting on the object It is the vector sum of all forces acting g on the object j Both F and a are vectors with a length and a direction m is a scaler It relates the x and y components of the force and acceleration vectors and also their lengths The direction of the force is the same as that of the acceleration Fx ma x Fy ma y F ma x 2 ma y 2 m a x2 a 2y ma tan F Fy Fx ma y ma x ay ax tan a Here F and a are angles with respect to the x axis Reading Quiz 1 Which of the following statements about mass and weight is correct A B B C D Your mass is a measure of the force gravity exerts on you Your mass is the same everywhere in the universe universe Your weight is the same everywhere in the universe Your weight is a measure of your resistance of being accelerated accelerated Slide 5 5 Inertial mass The unit Th it off mass is i kg k The inertial mass m is given by the number of neutrons and protons l nucleons in i the th object bj t It governs how h hard it is to accelerate an object M N nucleons 1 66x10 27 kgg Example A catapult t lt on an aircraft i ft is i capable bl off accelerating l ti a plane l from f 0 to t 56 m s in a distance of 80 m Find the magnitude of the average net force that the catapult exerts on a 13300 kg jet F ma mplane 13300 kg g v0 0 v 56 m s x 80 m F v 2 v 02 2a x v 2 v 02 v2 a 2 x 2 x v 2 v02 F m 2 x 56m s 13 300 2 80m 2 2 6x105 N Example A bi bicycle l hhas a mass off 13 13 1 1 kkg and d it its rider id hhas a mass off 81 7 81 7 kkg The rider is pumping hard so that a horizontal net force of 9 78 N accelerates them in the westward direction What is the acceleration a 0 103 0 103 m s 2 westt b 0 103 m s2 east c 0 120 m s2 west d 0 120 m s2 east e don t know F a m bike m rider mbike 13 1 kg mrider 81 7 81 7 kg F 9 79 N a 99 78N 78N 0 103m s 2 13 1kg 81 7kg Example A 36 5 36 5 kg k sphere h is i acted t d upon by b a 133 N force f directed di t d along l the th positive x axis What is the magnitude and direction of a second force such that the sphere experiences an acceleration of 3 96 m s2 directed at 210 above the positive x axis axis Fnet Fnet 36 5kg 3 96m s 2 144 5N 21o Fnet x 144 5N cos 21o 134 9N F1 F2 Fnet y 144 5N sin 21 51 8N o F2 x Fnet x F1 x 134 9N 133N 1 9N F1 133 N F2 y 51 8N 8N 2 y Fnet net yy F1 y 1y 5 F2 F2 m g 36 5 kg 2 1 9N 51 8N 51 8N 2 2 51 8N o 88 2 tan 1 9N 1 quiz A constant t t force f is i exerted t d for f a short h t time ti interval i t l on a cartt that th t is initially at rest on an air track This force gives the cart a certain final speed Suppose we repeat the experiment but instead of starting from rest rest the cart is already moving with constant speed in the direction of the force at the moment we begin to apply the force After we exert the same constant force for the same short time interval the increase in the cart s cart s speed a is equal to two times its initial speed b is equal to the square of its initial speed c iis equall tto ffour times ti its it initial i iti l speed d d is the same as when it started from rest e cannot be determined from the information provided v v 0 at v 0 F v t m F t m Reading Quiz 3 Which of these is not a force discussed in this chapter A B B C D The tension force The normal force force The orthogonal force The thrust force Slide 4 11 Examples of Forces Gravitational force Objects feel a force from gravity equal to their weights The weight W of an object equals its mass times the gravitation acceleration g i e W mg The weight of an object is less on the moon but the mass remains the same The direction of the gravitation force is towards the center of the Earth 5 kg T W mg String tension If a string pulls on an object we call its force the string tension It is always in the direction of the string Strings cannot push 5 kg A pulley can redirect the tension force The net or total force is the vector sum of all forces on an object The acceleration is inversely proportional to the net force T Example A 10 kkg mass hhangs ffrom a string t i The Th string t i pulls …
View Full Document
Unlocking...