Introduction to Mechanics Dynamics Forces Applying Newton s Laws

Transcription

1 Introdction to Mechanics Dynamics Forces Applying Newton s Laws Lana heridan De Anza College Feb 26, 2018

2 Last time kinds of forces and problem solving gravity normal force and elevators

3 Overview kinds of forces and problem solving normal force and inclines tension elevators again plleys

4 The Normal Force The normal force spports an object that sits on a srface, bt its magnitde is different in different circmstances. In general, one needs to work ot what it will be in each problem. ome cases where the normal force is different than the weight of an object are: the object is in an accelerating elevator. the object sits on an incline.

5 Object on an Incline Problems with an object placed on an incline often reqire s to find the net force on the object or its acceleration. 1 Figres from erway & Jewett

6 Object on an Incline d, the force again decreases from front to back. The copler connecting the loco ge force Problems to slow with down anthe object rest of placed the cars, on an bt incline the final often copler reqiremst to apply a for last car. find the net force on the object or its acceleration. Consider a car on a frictionless driveway. 1 (Or free to roll, with frictionless, massless wheels.) naway Car AM y riveway inclined. n he car, assming mg sin 11a to conceptyday eperience, ncline will accelsame thing 1 Figres hapfrom erway a & Jewett b mg cos F g = m

7 Object on an Incline AM y d n g mg sin - e, l- p- le r- a b mg cos F g = m g The forces acting on the car: weight and normal force. Figre 5.11 (Eample 5.6) (a) A car on a frictionless incline. (b) The free- thisdiagram case, it for isthe sefl car. The to pick black adot coordinate represents the system position that of is the rotated: center Inbody the of mass ais of the points car. We along will learn slope, abot the center y aisof perpendiclar mass in Chapter to 9. the slope.

8 car. Object on an Incline ay Car AM y ay inclined n r, assming mg sin o concepteperience, e will accelthing hapes not set.) The forces a acting on the car: weight and b normal force. Figre 5.11 (Eample 5.6) (a) A car on a frictionless incline. (b) The freebody diagram acts downwards for the car. The black anddot the represents normal the position force acts of the center in a as a particle The weight of mass of the car. We will learn abot center of mass in Chapter 9. tes. Frtherry common category of problems in which an object moves nder the inflence direction perpendiclar to the inclined srface. of e-body diagram for the car. The only forces acting on the car are the normal force hich acts perpendiclar to the plane, and the gravitational force Fg 5 mg, which lems involving inclined planes, it is convenient to choose the coordinate aes with mg cos F g = m g The normal force has a magnitde sch that it cancels ot the component of the weight perpendiclar to the srface.

9 Object on an Incline away Car AM y iveway inclined n e car, assming mg sin a to conceptay eperience, cline will accelme thing haprakes not set.) o, the forces a in the (tilted) y-directionb cancel: Figre 5.11 (Eample 5.6) (a) A car on a frictionless incline. (b) The free- car as a particle body diagram for the car. The black dot represents the position of the center of mass of the car. We Fwill y = learn n abot mg center cos of mass θ = in 0Chapter 9. erates. Frthera very common category of problems in which an object moves nder the inflence of Rearranging: free-body diagram for the car. The only forces acting on the car are the normal force e, which acts perpendiclar to the plane, and the gravitational force Fg 5 mg, which oblems involving inclined planes, it is convenient to choose the coordinate aes with iclar to beit as less in Figre than5.11b. the weight, With these mg. aes, we represent the gravitational force by sin along the positive ais and one of magnitde mg cos along the negative y ais. n = mg cos θ mg cos Fg = m g If θ > 0 (it is an incline, not a flat srface), the normal force will

10 st car. Object on an Incline away Car AM y iveway inclined n e car, assming mg sin a to conceptay eperience, cline will accelme thing haprakes not set.) weight: In the (tilted) a -direction, there is only ba component from the Figre 5.11 (Eample 5.6) (a) A car on a frictionless incline. (b) The free- car as a particle body diagram for the car. The black dot represents the position of the center of mass of the car. We will learn F erates. Frthera very common category of problems in which an object moves nder the inflence abot = mg center sin of mass θ in Chapter 9. of F net = (mg sin θ)i a = (g sin θ)i free-body diagram for the car. The only forces acting on the car are the normal force e, which acts perpendiclar to the plane, and the gravitational force F g 5 mg, which oblems involving inclined planes, it is convenient to choose the coordinate aes with iclar to it as in Figre 5.11b. With these aes, we represent the gravitational force by mg cos Fg = m g

11 Incline Eample 24 above the horizontal. (a) If the force eerted by the rings on each arm has a magnitde of 290 N, and is directed along the length of the arm, what is the magnitde of the force eerted by the floor on his feet? (b) If the angle his arms make with the hor- A 65-kg skier izontal speeds is greater down that 24, a trail, and everything as shown. else remains The the same, srface is is the force eerted by the floor on his feet smooth and inclined at an angle of 22 greater than, less than, or the same as the vale fond in part (a)? with Eplain. the horizontal. (a) Find the25. direction IP A65-kgand skier speeds magnitde down a trail, of as shown the inet Figre force acting on the The srface is smooth and inclined at an angle of 22 with the skier. horizontal. (a) Find the direction and magnitde of the net force (b) Does the net actingforce on the skier. eerted (b) Doeson the net the forceskier eertedincrease, on the skier increase, decrease, or stay the same as the slope becomes steeper? decrease, or stay the same as the slope becomes steeper? Eplain. Eplain. ck, as shown in Fige of 130 N at an angle f the raft. The second k, plls at an angle of wman pll so that the ward direction? FIGURE 5 27 Problems 25 and 38 1 Walker, Ch 5, #32. 22

12 ome types of forces N OF NEWTON LAW Tension 6 2 trings and prings A common way to eert a force on an object is to pll on it with a string, a rope, a cable, or a wire. imilarly, yo can psh or pll on an object if yo attach it to a The force eerted by a rope or chain to sspend or pll an object spring. In this section we discss the basic featres of strings and springs and how withthey mass. transmit forces. T T T T eavy rope FIGURE 6 5 Tension in a string A string, plled from either end, has a tension, T. If the string were to be ct at any point, the force reqired to hold the ends together is T. Problems involving tensions often reqire solving systems of vector eqations. trings and Tension 1 Imagine picking p a light string and holding it with one end in each hand. If yo Figre from

13 T ome types of forces Eample problems with gravity and tension. A common way to eert a force o cable, or a wire. imilarly, yo c spring. In this section we discss they transmit forces. T T 3 T 2 T 1 FIGURE 6 5 Tension in a st A string, plled from either en at any point, the force reqired FIGURE 6 6 Tension in a heavy rope Becase of the weight of the rope, the tension is noticeably different at points 1, 2, and 3. As the rope becomes lighter, however, the difference in tension decreases. In the limit of a rope of zero mass, the tension is the same throghot the rope. (ee also eample 5-5 on pg 126 and 6-5 of the tetbook.) 1 Figre from Walker, Physics. trings and Tension Imagine picking p a light string pll to the right with yor right hand with a force T, the string be tension T in the string. To be mo some point, the tension T is the Figre 6 5 that is, T is the force to hold the ct ends together. N

14 mmary normal force: inclines tension Homework Walker Physics: Ch 5, onward from page 138. Problems: 25, 27, 45, 49