Newton s Laws & Inclined Planes

Transcription

1 GP: ewton Law & Inclined Plane Phyic Mcutt Date: Period: ewton Law & Inclined Plane The ormal orce, Static and Kinetic rictional orce The normal orce i the perpendicular orce that a urace exert on an object. I a box it on a level table, the normal orce i imply equal to the weight o the box: I the box were on an inclined plane, the normal orce would be equal to the component o the weight o the box which i equal and oppoite to the normal orce: W y x mgco In thi cae, the component o the weight which i equal and oppoite to the normal orce i mgco. riction i a reitive orce between two urace which are in contact with each other. There are two type o riction: tatic riction and inetic riction. Static riction i the reitive orce between two urace which are not moving relative to each other, but would be moving i there were no riction. A bloc at ret on an inclined board would be an example o tatic riction acting between the bloc and the board. I the bloc began to lide down the board, the riction between the urace would no longer be tatic, but would be inetic, or liding, riction. Kinetic riction i typically le than tatic riction or the ame two urace in contact.

2 The ratio o the rictional orce between the urace divided by the normal orce acting on the urace i called the coeicient o riction. The coeicient o riction i repreented by the Gree letter µ (mu). Equation or the coeicient o tatic and inetic riction are max µ and µ, where i the tatic rictional orce and i the inetic rictional orce. ote that the coeicient o tatic riction i equal to ratio o the maximum rictional orce and the normal orce. The tatic rictional orce will only be a high a it ha to be to eep a ytem in equilibrium. When you draw a ree-body diagram o orce acting on an object or ytem o object, you would want to include the rictional orce a oppoing the relative motion (or potential or relative motion) o the two urace in contact. Example 1: A bloc o wood ret on a board. One end o the board i lowly lited until the bloc jut begin to lide down. At the intant the bloc begin to lide, the angle o the board i. What i the relationhip between the angle and the coeicient o tatic riction μ? Solution : Let draw the ree-body diagram or the bloc on the inclined plane: y x mgco At the intant the bloc i jut about to move, the maximum rictional orce directed up the incline i equal and oppoite to the +x-component o the weight down the incline, and the normal orce i equal and oppoite to the y-component o the weight.

3 max Then mg in mg co µ max mg in tan mg co Thi expreion i only valid or the cae in which the tatic rictional orce i maximum. Example : Ater the bloc in Example 3 jut begin to move, hould the board be lowered or raied to eep the bloc moving with a contant velocity down the incline? Explain your anwer. Solution : Since the coeicient o inetic riction i generally le than the coeicient o tatic riction or the ame two urace in contact, the bloc would require le orce directed down the incline (mgin ) to eep it liding at a contant peed. Thu, the board hould be lowered to a maller jut ater the bloc begin to lide to eep the bloc moving with a contant velocity. Practice Problem 1.) A bloc o ma m ret on an air table (no riction), and i pulled with a orce probe, producing the orce v. acceleration graph hown below.

4 (a) Determine the ma o the bloc. ewton nd law tate that m net. Thi ratio i the lope o the v. a a graph. So, 15 0 m lope 3g a 5m / 0 The bloc i now placed on a rough horizontal urace having a coeicient o tatic riction μ 0., and a coeicient o inetic (liding) riction μ 0.1. (b) What i the minimum value o the orce which will caue the bloc to jut begin to move? ( 0.)( 3g)( 10 m / ) µ µ mg 6 min L µ 0. ; µ 0.1 (c) Ater the bloc begin to move, the ame orce determined in part (b) continue to act on the bloc. What i the acceleration o the bloc? Once the bloc begin to move we mut ue the coeicient o inetic riction to determine the rictional orce. ( 0.1)( 3g)( 10m / ) µ µ mg 3 Then the net orce acting on the bloc i to the right. The acceleration o the bloc i a net m 3 3g 1m /

5 (d) The orce i now tripled to 3, which then pull the bloc up an incline o angle 0 and having a coeicient o inetic riction μ 0.1. i. Draw the ree-body diagram or the bloc a it i being pulled up the incline. 3 mgin mgco ii. Determine the magnitude o the rictional orce acting on the bloc a it µ µ mg co 0.1 3g 10m / co 0. lide up the incline. ( )( )( ) mg 8 iii. Determine the acceleration o the bloc a it i pulled up the incline. ( 6 ).8 ( 3g)( 10m / ) in 0 3 mg in 3 5 a net m 5 3g 1.67 m /

6 .) The diagram repreent a truc on a hill a it id to a top. The gravitational orce on the truc ha been reolved into component parallel (gp) and normal (g) to the ramp. Ue inormation in the diagram to calculate the acceleration o the idding truc. What i the acceleration o the truc coming to a top? To olve thi, you will ubtract by gp, then divide by the ma. ( ) g 5 m/ 3.) Here i the ame ind o diagram repreenting a truc on a hill a it id to a top. The gravitational orce on the truc ha been reolved into component parallel (gp) and normal (g) to the ramp. Ue thi inormation: gp 9000; 7000 & g 000. Ma i 1300 g. Calculate the acceleration o the idding truc. To olve thi, you will ubtract by gp, then divide by the ma. ( ) g 3.85 m/