Physics 20 Lesson 17 Elevators and Inclines

Transcription

1 Phic 0 Leon 17 Elevator and Incline I. Vertical force Tenion Suppoe we attach a rope to a teel ball and hold the ball up b the rope. There are two force actin on the ball: the force due to ravit and the applied force of the rope on the ball. Another nae for thi kind of applied force i the tenion force. The free bod diara for the ball i: If we appl a tenion force reater than the force due to ravit, the reult i upward acceleration. If we appl a tenion force aller than the force due to ravit, the reult i downward acceleration. If T and are balanced the acceleration i zero. Either the ball i at ret or it i ovin with contant velocit. T Exaple 1 A rope i attached to a 50 k a. What i the tenion force required to accelerate the a upward at.0 /? T Exaple = 50 k(9.81 / ) = 490 ET = T + a = T + 50 k(+.0 / ) = T + ( 490 ) T = +590 or 590 upward A rope i attached to a 50 k a. What i the tenion force required to lift the a upward at a contant peed? T = 50 k(9.81 / ) = 490 ET = T + 0 = T + (ince a = 0, ET = 0) 0 = T + (- 490 ) T = +490 or 490 upward Dr. Ron Licht

2 Exaple 3 A rope i attached to a 50 k a. If an upward force of 80 i applied on the rope, what i the reultin otion of the a? Elevator T = 80 = 50 k(9.81 / ) = 490 ET = T + a = T + T 80 ( 490) a = 4. / 50k The a accelerate downward at 4. /. When ou are tandin inide an elevator ou experience the effect of the otion of the elevator. When ou enter the elevator and pre the button, ou feel the noral aount of our weiht on our feet. When the elevator accelerate upward, ou feel lihtl heavier than noral. A the elevator continue up at contant peed ou feel our noral weiht aain, but a the elevator low to top at our floor ou feel lihtl lihter than noral. Wh do ou feel different thin a the elevator otion chane? Let u anale thi a little ore cloel. What ou feel, we call it our apparent weiht, i not the pull of ravit down on ou, rather what ou feel a our weiht i the floor puhin up on ou. (If ou have trouble rapin thi idea, iaine what ou feel our weiht to be if ou fall throuh the air. Since there i nothin puhin back at ou or holdin ou up, ou feel weihtle.) In other word, the apparent weiht ou feel i actuall the noral force of the elevator floor actin on ou ( apparent = ). urther, the noral force chane due to the otion of the elevator floor. To ee how thi work, conider the equation for net force fro the free bod diara. ET = + Since act in the (+) direction and act in the ( ) direction we et: ET = Rearranin the equation, our apparent weiht ( ) i iven b the equation: = ET + Inpection of the equation reveal that if ou are acceleratin up ( ET > 0) our apparent weiht will be reater. If ou are acceleratin down ( ET < 0) our apparent weiht will be aller, and when ou are at ret or ovin at contant peed ( ET = 0) our apparent weiht will be our noral weiht. Dr. Ron Licht

3 Exaple 4 If ou norall weih 706, what i our apparent weiht if ou are in an elevator that i lowin down at the rate of 1.65 /? firt calculate fro 706 = 7 k 9.81 = 706 (noral weiht = force due to ravit) ET = + = ET = a = 7 k( 1.65 / ) ( 706 ) = 587 Rocket The picture to the riht how the firt rocket ever launched fro Cape Canaveral in The thrut of a rocket doe two thin. (1) It overcoe the force due to ravit actin on the rocket and () it accelerate the rocket upward. The action force i the rocket enine puhin ae down out of the rocket. The reaction force i the ae puhin up on the rocket. thrut Exaple 5 A 100 k rocket produce of thrut. What i the velocit of the rocket 45 after launch? ET Thrut v v1 a t a Thrut v v at Thrut a ( 1177) a 100k a v (45 ) v 684 Dr. Ron Licht

4 II. Inclined plane When we place an object on a horizontal urface the force of ravit act traiht down toward the centre of the Earth and the noral force act traiht up. Recall fro Leon 15 and 16 that the noral force i the reaction force of the urface to an force actin on the urface. The anle between the urface and the reaction force i alwa 90 o (i.e. a noral anle). When the urface i horizontal, act exactl oppoite and the net force i zero. ow iaine that we lowl incline the urface fro the horizontal to oe anle. The ravitational force continue to act traiht down and the noral force continue to act at 90 o to the incline. But note that no loner act oppoite. Soe of the ravitational force i directed into the incline and oe i directed down the incline. Therefore, we break up the ravitational force ( ) into coponent. One coponent ( x ) act down the incline and the other ( ) act into the incline. ote that counter. An anali of the eoetr (ee optional ection below) reveal that =. Thu if we are iven the anle of inclination, the coponent a be calculated: x x in or in co or co A tated above, the noral force counteract the vertical coponent of the force of ravit: co Dr. Ron Licht

5 Exaple 6 A 30 k object i on an inclined plane et at 40 to the horizontal. What i the acceleration experienced b the object if the coefficient of friction i 0.5? co ince k(9.81 )co x in Calculate f f 30k(9.81 )in 40 x 189. x f 0.5(5.4) f The net force i ET x f ET ET The acceleration i ET a a 30k a 4.43 down theincline III. Proof that = (optional) a o ro abc we know that 90. Since and ide ab are parallel, the anle between and ca i. c b The anle between and ac i 90 o. o 90 o o Since 90 and 90 then Dr. Ron Licht

6 IV. Practice proble 1. A 490 object i upended fro a rope. a. What i the force required to raie it verticall at 5.00 /? (490 ) b. What i the force required to accelerate it down at 3.00 /? (340 ). A 0.0 k a i placed on a 50 o incline. If the coefficient of friction i 0.35, what i the acceleration of the a? (5.31 / ) 50 o Dr. Ron Licht

7 V. Hand-in Ainent 1. or each ituation below, draw accurate free-bod diara howin all force actin on the rock. A. Static B. Static C. Slidin without friction. D. Static friction prevent lidin. E. Static. Tied to a rope and pulled traiht upward. Acceleratin upward at 9.81 /. o friction. G. Tied to a rope and pulled traiht downward. Acceleratin downward at 19.6 /. o friction. Dr. Ron Licht

8 . A rope i ued to lift a 4.0 k rock verticall up at 0.5 /. What i the tenion in the rope? (39 ) 3. A jet accelerate verticall up at 8.5 /. What force doe the exhaut a exert on the 4400 k jet? (8.1 x 10 4 ) 4. A 360 force i applied horizontall to a 150 box which experience a force of friction of What i the net acceleration of the box? (18.6 / ) 5. A.0 k pendulu han in an elevator. Calculate the tenion in the trin upportin the pendulu if the elevator ove: a. with zero velocit (19.6 ) b. downward at a contant velocit of.5 / (19.6 ) c. upward at a contant velocit of.5 / (19.6 ) d. downward at a contant acceleration of.0 / (15.6 ) e. upward at a contant acceleration of.0 / (3.6 ) 6. A an eaure the acceleration of an elevator b uin a prin balance. He faten the cale to the roof, and upend a a fro it. The cale read 98 when the elevator i at ret, and 93 when the elevator i ovin. a. What i the acceleration of the elevator? (0.50 / ) b. In which direction i the elevator acceleratin? (down) 7. (Bonu) A fih han fro a prin cale upported fro the roof of an elevator. If the elevator ha an upward acceleration of 1. / and the cale read 00, what i the true force of ravit on the fih? (b) Under what circutance will the cale read 150? (c) What will the cale read if the elevator cable break? (1.8 x 10, 1.5 / down, 0) 8. A.5 k object i allowed to fall down a 60 o incline which ha a coefficient of friction of 0.1. What i the object' acceleration? (7.91 / ) 9. A 10.0 k a i allowed to accelerate down a 0 frictionle inclined plane. What i the block' final velocit if the incline i at an anle of 45 o? (16.7 /) 10. A 5.0 k a i on an incline which ake an anle of 50 o with the horizontal. The incline ha a coefficient of friction of a) If the a i releaed fro ret, at what rate doe it accelerate down the incline? ( 6.88 / ) b) What force ut be applied to caue the a to accelerate at.0 / up the incline? (50.65 ) Dr. Ron Licht