FREE BODY DIAGRAMS! For each of the layouts, draw the f.b.d.s for the bodies in the system. (The solutions follow--try each before looking!)! 3.)!

Transcription

1 1.)! FREE BODY DIAGRAMS! For each of the layouts, draw the f.b.d.s for the bodies in the syste. (he solutions follow--try each before looking!)! 3.)!! 1.)! 3.)! 2.)! 4.)!! 2.)! 4.)!

2 1.) answer 3.) answer! ( )! ( )g ( )g h g 5.)! 7.)! 2.) answer 4.) answer!! ( )g h g ( )g h g 6.)! 8.)!

3 5.)! 7.! 9.)! 11.)! 6.)! 8.)! 2 10.)! 12.)!

4 5.) answer! 7.) answer! ( )g ( )g g 13.)! 15.)! 6.) answer! 8.) answer! 2 ( )g ( )g ( 2)g 14.)! 16.)!

5 9.)! 11.)! 7 2 (7 ass oing to right initially with 2 ass breaking loose)! 2 17.)! 19.)! 10.)! (7 ass oing to left initially with 2 ass just barely holding on)! )! 7 2 frictional on both surfaces and assue eeryone has just broken loose and is accelerating in its appropriate direction (that is, there s no static friction but there is kinetic friction).! (ote that because there are no external force in the syste in the horizontal, the syste s center of ass ust stay where it is. hat eans any otion of the 7 ass ust be countered by otion of the 2 ass I HE OPPOSIE DIRECIO.) If this sees too obscure to wrap your brain around, just take a quick look at the solution and go on. Don t take a lot of tie on this!! 18.)! 20.)!

6 9.) answer! 11.) answer! 7 2 (7 ass oing to right initially with 2 ass breaking loose)! 2 ( )g ( 2)g Coent: As in #10, graity on the hanging ass goerns, so the hanging ass ust accelerate downward and the 7 ass ust accelerate (speeding up) to the right. Een though the 2 ass breaks loose, it will get dragged along to the right by its interaction with the 7 ass. As the only force acting in the horizontal on the 2 ass is kinetic friction, that force ust be to the right. hat eans a kinetic frictional force ust also act on the 7 ass to the left (ewton s hird) diinish the agnitude of the 7 ass s acceleration to the right.! ( 2)g floor g floor ( 7)g 21.)! 23.)! 10.) answer! 7 (7 ass oing to left initially with 2 ass just barely holding on)! Coent: otice that graity acting on the hanging ass is the only external force in the syste (disconnect and nothing accelerates). hat eans it goerns the net acceleration. As the hanging ass is accelerating downward, both the 7 and 2 asses ust be accelerating to the right (een though they are oing to the left), which eans they are slowing down and there better be a net force to the right in both cases. he only place the 2 guy can get its right-directed force is fro static friction between it and the 7 ass. hat eans there s a static frictional force on the 7 ass to the left (ewton s hird Law). Also, there s a kinetic frictional force on the 7 ass due to the floor and two different noral forces to deal with. Fun, eh?! 2 µ 1,static ( 2)g µ 1,static floor ( 7)g g,kinetic floor 22.)! 12.) answer! ( 7)g 7 ( 2)g floor 2 g floor frictional on both surfaces with elocities shown (this is tricky):! Coent: As before, the hanging ass accelerates downward aking, in this case, the 2 ass accelerate to the right. here will be kinetic friction between the 2 and 7 ass with that frictional force retarding 2 s acceleration by being directed to the left. By the sae token, the 2 ass will try to drag the 7 ass to the right ia that sae kinetic frictional force (L). In other words, you ight think that both the 2 and 7 blocks would accelerate to the right. he proble is that the center of ass of this syste has to stay in place (there is no outside force acting in the horizontal, so the center of ass stays put). he only way that can happen is if the 7 ass accelerates to the left. But how could it do that? It does it due to the tension force in the line that essentially acts on the 7 ass to the left (look at the sketch). If the pulley was attached to the table, this wouldn t be the case, but because it is attached to the 7 ass, you hae to include that tension force as it act both in the horizontal and ertical on the 7 ass! Een ore fun!! 24.)!

7 13.)! (elocities of 5 and asses are down incline--acceleration assued UP the incline with ass breaking loose)! ) answer! (elocities of 5 and 2 asses are down incline--acceleration assued UP 1 5 the incline and ass has broken loose)! Coent: Don t take a lot of tie on this as it is tricky. If both the and 5 blocks are oing down the incline, and if both are slowing (as ust be the case if the acceleration is UP the incline), how would the unencubered ass act relatie to the 5 ass with a tension pulling back on the 5 ass? he 5 ass is being slowed down by the tension force on it, whereas the ass will slow down OLY due to friction between it and the 5 ass. hat eans the kinetic friction force on the ass ust be Up the incline. Due to L, a reaction kinetic friction force ust be exerted on the 5 ass down the incline. here will also be a kinetic friction force due to the table on the 5 ass that is up the incline (the 5 guy is oing down the incline), and there are two noral forces to deal with.! ( )g floor g floor ( 5)g 25.)! 27.)! 14.)! (elocities shown with ass breaking loose and both accelerating DOW incline, which eans they are slowing down)! 26.)! ) answer! 1 Coent: Don t take a lot of tie on this as it is tricky. If both the and 5 blocks are oing up the incline, and if both are slowing (as ust be the case if the acceleration is DOW the incline), what is otiating the asses to slow? It s the coponent of graity down the incline. he coponent of the 5 ass will be larger than the coponent of the ass, so the 5 ass will slow down faster (the ass also has a tension force pulling it UP the incline). hat eans the 5 ass will be oing slower than the ass and the ass will be oing toward the top of the incline RELAIVE O HE 5M MASS! In other words, the kinetic frictional force on the ass will be DOW the incline. L aintains that there ust, therefore, be a kinetic friction force on the 5 ass due to the ass that is UP the incline (see f.b.d.).! floor (elocity of 5 ass shown with ass breaking loose and both accelerating DOW incline)! ( )g floor ( 5)g g 28.)!