Simple Harmonic Motion MC Review KEY

Transcription

1 Siple Haronic Motion MC Review EY. A block attache to an ieal sprin uneroes siple haronic otion. The acceleration of the block has its axiu anitue at the point where: a. the spee is the axiu. b. the potential enery is the iniu. c. the spee is the iniu.. the restorin force is the iniu. e. the kinetic enery is the axiu. *C. The acceleration is a ax. at the turnaroun points---this is where the sprin is axially stretche or copresse an so the pull back to equilibriu is the stronest. By efinition of a turnaroun point, this is where the spee is zero.. A stuent easures the axiu spee of a block uneroin siple haronic oscillations of aplitue A on the en of an ieal sprin. If the block is replace by one with twice the ass but the aplitue of its oscillations reains the sae, then the axiu spee of the block will: a. ecrease by a factor of 4. b. ecrease by a factor of. c. ecrease by a factor of. reain the sae. e. increase by a factor of. * C. Copare TME s when all the enery is kinetic (at the equilibriu) an all of the enery is store (at turnarouns): MVax A Solvin for V : V Max A Thus, oublin the ass woul ecrease the ax spee by a factor of

2 3. A linear sprin of force constant is use in a physics lab experient. A block of ass is attache to the sprin an the resultin frequency, f, of the siple haronic oscillations is easure. Blocks of various asses are use in ifferent trials, an in each case, the corresponin frequency is easure an recore. If f is plotte versus /, the raph will be a straiht line with slope of: 4 4 a. b. c e. 4 * D. Start with the forula for the perio of a sprin: T The frequency is the reciprical of the perio, so flip everythin: f Now,square everythin to atch what is raphe : f 4 Factor out the/, yiels : 4 4. A siple penulu executes siple haronic otion as it swins throuh sall anles of oscillation. If ax enotes the aplitue of the oscillations, which of the followin stateents is true? a. When = 0, the tanential acceleration is zero. b. When = ax, the tanential acceleration is zero. c. When = 0, the spee is zero.. When = 0, the restorin force is axiize. e. When = ax, the spee is axiize. *A. The tanential acceleration is cause by the coponent of weiht that is tanent to the path (as oppose to the centripetal acceleration neee for the penulu to travel in a circle). At the botto of its path, the weiht vector is actin raially own, which causes no acceleration. At any other position, a coponent of the weiht (sin ) is actin tanent to the path, causin the penulu to spee up or slow own.

3 5. When a ass is hun on a certain ieal sprin, the sprin stretches a istance. If the ass is then set oscillatin on the sprin, the perio of oscillation is proportional to: a. b. c.. e. * A. This proble cobines two concepts: the forula for perio an the efinition of equilibriu for a vertical sprin: T Tofin : use the fact that when a weiht of hans on the sprin it stretches a istance : Thus, the upwar force of thesprin so Substitutin this : T

4 6. A particle oves in a circle in such a way that the X- an Y-coorinates of its otion are iven in eters as functions of tie t in secons by: X = 5 cos (3t) Y = 5 sin (3t) What is the perio of revolution of the particle? a. /3 secon. b. 3 secons.. secons 3 3 e. secons f. 6 secons. * D. First off, on t be confuse by the fact that there is an X an a Y function. Reeber the phonoraph eo. Whether you just looke at the horizontal or just looke at the vertical position, either one woul oscillate in siple haronic otion, so just focus on one. Reeber that the forula for SHO is X = A cos ( t) So, the rotational spee is 3 raians/sec. We nee to convert this to the tie to coplete one revolution: secon raians T 3raians revolution 3

5 7. The isplaceent vs. tie for a particle in siple haronic otion is shown above. Which of the followin raphs shows the kinetic enery,, of the particle as a function of tie, t, for one cycle of otion? a. b. c.. e.

6 * B First off, you know the E can never be neative, which throws out raphs A, D, an E. Secon, E is proportional to velocity square. So, think about takin the erivative of the position raph an then squarin it. This eans ax s on the position raph becoe zeros of the E raph. This shoul square with what you know about SHO ax positions are turnaroun points = no E. 8. The lenth of a siple penulu with a perio on Earth of one secon is ost nearly: a. 0. eters. b. 0.5 eters. c eters...0 eters. e. 0.0 eters. *B. T sec (3) 0/s say 3.4 is about square both sies Note:if you on' t approxiate anythin, the answer is A ball is roppe fro a heiht of 0 eters onto a har surface so that the collision at the surface ay be assue elastic. Uner such conitions the otion of the ball is: a. siple haronic with a perio of about.4 secons. b. siple haronic with a perio of about.8 secons. c. siple haronic with an aplitue of 5.. perioic with a perio of about.8 secons but not siple haronic. e. otion with constant oentu. * D. The otion is not siple haronic because the position function of free fall is parabolic (constant acceleration), not sinusoial (acceleration that ecreases as object heas towars equilibriu). If you use kineatics to fin tie to fall you et.4 secons, so the tie to return to oriinal position is about.8 secons. The collision ust be elastic or the object will not return to its oriinal position.

7 Questions 0 an : 0. (984) A 0. k block is attache to an initially unstretche sprin of force constant = 40 N/ as shown above. The block is release fro rest at tie t = 0. What is the aplitue of the resultin siple haronic otion of the block? a. 40 b. 0 c. 4. e. * A. The release point is the top turnaroun point. The ifference between this point an equilibriu is the aplitue: Equilibriu : x (40N / )( A) (.k)(0 / s ) A 40

8 . (984) At what tie after release will the block first return to its initial position? a. s 40 b. s 0 c. s 0. s 5 e. s 4 *C This is the efinition of one full perio: T.k 40N / (993) A siple penulu consists of a k brass bob on a strin about.0 eters lon. It has a perio of.0 secons. The penulu woul have a perio of.0 secon if the: a. strin were replace by one about 0.5 eters lon. b. strin were replace by one about.0 eters lon. c. bob were replace by a.5 k brass sphere.. bob were replace by a 4.0 k brass sphere. e. aplitue of the otion were increase. * A They ive you a lot of excess inforation here to trick you. Reeber that the perio of a penulu epens only on its lenth an the planet it is on. You can check that a penulu on Earth of lenth eter oes have a perio of about secons. To cut its perio in HAF, you woul nee to reuce the lenth by a factor of FOUR, since it is uner a square root in the perio forula.

9 3. (974) The forces prouce by two sprins as they are stretche are shown in the raph above. Sprin inicate by the ashe line is linear (Hookian), but sprin is not. The perio of oscillation for a ass attache to sprin is: a. epenent on aplitue but never reater than for sprin. b. epenent on aplitue but never less than for sprin. c. epenent on aplitue but always equal to that of sprin.. inepenent of aplitue an never reater than for sprin. e. inepenent of aplitue an never less than for sprin. *A. This one is tricky. Because the sprin is nonlinear, the solution to the ifferential equation is not a sine function an the perio oes epen on the aplitue. If you look at the raph closely, you will see that the FORCE of sprin increases with isplaceent faster than the force for sprin. It shoul ake sense that if the restorin force is GREATER than it woul be for stanar siple haronic otion, the sprin will pull the ass back to equilibriu ore quickly, reucin the perio.

10 4. (974) An object is suspene fro a sprin whose ass is neliible copare to that of the object. The object is isplace slihtly, an the perio of its otion is observe to be T secons. The sprin is then cut in half an the object is suspene fro one of the halves. The object is isplace slihtly an its perio is observe to be T secons. The ratio T /T is: a. ½ b. c.. e. * B T Cuttin the sprin in half actually DOUBES the sprin constant becuase there are fewer coils, so less totalstretch for a iven wei ht. T So, the ratio is : T T

11 5. (004, 46 %) A siple penulu has a perio of secons for sall aplitue oscillations. The lenth of the penulu is ost nearly: a. /6 eters. b. ¼ eters. c. ½ eters.. eters. e. eters. * D T