PHYSICS 211 MIDTERM I 22 October 2003

Transcription

1 PHYSICS MIDTERM I October 3 Exm i cloed book, cloed note. Ue onl our formul heet. Write ll work nd nwer in exm booklet. The bck of pge will not be grded unle ou o requet on the front of the pge. Show ll our work nd explin our reoning (except on #). Prtil credit will be given (not on #). No credit will be given if no work i hown (not on #). If ou hve quetion, rie our hnd or come to the front.. ( point) For ech of thee multiple choice quetion, indicte the correct repone (A, B, C, or D (where needed)) on the pge for problem in our exm booklet. i) Two block re puhed cro frictionle floor b horizontl force F pplied to block. I the mgnitude of F (the force on block due to block ), greter thn, le thn, or the me the mgnitude of F? A) Greter thn. B) Le thn. C) The me. ii) To drive from point A to point B, there re four poible route, hown t right. If the time to drive ech route i the me, long which route i the verge peed gretet? A) B) C) 3 A D) 3 F m m B iii) The m m i ttched b rope to pot t the upper end of the rmp. Wht hppen to the mgnitude of the norml force on the block (due to the rmp) the ngle θ of the rmp i increed? A) It incree. B) It decree. C) It doe not chnge. m θ iv) The figure t right how three ditinct poibilitie for the velocit nd ccelertion of prticle t prticulr intnt. For which poibilit (A, B, or C) i the peed of the prticle not chnging t thi prticulr intnt? v v v A B C v) Two bll re thrown imultneoul in the ir nd follow the prbolic trjectorie hown t right. Which bll h the lrget mgnitude of the verticl component of velocit when it hit the ground? A) B) C) The bll hve the me verticl component of velocit.

2 . ( point) The grph below how the velocit of our cr ou trvel from home (trting t t = ) to the tore (rriving t t = ): velocit (m/) time (econd) ) Drw grph of the ccelertion of our cr during the journe. b) How fr did ou trvel from our houe to the tore? c) Wht w our verge velocit during the time intervl -> econd? d) Wht w our verge ccelertion during the time intervl -> econd? 3. ( point) A bll i thrown from the ground into the ir. When the bll i t height of.8 m, the velocit i oberved to be v r = 9. mˆi + m ˆj ( î horizontl nd ĵ upwrd). Aume g = m/. ) To wht mximum height bove the ground will the bll rie? b) How fr doe the bll lnd from where it w thrown (uming flt ground)? c) How long doe the bll remin in the ir?. ( point) A 5 kg bowling bll i dropped from tower into deep vt of melted chocolte. When the bll hit the chocolte it h peed of 8 m/. The bll come to ret in the chocolte fter trveling ditnce of 8 m. Aume g = m/. () Wht i the ccelertion of the bll in the chocolte, uming it remin contnt? (b) Wht i the force exerted b the chocolte on the bll it i moving in the chocolte? (c) How long doe it tke for the bll to come to ret fter entering the chocolte? 5. ( point) Conider pulle tem in the initil tte hown t right. The green dog i up. The ellow dog i down. The green dog h m (m ) three time the m (m ) of the ellow dog. Ignore the m of the bucket, the rope, nd the pulle. Ignore friction. Grvit (g) point down. () Drw free-bod digrm for ech dog. (b) Find the ccelertion of the dog, in term of g. (c) Find the tenion in the rope. (d) Compre (i.e., >, <, or =) the tenion in the rope to the weight of the green dog? I thi wht ou would expect? Wh? m m

3 PHYSICS MIDTERM I SOLUTIONS October 3. i) B The force F h to ccelerte both me, while the force F onl h to ccelerte m m. Since the block both ccelerte together, the mgnitude of F i le thn the mgnitude of F. ii) D Route h the longet pth from A to B. Since verge peed i totl ditnce trveled divided b time tken, route will hve the lrget peed. iii) B The norml force blnce the component of grvit tht i perpendiculr to the inclined plne. A the ngle θ incree, thi component of grvit will decree, cuing the norml force to decree. iv) A In ce (A), the ccelertion i perpendiculr to the velocit, which i the itution for uniform circulr motion. The velocit chnge direction, but the peed i contnt. v) A For n bll thrown up in the ir, the verticl component of velocit upon return i oppoite the originl verticl component of velocit. Since bll goe to higher height, it mut hve hd lrger initil verticl component of velocit, o it hit the ground with lrger verticl component of velocit.

4 PHYSICS MIDTERM I SOLUTIONS October 3. ) The velocit i onl chnging during three intervl of the motion. During ech of thee, the ccelertion cn be found with = v/ t, which men find the lope. The plot i hown below. ccelertion (m//) time (econd) b) Since the poition i the integrl of the velocit, the totl ditnce trveled cn be found b finding the re under the velocit curve. Note tht ech rectngle in the figure h n re of m. There re 6 rectngle under the curve, o the totl ditnce trveled i x = 6 x m = m. c) The verge velocit i the diplcement divided b the time: v x m = = t v =. m/ d) The verge ccelertion i the chnge in velocit divided b the time, but the initil nd finl velocitie re both zero, o there i no chnge in velocit nd hence no verge ccelertion. = m/

5 PHYSICS MIDTERM I SOLUTIONS October 3 3. Put the origin t the poition where the bll w thrown (t t = ). Let t be the time when the velocit i oberved, t be the time when the mximum height i reched, nd t 3 be the time when the bll return to the ground. h =.8 m H 3 O R ) Ue the height = h nd the velocit v r = 9. m/ ˆ i + m/ ˆj to find the initil velocit, which will help olve the ret of the problem: v = v + ( ) v = v + ( g)( h ) v = v + gh v = v + gh = ( m/ ) + ( m/ )(. 8m) = m/ At the top of the pth, v =, o we cn olve for the mximum height H: v = v + ( ) = v + ( g)( H ) H v ( m/ ) = = g ( m/ ) H = m b) We know tht for uch prbolic pth, t 3 = t (i.e., time up = time down). Since the horizontl velocit i unchnged during the flight, we cn olve for the rnge R: R= vxt3 = vxt v v = v gt t = ince v = g vxv 9 (. m/ )( m/ ) R = = g m/ R= 36m c) The time of flight cn be found uing the time eqution found bove: t t v m t / = = = g m/ = 3 3 3

6 PHYSICS MIDTERM I SOLUTIONS October 3. Let the -dimenionl coordinte tem hve it origin t the urfce of the chocolte o tht =, v = -8 m/. The bll come to ret t = -d = -8 m, o we know tht v =. -8m ) To find the ccelertion ue: v = v + ( ) = v + ( d ) v ( 8m 6m = = / ) / = d 8 ( m) 6m = m/ b) Firt drw free bod digrm for the bll. Then write down the eqution of motion. F mg= m F = m+ mg= m( + g) F = 5kg( m/ + m/ ) F = 7N F mg c) The time for the bll to come to ret i found from: v = v + t = v + t v 8m t = = ( / ) m/ t =

7 PHYSICS MIDTERM I SOLUTIONS October 3 5. ) Cll the tenion in the rope T, which i the me for ech dog. Since the green dog i hevier, we expect it to go down, nd o we ume it ccelertion to be down hown, which men tht the ellow dog will go up with the me ccelertion, lo hown. Green dog Yellow dog T T m m m g m g b) The eqution of motion for the two dog re mg T= m T mg = m Adding the two eqution together, nd uing m = 3 m, we cn find : mg mg = ( m+ m) m m m m g 3m m m m g m = = = m g g = c) We cn find the tenion from either of the eqution of motion: g T = m( g ) = m( g ) mg T = mg or T = 3 d) From bove we ee tht mg T = T < m g So the tenion i le thn the weight of the green dog. Thi i wht we expected, ince we id originll tht we expected the green dog to fll down. Thi mut men tht the force down, m g, i greter thn the force up, T, giving net force down. 5