Group Problem Week 9
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Apr 3, 2024
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I Physics 131 Group Problems: Week 9 Leaming Goals After working through this worksheet, students will be able to: 1. Draw a coordinate system either aligned with the force or with the displacement vector; use it to find the parallel component of the other; and use the parallel component to find the work done by the force. 2. Graphically determine the work done by a force using a force vs. position graph. 3. Determine the net work done on an object or system by adding up the work done by each individual force acting on it. 4. Use the net work done on an object or system to determine its change in kinetic energy. Problem 1: Calculating work using force and displacement components To find the work done on an object by a force, we need to define a new coordinate system that aligns with either the force or the displacement vectors. This is just like what we did when finding the torque a force exerts on an object; the difference is that we're now concerned with the parallel component of either the force or the displacement. A train moves 20 km along a track to the north-east. As it moves, the wind blows against the side of the train, exerting a 150 kN force at an angle of 60° from the displacement. ,s• w: ... ,s O '
00
" ,.1 A. Compute the work done on the train using the parallel component of the force: W = F
11 lctl, where dis the displacement and F
11 is the component '
·
: of the force parallel to the displacement. ,. 1. On the diagram at right, sketch a coordinate system which has one coordinate axis parallel to the displacement, and one perpendicular to the displacement. / l.: 2. Use your i:oordinate system to find the parallel component of the force. F,
,
:. IF I CA>l~ =-
\So \L
'
"' o,~
. (oo 1 \!-i, 3. How much work does the wind do on the train? v-> f II I?-\ ; 7 Soo o -1-
,z..,o coo= \ -c; • ,c, .. J B. Compute the work done on the train using the parallel component of the displacement: W = d
11
IFI, where.Fis the force and d
11 is the component of the displacement parallel to the force. 1. On the diagram at right, sketch a coordinate system which has one coordinate axis parallel to the force, and one perpendicular to the fore~. F 2. Use your coordinate system to find the parallel component of the displacement. ~
., ,.,[
a\
c...o~ -:.1.,,0 c"~\oO ::. \Oo
0
o~ 3. How much work does the wind do on the train? w==-
O-t1 Ir/= (oOO' \"St:> (J'>b -:. \,S· 10" 1 1
Problem 2: Work due to a single force Three ice skaters are skating across an outdoor ice rink while a wind exerts a drag force on them. The skaters each move the same displacement to the right, and the magnitude of the drag force is the same. The direction of the drag force is different in each case, as shown in the diagrams at right. Case I ,i ~J
. VJ-:;~.~ A. Rank the three skaters according to the magnitude of the work done by the wind on them, from largest to smallest. If the work is zero for any skater, state so explicitly. J ,i
,2 F;~
' = f ~e,o\e I > -2. > J •~ c:i L"'" ~"
~~\' . . . . c.,,..,,_~\•-..J
' B. Is the kmetlc energy of any of the skaters mcreasmg? If so, which ones? Case 3 F;-s! LI J C. Suppose the wind blew on a fourth skater such that the skater's kinetic energy decreased. In the space below, sketch two different possible diagrams for this skater, showing the direction of their displacement and the direction of the wind force on them. (There are an infinite number of possible diagrams that would all work, each with different angles and magnitl,ldes of the drag force. You should draw two of them.) .,. C, ,,, _t
;.1 ;, t "' ' D. Compute the work done by the wind force on the skater for case 2, if the magnitude of the wind force lfff is 12 N, the angle that the force vector makes with the horizontal direction is 40°, and the magnitude of the displacement vector is 2 m. 2
Problem 3: N
et work done on a single object by multiple forces In this problem we will compute the net work done by several different forces on an object and use the work-energy relation W = t:.K to compute the change in the kinetic energy of the object. Consider a person moving a box across a floor by exerting a force Fpull, with a magnitude of 80 N at an Fpull angle of 40° from the negative x-axis. The mass of the box is 10 kg, and the floor exerts a friction force on the box with a magnitude of 45 N. The box is dragged 3 m to th.e left. A. Draw a point free-body diagram of the box. ~J~F•qs, .,. B. Since the displacement is horizontal, it will be easie's't to use a coordinate system aligned C. with the displacement and find the work usirig" the parallel component of each force. For each force, first find its parallel component (including the sign) and then find the work it does. 1. The gravitational force: Fu= 0 W= O--s 2. The normal force: Fu= 0 W=
O-S 3. The pull force: Fi1 = '60cos ~v a W= 0\. '
'b r--
' • :s = ,~')_,,'1--S 4. The friction force: Fi1 = -~~t-1 W= r-11 ·
~
-: -\~6'S What is the net work done on the object? 6vJ : v,) I -I i,J '2. t W 1' v-J L\ :: 0-+ 0 +-
1"(1
.Gi -
l?.
s --
4 .~ 1 D. What is the kinetic energy of the box after it has been dragged for a distance of 3 m, assuming that it started at rest? vJ = I<... 6 =-
~i -
\c
, Lt i. = -
== "'i ·
1
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