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?????? ?2??????????? ???????(1)
?2? ????????? ????
?????
1(C)?2(E)?3(D)?4(C)?5(C)?6(B)?7(C)?8(C)?9(B)?10(C)?11(D)?12(A)?13(D)
?????
(1). ?2=12rad/s?A=0.027J (2). 290J (3). 3J (4). 18 Ns
??3(5). ti?2tj (SI) 3
(6). 16 Ns?176 J (7). 16 Ns ?176 J (8). l0k/M?(9). i?5j (10).
Ml0k
M?nmM
??
2mv? ?????????45
?????
1. ??????m????x??????????????????????????????????x????????f??k/x?k?????????? x=A???????????x=A /4????????
??????????
2
kdvdvdxdv
?m?m??mv2
dtdxdtdxx
vA/4
dxk
,vdv??dx? vdv??k2?mx2?mx0A
f??
12k413
v?(?)?k 2mAAmA
?v?6k/(mA)
2. ???m??????v 0???????????????????????????????????????????????
(1) ????????????????????(2) ????????????
??(1) ????????????v??????
?Kv?m
? ?
Kdvdt?,mv
dv
dt
tvKdv??dt??
mv0v0
?v?v0e(2) ????? ????
v?
?Kt/m
dx
dt?Kt/m
dtdx?v0e
x
t
?
dx?v0e?Kt/mdt
?Kt/m
?
? x?(m/K)v0(1?e
)
xmax?mv0/K
dvdvdxdv
???? ?Kv?m?m()()?mv
dtdxdtdxm
?dx??dv
Kxmax0
m
?dx???dv
K0v0
? xmax?mv0/K
3
3. ??????x?ct??????????????c????t???????????????????????????k??????x?0???x?l?????????
???x?ct3???????? v?
2
dx
?3ct2 dt
24
4
???????????f?kv?9kct?9kcx??????????
?27l W??dW =??9xdx =
07
l
4. ????2 kg?????xy??????????F?4i?24tj (SI)????t = 0
??
2
?
????
????????v0?3i?4j (SI)??t = 1 s?????????????Fn.
????2
??? a?F/m?2i?12tj
?????2
?a?dv/dt? dv?(2i?12tj)dt
?
tv
???2
?dv??(2i?12tj)dt
????3
? ? v?v0?2ti?4tj
??????33
?v?v0?2ti?4tj?(3?2t)i?(4?4t)j
??
?t = 1 s?? ? v1?5i ?x?
???
????an?ay??12j
?v0
???
?Fn?man??24j (SI)
5.??????????????v0??????????????????m0???????????????????
????????????????
(1) ??????????
(2) ????????????
(3) ???????????????????????????????
??(1) ?????t?????????????????????????F ?????????? F?t?(M?m0?t)v0?Mv0 ??? F?m0v0(2)P?Fv0?m0v0
2
12
? m0v0
2
???????????????E?P
1
EK/E??50?
2
(3) ???????????? EK?
??50???????????????????????????????????
6.??????l????m????????????????? ??????a???????????????????????????????
?a
(1)?????????????????????????(2)???????????????
??(1)??????.
????????????y,??????? l?a
y
f??mg
l
????? Wf? =
?
l?a
fdy???
l?a
m
gydy l
(l?a)2
112
? mv2?mv0
22
?mg
2l
y2
l?a
=?
?mg
2l
(2)???????????????? ?W?
?? ?W = W P?Wf?v0 = 0
mgmg(l2?a2)
xdx?WP =?Pdx=?ala2l
?mg(l?a)2
???? Wf??
2l
l
l
mg(l2?a2)?mg1
?? ?(l?a)2?mv2
2l2l2
g(l2?a2)??(l?a)2???
?v?
?
7. ????????????O?????????????????????m = 4 kg???????????????????????????????
R0 = 0.5 m????????????4 m/s?????????????
????????????????? 600 N???????????????????R?????
????????????????????
?????????????????????????????v0?J0??0?v?J????
J0?0?J? ? ????????????????????????????
2mR0v0/R0?mR2v/R
?????R?R0v0/v?
??????????????????F?mv/R 1? ??????? R?(mR0v0/F)
2
2
1/3
2
?F = 600 N???????????????????R = 0.3 m
3
8.??????????????????????????r??????f?kr?k????????????????r???????????????????????
3
???????????? f?kr
??f?0?r????????, ???
???k
EP?WP???f?dr??3dr
rrr2
?k(2r)
?
? ???
1. ????????????????????????????????????????????????
?????
?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? ???????????????????????????????????????????????????????????????????????????????????????
?????????????
???????????????????????????????????????????????????????????????
2. ????????????????
?????
?t2????
?????????????????I??Fdt?P2?P1??P t1
??
??????????????P????????????F??????
3. ?????????????????????????????????????
?????
????????????????????.????????????????
???????????????????????????????????????????????????????????????????????????????????????????????.????????????????????????m ???????????????????h??????????????????????????????? mgh?????????????????
???????????????????????????????????????????????????????????????????????????????????????????????????????????h????????????????????????????.?????????? E0=0??????????????????v????mv 2/2??????? mv???????? E =mv2/2 ? mgh = E0=0.
4. ????????????????????????????????????????????????????????????????????????????????
?????
??????????
?
??????????v0??????????????????????????????????????????????????????
?
????????????????????????v????
?????
????v??v0?v?v?????T?????????????
???????????????????????????????????????????????????????????
5. ?????????????????????????????????????????????????? ?????
??????????????????????
????????????????
?????? ?2??????????? ???????
?2? ????????? ????
?????
1(C)?2(E)?3(D)?4(C)?5(C)?6(B)?7(C)?8(C)?9(B)?10(C)?11(D)?12(A)?13(D)
?????
(1). ?2=12rad/s?A=0.027J (2). 290J (3). 3J (4). 18 Ns (5).
??t3i?2tj 3
(SI)
(6). 16 Ns?176 J (7). 16 Ns ?176 J (8).
l0k/M?
?
?
Ml0k
M?nmM
(9). i?5j
(10). 2mv? ?????????45 ?????
1. ??????m????x??????????????????????????????????x????????f??k/x?k?????????? x=A???????????x=A /4????????
2
?????????? f??k?mdv?mdv?dx?mvdv
x2
dt
dxdt
dx
? vdv??kdx2,?vdv???k2dx
mx0Amx
1v2?k(4?1)?3k
2mAAmA?v?6k/(mA)
2. ???m??????v 0???????????????????????????????????????????????
vA/4
(1) ???????????????????? (2) ????????????
??(1) ????????????v???????Kv?mdv ?
dt
Kdv?dt?,mv
Kdv
??dt??mv0v0
?Kt/m0
tv
?v?ve
(2) ?????
????v?dx
dt
dx?ve
?Kt/m
dt
x
?
dx?v0e?Kt/mdt
t
?
? x?(m/K)v(1?e)x?mv/K???? ?Kv?mdv?m(dv)(dx)?mvdv
?Kt/m
max
dtdxdtdx
?
xm
ax
dx??
mdv K
?dx???mdv
K
v0
?
3
xmax?mv0/K
3. ??????x?ct??????????????c????t???????????????????????????k??????x?0???x?l?????????
???x?ct3???????? v?dx?3ct
2
dt
???????????f?kv?9kct?9kcx??????????
2
24
W??dW
=?0?9kcxdx =?27kcl
7
l
4. ????2 kg?????xy????????????
?F?4i?24tj (SI)????t = 0????????
???
v?3i?4j (SI)??t = 1 s??????????????F.
2
n
???
????2
a?F/m?2i?12tj
?
??
a?dv/dt
?v?v0
?
???
dv?(2i?12t2j)dt
t
???2(2i?12tj)dt dv???
????3
? ? v?v0?2ti?4tj
??????33
?v?v0?2ti?4tj?(3?2t)i?(4?4t)j
??
?t = 1 s?? ? v1?5i ?x?
???
????an?ay??12j
?F
?
n
??
?man??24j
(SI)
5.??????????????v0????????????????
??m0????????????????????
(1) ?????????? (2) ???????????? (3) ??????????????????
???????????????
????????????? ??(1) ?????t?????????????????????????F
?????????? F?t?(M?m?t)v?Mv ??? F?mv (2)P?Fv?mv
200
(3) ????????????
EK?
12m0v0 2
?
???????????????E?P E/E?1?50?
K
2
??50???????????????????????????????????
6.??????l????m???????????????????????a???????????????????????????????
?a
(1)?????????????????????????
(2)???????????????
??(1)??????.l?a
????????????y,???
????
f??myg
l
00
????? Wf??l?afdy??l?a?mgydy l
=?mgy2l0
?a =??mg(l?a)2
2
l2l
(2)???????????????? ?W?
11
mv?mv? 22
2
2
?? ?W = W P?Wf?v0 = 0
mgmg(l2?a2)
WP =?aPdx=?axdx?
l2l
l
l
????2?????????????????????????
2 ????????? ????
2.1????????????
?
1. ?????????A?????????????????????F?????????A??????????F????????????
(A) sin?????(B) cos?????
(C) tg????? (D) ctg???????? (C)
?????
?????????????
Fcos??(mAg?Fsin?)??mAa,
?
?????a????? ???????????????? ?
dad?
?0,??tg???.
?????
?????????????????????
1.????m???????????????????????00???900?????????????????f?????????????????????????.????????????????????????0 ?????0??????????
(A)?(B)???sin??????(B)?(A)???tg??0???
??? (B)
?????
(1) ???????????????????f?mg
(??????0???0???f?????)
(2) ?????0? (tg??0??)???????? (3) ???0???????f??mgcos?,
sin?;
(????????0?90???f????) .
2.2????????????
1. ????????????????????????????????A?C??????????????????
(A) ???????????????????
(B) ????????? (C) ??????????????????? (D) ?????????? (E) ???????????????? (E)
?????
????????????????
Fn?m
?
2
A
R
,??Ft?m
d?dt
.
Fn?N?mgsin?,??Ft?mgcos?.
???????????A?C??????????????????????????????????
?????????????????????
1.1?????????????????????????? (A)???(B)????
??? (E)
?????
????????????????????????????????????????????????????????????????????????????????
2.3???????
1. ???????????????5kg?????????????????????70N???.?????????????.??????50N?? (A)???????(B)???????(C)???????(D)?????????? (D) ?????
??????????????????????????????50 N<70 N(?
???????)?????????????????
?????????????????????
1.1????????????????????????????????????????????????????????????????????
?????
????????????????????????????????????????
??????????????????????????????????
?(F??t????????????????????????????????????????????????????????????
2.4?????????
1. ?????????????
(A) ?????????????????? (B) ??????????????????? (C) ??????????????????? (D) ????????????????????????? (C) ?????
????????????????????????????????????????????????????????????????????
?????????????????????????
?????
???????????????????L?r?P?r?mv,?????????L?mvR?mR2????????????
??????????????????????????????????
?????????????????????
1.1 ????????????????????????
(A)???????????? (B)????????????
??? (A)
?????
???????????????????????????????????????????
?????????????????????
1.1.1 ???????????????????????
???????????????????????????????
????????????????????????????????????????????????????????
????????????????????
?
?iFi??0
?????????
?M?ii??0
???????????????????????????????????????????????????????????????????????
2. ?????????????????????????????????????????????????????????????????????????????????????? (A)????? (B)????? (C)????? (D)???????????? (C)
?????
??????????????????
????????????, ????????????????????????.
?????????m1?m2??m1= m2?? ? m1v1R?m2v2R? ? v1?v2.????.
?m1?m2???????????????????????????????????
?????????????????????
2.1?????????????????????
?????
?????????????????????????????????????????????????????????????????????????????????
?
??????L????????????????
?????
L?r?P?r?mv
??
r???????????????P????????????????????
??
????????r?v?????????????
L?mvr?mvR (r?R)
??????????????????????????????????????????????
??dLM?
dt
.
t2
??????????????????????????????????????????????????????
t1
??Mdt??L
???????????????????????????????????????????????????M?????????????????M???????????????????????????
2.5?????????
1. ??????????????v???t?????????????t1?t2??????W1 ???t2?t3??????
W2 ???t3?t4??????W3 ??(A) W1?0?W2?0?W3?0? (B) W1?0?W2?0?W3?0? (C) W1?0?W2?0?W3?0?(D) W1?0?W2?0?W3?0??? (C)
?????
???????W
??Fdx?
12mv2?
2
t
12
mv1,
2
t1?t2????????????W1=0?t2?t3????????????W2?0???t
3?t4?????????????????W3?0?
?????2??????????????????(1)????????
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