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7/28/2019 Pse 5e Problem 5.65
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A block of mass m = 2.00 kg rests on the left edge of a block of
larger mass M = 8.00 kg. The coeffi-
cient of kinetic friction between the two blocks is 0.300, and
the surface on which the 8.00-kg block
rests is frictionless. A constant horizontal force of magnitude
F = 10.0 N is applied to the 2.00-kg block,
setting it in motion as shown in Figure P5.65a. If the length L
that the leading edge of the smaller block
travels on the larger block is 3.00 m, (a) how long will it take
before this block makes it to the right side
of the 8.00-kg block, as shown in Figure P5.65b? (Note:Both
blocks are set in motion when F isapplied.) (b) How far does the
8.00-kg block move in the process?
In[2589]:= sumForcesXforces_ :
ApplyPlus, MapFunctionelt, elt1 Coselt2, forces
sumForcesYforces_ :
ApplyPlus, MapFunctionelt, elt1 Sinelt2, forces
In[2593]:= forces1 F, 0 , Fn1, 90 , Ff, 180 , Fg1, 270 ;
forces2 Ff, 0 , Fn2, 90 , Fg1, 270 , Fg2, 270 ;
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7/28/2019 Pse 5e Problem 5.65
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How long will it take before this block makes it to the
right side of the 8.00-kg blockIn[2647]:=
sumForcesXforces1 m a1,sumForcesYforces1 m 0,
Ff Fn1 k,
Fg1 m g,
sumForcesXforces2 M a2,
sumForcesYforces2 M a2,
Fg2 M g,
M 0,
xf1 xi1 vxi1 t 1 2 a1 t^2,
xf2 xi2 vxi2 t 1 2 a2 t^2,
xf1 xf2 L,
xi1 0, vxi1 0, xi2 0, vxi2 0,
F 0, L 0, g 0, k 0;
Reduce, t, xf1, xf2, a1, a2
. L 3, m 2, M 8, F 10, g 9.8, k 0.3
Out[2648]= xi2 0 && xi1 0 && vxi2 0
&&vxi1 0 && Fn2 g m M m k &&Fn1 g m
&&Fg2 g M &&Fg1 g m & & Ff g m k &&
F M g m2 k g m M k 0 &&
t 2 L m M
F M g m2 k g m M k
t 2 L m M
F M g m2 k g m M k
&&
M 0 && xf1 2 L M g m t2 k
2 M
&& xf2 L xf1 &&
t 0 && a1 2 xf1
t2&&a2
2 L xf1
t2&& F g k 0
Out[2649]= xi2 0 && xi1 0 && vxi2 0
&&vxi1 0 && Fn2 103.88 && Fn1 19.6
&&
Fg2 78.4 && Fg1 19.6 && Ff 5.88 &&t
2.12798 t 2.12798 &&
xf1 1
1648 5.88 t2 && xf2 3 xf1&& t 0 &&
a1
2 xf1
t2&&a2
2 3 xf1
t2
2 PSE 5E PROBLEM 5.65.nb
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7/28/2019 Pse 5e Problem 5.65
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How far does the 8.00-kg block move in the
process?In[2662]:=
sumForcesXforces1 m a1,
sumForcesYforces1 m 0,
Ff Fn1 k,Fg1 m g,
sumForcesXforces2 M a2,
sumForcesYforces2 M a2,
Fg2 M g,
M 0,
xf1 xi1 vxi1 t 1 2 a1 t^2,
xf2 xi2 vxi2 t 1 2 a2 t^2,
xf1 xf2 L,
xi1 0, vxi1 0, xi2 0, vxi2 0,
F 0, L 0, g 0, k 0
;
Reduce, xf2, xf1, a2, a1, t
. L 3, m 2, M 8, F 10, g 9.8, k 0.3
Out[2663]= xi2 0 &&xi1 0 &&vxi2 0 &&
vxi1 0 &&Fn2 g m M m k && Fn1 g m &&
Fg2 g M && Fg1 g m & & Ff g m k & & F g
m k &&xf2 L &&xf1 0 & & M 0 &&
a2 g m k
M&&a1 0 && a2 0 && t
2 L
a2
t 2 L
a2
&& L 0
xi2 0 && xi1 0 &&vxi2 0 &&vxi1 0
&&Fn2 g m M m k && Fn1 g m &&
Fg2 g M && Fg1 g m & & Ff g m k && F M g
m2 k g m M k 0 &&
xf2 g L m2 k
F M g m2 k g m M k&& xf1 L xf2 && M 0 &&
a2
g m k
M&& xf2 0 &&
a1 a2 L xf2
xf2&&a1 0 && t
2 L xf2
a1
t 2 L xf2
a1
&& F 0
Out[2664]= xi2 0 && xi1 0 && vxi2 0
&&vxi1 0 && Fn2 103.88 && Fn1 19.6
&& Fg2 78.4 &&
Fg1 19.6 && Ff 5.88 && xf2 1.66415 &&
xf1 3 xf2 && a2 0.735 &&
xf2 0 && a1 a2 3 xf2
xf2&&a1 0 && t
2 3 xf2
a1
t 2 3 xf2
a1
PSE 5E PROBLEM 5.65.nb 3
