pse 5e problem 5.64
TRANSCRIPT
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7/28/2019 Pse 5e Problem 5.64
1/4
A 2.00-kg aluminum block and a 6.00-kg copper block are connected by a light string over a frictionless
pulley. They sit on a steel surface, as shown in Figure P5.64, and 30.0. Do they start to move once any
holding mechanism is released? If so, determine (a) their acceleration and (b) the tension in the string.
If not, determine the sum of the magnitudes of the forces of friction acting on the blocks.
In[2503]:= sumForcesXforces_ :
ApplyPlus, MapFunctionelt, elt1 Coselt2, forces
sumForcesYforces_ :
ApplyPlus, MapFunctionelt, elt1 Sinelt2, forces
In[2508]:= forces1 T, 0, Fn1, 90 , Fsf1, 180 , Fg1, 270 ;forces2 Fn2, 90 , T, 180 , Fsf2, 180 , Fg2, 270 ;
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Do they start to move once any holding mechanism is
released?In[2543]:=
sumForcesXforces1 m1 a,sumForcesYforces1 m1 a,
sumForcesXforces2 m2 a,
sumForcesYforces2 m2 a,
Fsf1 sas Fn1,
Fsf2 scs Fn2,
Fg1 m1 g,
Fg2 m2 g,
m1 0, m2 0, g 0, scs 1, sas 1
;
Reduce, a, Fsf1, Fn1, T, Fn2, Fsf2
. m1 2, m2 6, sas 0.61, scs 0.53 , g 9.8, 30
Out[2544]= Fg2 g m2 && Fg1 g m1 &&m1 m2 m1 sas m2 scs 0 &&
a g m1 sas g m2 scs Cos g m2 Sin
m1 m2 m1 sas m2 scs&&
Fsf1 a m1 a m2 a m2 scs g m2 scs Cos g m2 Sin &&
Fn1 a g m1 && T a m2 a m2 scs g m2 scs Cos g m2 Sin &&
Fn2 m2 a g Cos && Fsf2 m2 scs a g Cos &&
g m1 m2 g m1 m2 sas g m1 m2 scs g m1 m2 sas scs 0
1 scs scs Cos Sin 0 && sas scs Cos Sin
1 scs scs Cos Sin
&&
m1 m2 1 scs scs Cos Sin && Fg2 g m2&&
Fg1 g m2 1 scs scs Cos Sin &&
Fsf1 a g m2 scs Cos Sin &&
Fn1 a g m2 1 scs scs Cos Sin &&
T a m2 a m2 scs g m2 scs Cos g m2 Sin &&
Fn2 m2 a g Cos && Fsf2 m2 scs a g Cos &&g m2 g m2 scs 0
Out[2545]= Fg2 58.8 && Fg1 19.6&& a 0.769743 && Fsf1 2.41118 11.18 a && Fn1 2 9.8 a &&
T 2.41118 9.18 a && Fn2 6 8.48705 a && Fsf2 3.18 8.48705 a
2 PSE 5E PROBLEM 5.64.nb
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7/28/2019 Pse 5e Problem 5.64
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If not, determine the sum of the magnitudes of the
forces of friction acting on the blocks.In[2559]:=
sumForcesXforces1 m1 0,sumForcesYforces1 m1 0,
sumForcesXforces2 m2 0,
sumForcesYforces2 m2 0,
Fsf1 sas Fn1,
Fsf2 scs Fn2,
Fg1 m1 g,
Fg2 m2 g,
m1 0, m2 0, g 0, scs 1, sas 1
;
Reduce, Fsf1, T
Out[2560]= sas 0 && m1
m2 scs Cos m2 Sin
sas&& Fsf2 g m2 scs Cos &&
Fn2 g m2 Cos && Fn1 g m1 &&Fg2 g m2 && Fg1 g m1 &&
Fsf1 g m2 scs Cos g m2 Sin && T g m2 scs Cos g m2 Sin &&
g m2 scs Cos g m2 sas scs Cos g m2 scs2 Cos g m2 sas scs2 Cos
g m2 Sin g m2 sas Sin g m2 scs Sin g m2 sas scs Sin 0
Sin 0 &&Cos 0 && sas 0 &&Fsf2 0 && Fn2 0 && Fn1 g m1&&
Fg2 g m2 && Fg1 g m1 &&Fsf1 0 & & T 0 && g m1 m2 g m1 m2 scs 0
Cos 0 && scs Tan && sas 0 && Fsf2 g m2 Sin &&
Fn2 g m2 Cos && Fn1 g m1 &&Fg2 g m2 && Fg1 g m1 &&
Fsf1 0 & & T 0 && g m1 m2 Cos g m1 m2 Sin 0
In[2573]:= Fsf1 g m2 scs Cos g m2 Sin
. m1 2, m2 6, sas 0.61, scs 0.53 , g 9.8, 30
Out[2573]= Fsf1 g m2 scs Cos g m2 Sin
Out[2574]= Fsf1 2.41118
PSE 5E PROBLEM 5.64.nb 3
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In[2569]:=
sumForcesXforces1 m1 0,
sumForcesYforces1 m1 0,
sumForcesXforces2 m2 0,
sumForcesYforces2 m2 0,
Fsf1
sas
Fn1,Fsf2 scs Fn2,
Fg1 m1 g,
Fg2 m2 g,
m1 0, m2 0, g 0, scs 1, sas 1
;
Reduce, Fsf2, T
Out[2570]= sas 0 && m1 m2 scs Cos m2 Sin
sas&& Fsf1 g m2 scs Cos g m2 Sin &&
Fn2 g m2 Cos && Fn1 g m1 &&Fg2 g m2 && Fg1 g m1 &&
Fsf2 g m2 scs Cos && T g m2 scs Cos g m2 Sin &&
g m2 scs Cos g m2 sas scs Cos g m2 scs2 Cos g m2 sas scs2 Cos
g m2 Sin g m2 sas Sin g m2 scs Sin g m2 sas scs Sin 0
Sin 0 &&Cos 0 && sas 0 &&Fsf1 0 && Fn2 0 && Fn1 g m1&&
Fg2 g m2 && Fg1 g m1 &&Fsf2 0 & & T 0 && g m1 m2 g m1 m2 scs 0
Cos 0 && scs Tan && sas 0 && Fsf1 0 &&Fn2 g m2 Cos &&
Fn1 g m1 && Fg2 g m2 &&Fg1 g m1 && Fsf2 g m2 Sin &&
T 0 && g m1 m2 Cos g m1 m2 Sin 0
In[2571]:= Fsf2 g m2 scs Cos
. m1 2, m2 6, sas 0.61, scs 0.53 , g 9.8, 30
Out[2571]= Fsf2 g m2 scs Cos
Out[2572]= Fsf2 26.9888
In[2575]:= 2.4111843164617532` 26.98881568353825`
Out[2575]= 29.4
4 PSE 5E PROBLEM 5.64.nb