pse 5e problem 5.63
Post on 07-Nov-2014
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A 1.30-kg toaster is not plugged in. The coefficient of static friction between the toaster and a horizontal
countertop is 0.350. To make the toaster start moving, you carelessly pull on its electric cord. (a) For
the cord tension to be as small as possible, you should pull at what angle above the horizontal? (b)
With this angle, how large must the tension be?
In[2388]:= sumForcesX@forces_D :=
Apply@Plus, Map@Function@elt, elt@@1DD * Cos@elt@@2DDDD, forcesDDsumForcesY@forces_D :=
Apply@Plus, Map@Function@elt, elt@@1DD * Sin@elt@@2DDDD, forcesDD
In[2391]:= forces = 88Fc, Θ<, 8Fn, 90 °<, 8Fsf, 180 °<, 8Fg, 270 °<<;
In[2412]:= 8sumForcesX@forcesD � m * 0,
sumForcesY@forcesD � m * 0,
Fsf � Μs * Fn,
Fg � m * g,
Fc ¹ 0, m ¹ 0, g ¹ 0, Sin@ΘD ¹ 0, Cos@ΘD ¹ 0
<;
Reduce@%, 8Fc, Fn, Fsf<D
Out[2413]= Fg � g m && Cos@ΘD + Μs Sin@ΘD ¹ 0 && Fc �
g m Μs
Cos@ΘD + Μs Sin@ΘD &&
Fn � g m - Fc Sin@ΘD && Fsf � Fc Cos@ΘD && g m Μs Cos@ΘD Sin@ΘD ¹ 0
In[2439]:=
g m Μs
Cos@ΘD + Μs Sin@ΘD;
% �. 8g ® 9.8, m ® 1.3, Μs ® 0.35<;
Plot@%, 8Θ, 0 °, 90 °<D
Out[2441]=
0.5 1.0 1.5
6
8
10
12
In[2442]:= DBg m Μs
Cos@ΘD + Μs Sin@ΘD, ΘF;
% �. 8g ® 9.8, m ® 1.3, Μs ® 0.35<;
Plot@%, 8Θ, 0 °, 90 °<D
Out[2444]=
0.5 1.0 1.5
5
10
15
20
In[2491]:= DBg m Μs
Cos@ΘD + Μs Sin@ΘD, ΘF � 0;
Reduce@%, ΘD;
% �. 8g ® 9.8, m ® 1.3, Μs ® 0.35, C@1D ® 0<Out[2493]= Θ � -2.80492 ÈÈ Θ � 0.336675
In[2464]:= 0.33667481938672716` � °
Out[2464]= 19.29
In[2469]:= Fc �
g m Μs
Cos@ΘD + Μs Sin@ΘD;
% �. 8g ® 9.8, m ® 1.3, Μs ® 0.35, Θ -> 0.337<
Out[2470]= Fc � 4.20866
2 PSE 5E PROBLEM 5.63.nb
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