Pse 5e Problem 5.63

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