An inventive child named Pat wants to reach an apple in a tree without climbing the tree. Sitting in a

chair connected to a rope that passes over a frictionless pulley (Fig. P5.55), Pat pulls on the loose end

of the rope with such a force that the spring scale reads 250 N. Pat’s weight is 320 N, and the chair

weighs 160 N. (a) Draw free-body diagrams for Pat and the chair considered as separate systems, and

draw another diagram for Pat and the chair considered as one system. (b) Show that the acceleration of

the system is upward and find its magnitude. (c) Find the force Pat exerts on the chair.

Show that the acceleration of the system is upward

and find its magnitude.

In[1447]:= 8SumFy � T + T - Fgb - Fgs,

SumFy � Hms + mbL * a,

Fgb � mb * g,

Fgs � ms * g,

T ¹ 0, g ¹ 0, mb ¹ 0

<;

Reduce@%, 8a, SumFy, mb, ms<D% �. 8Fgb ® 320, Fgs ® 160, T ® 250, g ® 9.8<

Out[1448]= Fgb + Fgs ¹ 0 && a �

-Fgb g - Fgs g + 2 g T

Fgb + Fgs

&&

SumFy � -Fgb - Fgs + 2 T && g ¹ 0 && mb �

Fgb

g

&& Fgb ¹ 0 && ms �

Fgs mb

Fgb

&& T ¹ 0

Out[1449]= a � 0.408333 && SumFy � 20 && mb � 32.6531 && ms �

mb

2

Find the force Pat exerts on the chair.

In[1481]:= 8SumFy � T + T - Fgb - Fgs,

SumFy � Hms + mbL * a,

Fgb � mb * g,

Fgs � ms * g,

T + Fn - Fgb � mb * a,

T ¹ 0, g ¹ 0, mb ¹ 0

<;

Reduce@%, 8Fn, ms, mb, a, SumFy<D% �. 8Fgb ® 320, Fgs ® 160, T ® 250< �� N

Out[1482]= Fgb + Fgs ¹ 0 && Fn �

HFgb - FgsL T

Fgb + Fgs

&& g ¹ 0 && ms �

Fgs

g

&&

mb �

Fgb

g

&& mb ¹ 0 && a �

-Fgb + Fn + T

mb

&& SumFy � -Fgb - Fgs + 2 T && T ¹ 0

Out[1483]= Fn � 83.3333 && g ¹ 0. && ms �

160.

g

&& mb �

320.

g

&& mb ¹ 0. && a �

-70. + Fn

mb

&& SumFy � 20.

2 PSE 5E PROBLEM 5.55.nb