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

Question

An inventive child 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, the child pulls on the loose end of the rope with such a force that the spring scale reads 250N.  The childs true weight is 320N and the chair weighs 160N.  The childs feet are not touching the ground.  

Show that the acceleration of the system is upward and find its magnitude. ( please be VERY specific)

find the Force the child exerts on the chair (also be Very specific)

Explanation / Answer

Consider a FBD of the child plus chair
the tension of the rope upward 260
the force the child applies to the hanging rope 250
and the downward force due to gravity
-320 -160

add these together to get net force
250+250-320-160

20 N upward, so the chair accelerates
20=(320+160)*a/g
a=20*g/(320+160)
0.416 m/s ^2 upward

The force on the chair is 320-260=60 N

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