Question

An inventive child named Nick 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. P5.81), Nick pulls on the loose end of the rope with such a force that the spring scale reads 250 N. Nick's true weight is 320 N, and the chair weighs 160 N. Nick’s feet are not touching the ground. (a) Draw a pair of diagrams showing the forces for Nick and the chair considered as separate systems and another diagram for Nick 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 Nick exerts on the chair.

Answer 1

A) diagram is shown on the image below 

b) Mass m = 450/9.8 = 45.918 KgNet upward force = T + T = 2T = 620 NNet downward force = 290 + 160 = 450 NResultant force F = Net upward force - Net downward force                     ma = 620 - 450           45.918 a = 170   Acceleration    a = 170/45.918 = 3.7 m/s^2   (upward)Here  Net upward force  > Net downward force, So the resultant force directed upwards, hence acceleration will be upward.   

(c)Consider the case of boy alone, then from Newtons law of motion we can write                                      Net force F = n + T - 290                                                   ma = n + 310 - 290 where m = 290/9.8 = 29.59 Kg                                     29.59 * 3.7 = n + 20                                            109.483 = n + 20                                                      n = 89.483 N