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 (see figure below), Nick pulls on the loose end of the rope with such a force that the spring scale reads 280 N. Nick's true weight is 310 N, and the chair weighs 160 N. Nick's feet are not touching the ground.

(b) Show that the acceleration of the system is upward. (Do this on paper. Your instructor may ask you to turn in this work.)

Find its magnitude.

Answer 1

First find the mass of nick and his chair.
mass=Weight/9.8

=(310+160)/9.8=47.96 kg
We know Net force=mass*acceleration

a=Fnet/mass
we need to find a,

we know what mass is and we know some parts of the forces
assuming down direction is negative so

g=(-9.8m/s^2)
Fnet=Force applied-Force of gravity
Fnet=Fa-(M+m)g
Fnet=280-(47.96)(-9.8)
Fnet=280-(47.96)(-9.8)=750N
go back to the first equation
a=Fnet/m
=750/47.96 =15.64 m/s^2
Since we said down is negative and up is positive, our a is positive so therefore it is moving upwards