Physics force problem?

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 320 N. The child's true weight is 280 N, and the chair weighs 160 N.

(a) Show that the acceleration of the child-chair system is upward and find its magnitude.
___ m/s2
(b) Find the force the child exerts on the seat of the chair.
___ N

Thank you so much!

The answers m=28.57kg and 11.2m/s² did not work. I really need help. A group of classmates and I worked all night trying to figure out this answer and we couldn't figure it out. It's due tomorrow. Any help will be greatly appreciated. Thank you so much! If you figure it out you are a genius. :)

280N is also not correct. Please help. :/

I missed the problem, but the answers were:
4.6 m/s^2 and 87.3 N.

Does anyone know how to get to those answers though (so I can actually learn how to do it)? Sorry for asking, but my own teacher doesn't even know how to do it. Thank you!

Answer 1

(a) a=f/m, find m, W/g=m, 280N/9.8m/s²=m, m=28.57kg

a=f/m, a=320N/28.57kg=11.2m/s²

(b) find force, the force exerted is equal to the force inputted. so its 280N

Answer 2

The new "weight" is 320 N. With the relative acceleration (g-a),
we get M(g - a) = 320.

or, Mg - 320 = Ma, where M is total system's mass.
M = 440/g
Therefore, a = 120*g/440 m/s^2 = 2.7 m/s^2

From the free body diagram of the child,

R - mg = ma, here m is child's mass.
R = m(g+a) = 280/g(g+2.7) = 357 N approx.

Answer 3

Given quantities,
Force(f)=320 N,
Weight of the system= weight of the child+weight of the chair=
280+160=440N.
So,total mass of system=weight of the system/acc.due to gravity
=440/9.81=44.89kg
now, force=mass*acceleration
acc=force/mass=320/44.89=7.12m/s2(ANS)


2)force=280 N

Answer 4

Not a physics fan. Sorry.