How to find weight and acceleration?

Question

When you lift a bowling ball with a force of 82N, its upward acceleration is a. If you lift it with a force of 92N, the ball's acceleration is 2a. Find (a) the weight of the bowling ball and (b) the acceleration a.

Answer 1

F=M*A

forces acting on the ball are gravity and the force we give

gravitational force= weight =W
From the given data we know,

82-W=M*a
92-W=M*2a

divide the 1st eqn by da 2nd 1

we get (82-W)/(92-W)=1/2

so 164-2W=92-W
W=72 N = weight of bowling ball;

W=M*g=M*10
so M= 72/10=7.2kg=mass of bowling ball

in da 1st eqn
82-72=7.2*a
so a=10/7.2
a=1.388m/s^2=acceleration of ball

Answer 2

Well, obviously there is a resistive force, the weight.

So let the weight be x N

Resultant Force = mass x acceleration
(82-x)/m = a
(92-x)/m = 2a

(92-x)/m = 2[(82-x)/m]
(92-x)/m = (164-2x)/m
so 92-x = 164-2x

x = 72N
so a = (82-72)/ (72/9.8)
= 1.3611
= 1.36 m/s^2

Answer 3

a. Weight of ball, w.

F=82-w
F=ma
=wa/g

Therefore,

82-w=wa/g
a=g/w(82-w)

The other case:

F'=92-w
F'=m(2a)
=2wa/g
92-w=2wa/g
a=1/2(g/w)[92-w)

Equate the two expressions since each is equal to a:

g/w(82-w)=1/2(g/w)[92-w)

82-w=1/2(92-w)
164-w=92-w
w=72N

b. acceleration, a

a=g/w(82-w)
=9.8/72(82-72)
=13.6m/s^2

Please check the calculations.