Question regarding Newton's laws?

Question

Assume ideal conditions for the apparatus illustrations in the picture. What is the acceleration of the system if...


(a) m1 = 0.25 kg, m2 = 0.50 kg, and m3 = 0.25 kg

(b) m1 = 0.35 kg, m2 = 0.15 kg, and m3 = 0.50 kg

I made a quick version of the picture on paint, http://www.geocities.com/grouchy187/picture.bmp

Any help would be appreciated, thx in advance.

Answer 1

If everything's ideal and there's no friction, then only masses m1 and m2 are being acted on (by gravity). And, since the hanging masses are opposing each other, you can consider the mass being acted on is just the difference between m1 and m2 (this makes sense: think about what would happen if m1 and m2 were identical: the weights would all balance, no matter what m3 was).

Since gravity is the only force acting here, acceleration in both examples is that of gravity (9.81 m/s^2).

Answer 2

it will travel h=0.5a*t^2, and will attain speed v=a*t in time t; it will attain kinetic energy E=0.5*(m1+m2+m3)*v^2 because of loss of potential energy W= (m2-m1)*gh; so E=W or 0.5(m1+m2+m3)*(at)^2 = (m2-m1)*g*0.5a*t^2;
thence a = (m2-m1)g /(m1+m2+m3);
(a)a = (50–25)*9.8 /(25+50+25) = 0.25*9.8 m/s – m3 moving to the right.
(b)a = (15-35)*9.8 /(35+15+50) = -0.20*9.8 m/s – m3 moving to the left.
Happy new year, and don’t grouch.

Answer 3

a)force on m3 due to m1=.25*10(ie g)=2.5N
while due to m2=5N
net foce on m3=2.5N in direction of m2
since force on m3=2.5 therefore m3*acc=2.5
2.5=m3a
a=2.5/.25
a=10m/sec^2
acc on total system=9.8 ie g
b) why dont u try urself

Answer 4

I got 19.6m/s^2 for part (a) & 4.2m/s^2 for part (b)

Answer 5

sorry its not clear