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

I also found the answer in the back of the book...
a) 2.5 m/s^2 to the right
b) 2.0 m/s^2 to the left

Any help would be appreciated, thx in advance.

Answer 1

sheepishb... used some bad logic but got lucky and got the right answer. Let me explain.

a. The net force is the difference in weight of the 2 hanging weights.
Fnet = Wm1-Wm2 = m1*g - m2*g = (m1 - m2)*g
Fnet = -0.25*10 Newtons = -2.5 Newtons
This force acts on all 3 masses.
Fnet = -2.5 Newtons = (m1+m2+m3)*a
a = -2.5 Newtons / 1 kg = -2.5 m/s^2
Doing it wrong worked only because the 3 masses add up to 1 kg.

You can't ignore m3. If it had been 1 kg all by itself, the 2.5 Newtons would have had to accelerate 1.75 kg and the acceleration would have come out as
a = -2.5 Newtons / 1.75 kg = -1.4 m/s^2

b. You can do that the same way. The problem was again set up so all 3 masses add to 1 kg. Puzzling. It allows you to make a common mistake and get the right answer.

Answer 2

Well, assuming the parameters are all ideal, i.e. no friction,no air resistance etc. etc, the mass m3 can be taken out of the equation since it does not play any significance of the whole system. If the system is ideal, and the diagram is as illustrated, then it would be a very simple mechanics system to solve.

For (a),
the acceleration is: (m1 - m2) x g
where g is the acceleration of free fall, I assume in this case it is 10,
therefore: (0.25 - 0.50) x 10 = -2.5 m/s^2
The negative sign indicating the direction, therefore the acceleration of m3 is 2.5 m/s^2 to the right.

For (b),
the acceleration is (m1-m2) x g
= (0.35 - 0.15) x 10
= 2.0 m/s^2
m3 being accelarated to the left.

Answer 3

How smart Do you think the N.S.A is 200 years ago dirt floors!?
How smart Do you think the N.S.A is 200 years ago dirt floors!
do they not think a higher inetllgnece that made the billions of computational d.n.a that they have found on this planet and yet what they are doing know There are knows knowns and unknows and they have taken all technolgy away 1950 never happen!!!!
www.beyond-science.com www.beyond-science.net