Physics Another Physics question

Question

Three objects are connected by light strings as shown in Figure P4.62. The string connecting the m1 = 5.50 kg mass and the m2 = 4.20 kg mass passes over a light frictionless pulley.

Figure P4.62 Image of figure in link ( http://www.webassign.net/sf/p4_62alt.jpg  )

(a) Determine the acceleration of each mass.
            m/s2 (magnitude)
(b) Determine the tension in the two strings.
            N (string between m1 and m2)
            N (string between m2 and the 3.00 kg mass)

Answer 1

If you draw free body diagrams for each mass, you will obtain these three equations. (Sorry I can not show you the diagrams) For each diagram, you have to apply the Newton's 2nd law.

1) for m3: 3g - T3 =3a (T3 is the tension between m2 and m3, "g" is gravitational acceleration = 9.8 m/s²  and "a" is the acceleration of the three masses which falling to the m2 and m3 side)

2) for m2: 4.2g + T3 -T2 = 4.2g (T2 is the tension between m1 and m2)

3) for m1: T2 - 5.5g = 5.5a (Please be careful when you write this eaquation, you have to consider the direction of acceleration. Put the direction of acceleration as a positive direction)

If you substitute 9.8 for "g" and solve the 3 linear first order equations then you can obtain the answers.

(a) acceleration a = 1.312 m/s² for each mass

(b) T2 = 61.116 N and T3 = 25.466 N

The problem wants up to 2nd decimal position so you have to round the given answers to fit the given significant numbers. If there are any required conditions, you have to fit that requirement related with the significant numbers.

I hope you can understand this question without diagrams. I feel sorry about the limitation of this answering box.

 

Answer 2

I deleted this answer and tried to post a corrected comment with better formatting...and a sign correction (thanks sung!)