It\'s a question related to physics lab (Dynamic) 1) Figure 5.3-1 shows the free

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It's a question related to physics lab (Dynamic)
1) Figure 5.3-1 shows the free body diagrams and the resulting equation... 2)Consider an Atwood's machine with.... Can you help me solving this problem Experiment 5. Dynamics 63 5.5 Preliminary Assignment 1) Figure 5.3-1 shows the free body diagrams and the resulting equations of motion that are found by applying Newton's second law of motion to the Atwood's machine. From the equations of motion, derive equations (5.2) and (5.3). (Hin: Think two equations and two unknowns. Consider an Atwood's machine with m,-(110.0±0.1) g and m,-(175.0±0.1) g. the acceleration of the masses. 2) Determine

Explanation / Answer

for block 1:

block 1 is moving up

writing force balance equation:

T-m1*g=m1*a

==>T=m1*(g+a)...(1)

for block 2:

block 2 is moving down

writing force balalce equatino for block 2:

m2*g-T=m2*a

putting expression for T from equation 1:

m2*g-m1*(g+a)=m2*a

==>(m2-m1)*g=(m1+m2)*a

==>a=(m2-m1)*g/(m1+m2)....(proved)

using the expression for a, in equation 1:
T=m1*g+m1*(m2-m1)*g/(m1+m2)

=2*m1*m2*g/(m1+m2) (proved)

Q2.

m1=110 grams=0.11 kg

m2 =175 grams=0.175 kg

then a=(m2-m1)*g/(m1+m2)

=(0.175-0.11)*9.8/(0.175+0.11)=2.2351 m/s^2

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