Three masses are connected by light strings as shown in the gure. The string con

Question

Three masses are connected by light strings as shown in the gure. The string connecting the m1 and the m2 passes over a light frictionless pulley. Given m1 = 1.98 kg, m2 = 7.08 kg, m3 =8.57 kg, and g = 9.8 m/s2. The acceleration of gravity is 9.8 m/s2. Find the downward acceleration of m2 mass. Answer in units of m/s2

This is what i tried:

I added the force equations to get a=g(m3-m1)/m1+m2+m3

I plugged in the info and get 3.66 m/s2. Homework system says its wrong. Kind of stuck here.

Three masses are connected by light strings as shown in the ?gure. The string connecting the m1 and the m2 passes over a light frictionless pulley. Given m1 = 1.98 kg, m2 = 7.08 kg, m3 =8.57 kg, and g = 9.8 m/s2. The acceleration of gravity is 9.8 m/s2. Find the downward acceleration of m2 mass. Answer in units of m/s2 This is what i tried: I added the force equations to get a=g(m3-m1)/m1+m2+m3 I plugged in the info and get 3.66 m/s2. Homework system says its wrong. Kind of stuck here.

Explanation / Answer

So m3 and m2 can be thought of as a single mass m3+m2 Taking a to be accelerating towards to the left for the left side: F=ma (m3+m2)g-T=(m3+m2)a For the right F=ma -(m1)g+T=(m1)a Add these equations together to cancel the Tension (T): (m3+m2)g+(m1)g=(m3+m2)a+(m1)a g(m3+m2-m1)=a(m3+m2+m1) a=g(m3+m2-m1)/(m3+m2+m1) =9.8(1.98+7.08-8.57)/(1.98+7.08+8.57) =0.272 ms^-2 which accelerates to the left

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