Question

Assuming ideal frictionless conditions for the apparatus shown in the figure, what is the acceleration of the system if (a) m1=.25 kg, m2=.50kg, and m3=.25kg, and (b) m1=.35kg, m2=.15kg and m3=.50 kg? Please show all work.

Answer 1

a)

from the force diagram , force equation for the motion of block m₁ is given as

T₁ - m₁g = m₁ a

T₁ = m₁g + m₁ a                          eq-1

from the force diagram , force equation for the motion of block m₂ is given as

m₂ g - T₂ = m₂ a

T₂ = m₂ g - m₂ a                  eq-2

from the force diagram , force equation for the motion of block m₃ is given as

T₂ - T₁ = m₃ a

(m₂ g - m₂ a) - (m₁g + m₁ a ) = m₃ a

(m₂ - m₁) g = (m₁ + m₂ + m₃) a

a = (m₂ - m₁) g / (m₁ + m₂ + m₃)

a = (0.50 - 0.25) (9.8) / (0.25 + 0.50 + 0.25)

a = 2.45 m/s²

b)

a = (m₂ - m₁) g / (m₁ + m₂ + m₃)

a = (0.15 - 0.35) (9.8) / (0.35 + 0.15 + 0.50)

a = - 1.96 m/s²               in opposite direction of what the diagram shows