Atwood?s machine is a system consisting of two objects connected by a string tha

Question

Atwood?s machine is a system consisting of two objects connected by a string that passes over a frictionless pulley, as shown in the figure above. Earlier in the course, we neglected the effect of the pulley, but now we know how to account for the pulley?s impact on the system. The mass of the object on the left is M = 7.00 kg. The mass of the object on the right is m = 1.00 kg. The mass of the pulley is mp = 1.00 kg. Use g = 10.0 m/s^2.

What is the magnitude of the acceleration of the system? (m/s^2)

Explanation / Answer

I didn't think about the inertia of the pulley before. Using same sign convention as above:

(F_{M} = Ma = Mg - T_{1}) where T_1 is the tension of the string on the side of M

(F_m = ma = T_2-mg) where T_2 is the tension of the string on the side of m

(F_{m_p} = { au_{m_p} over r } = { {Ilpha} over r } = { Ia over r^2 }) for moment of inertia I and radius r.

Then:

(F_{net} = sum_{i} F_i = a( M + m + {I over r^2} ) = (Mg - mg))

And subsequently:

(a = { g(M-m) / (M+m+ {I over r^2} ) })

The moment of inertia I of the pulley in this situation is defined to be: (I = { 1 over 2 }m_pr^2)

Substituting this and M=7.00kg, m=1.00kg, mp = 1.00kg, g = 10.0 m/s^2, yields:

(a = (10.0 ms^{-2})( 7.00kg - 1.00kg ) / (7.00kg + 1.00kg + 0.50 kg))

(= (10.0 ms^{-2} ){ 6.00kg over 8.50kg } pprox 7.059 { m over s^2 })

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.