Adevice known as atwood's machine consists of two masses hanging from the ends of a vertical rope that passes over a pulley. assume the rope and pulley are massless and there is no friction in the pulley. mass m1 is greater than mass m2. find expressions for the magnitude of their acceleration, , and the tension in the rope, t. express your answers in terms of the masses and the acceleration due to gravity.

Explanation:

We apply Newton's second law:

∑F = m*a (Formula 1)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Problem development

M1 free body diagram : Look at the attached graphic

∑F = m₁*a

W₁ -T= m₁*a

W₁ - m₁*a = T  Equation 1

M2 free body diagram :Look at the attached graphic

∑F = m₂*a

T-W₂= m₂*a

W₂ + m₂*a = T  Equation 2

Equation 1  = Equation 2

W₁ - m₁*a = W₂ + m₂*a

W₁ - W₂ =  m₁*a + m₂*a

m₁*g -m₂*g = a* (m₁ + m₂)

a = (m₁*g -m₂*g) / (m₁ + m₂)

Calculation of the tension in the rope (T)

We replace a in the equation 2

W₂ + m₂*a = T

W₂ + m₂*g*(m₁ -m₂) /  (m₁ + m₂) = T

m₂*g + m₂*g*(m₁ -m₂) /  (m₁ + m₂) = T

m₂*g( (1+ (m₁ -m₂)) /  (m₁ + m₂) = T

m₂*g (1+m₁ -m₂) /  (m₁ + m₂) = T

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