Two masses 26 kg and 24 kg are attached to the ends of a string which passes over a frictionless pulley. 26 kg mass is lying over a smooth horizontal table. 24 N mass is moving vertically downward. Find the tension in the string and the acceleration in the bodies. Ans. (125 N, 4.8 ms⁻²)
Given:
Mass of the 1st body moving vertically = m₁ = 24 kg
Mass of the 2nd body moving horizontally along the table= m₂ = 26 kg
Gravitational Acceleration = g = 10 m s⁻²
To Find:
Tension in the string = T = ?
Acceleration in the bodies = a = ?
Acceleration in the bodies = a = ?
Solution:
Formula for Tension in the string when the one body is moving vertically and the 2nd body moves horizontally
T = `\ frac {m₁m₂}{m₁ + m₂}` g
putting values
T = `\ frac {24 kg x 26 kg}{24 kg + 26 kg}` x 10 m s⁻²
T = `\frac{6240kg²}{50kg}` m s⁻²
T = 124.8 kg m s⁻²
T ≈ 125 N
Formula for acceleration in the bodies when one body is moving vertically and the 2nd body moves horizontally
a = `\ frac {m₁}{m₁ + m₂}` g
by putting values
a = `\ frac {24 kg}{24 kg + 26 kg}` x 10 m s⁻²
a = `\frac{240 kg}{50 kg}` m s⁻²
a = 4.8 m s⁻²
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