Question

Atwood machine. A 20kg box and a 30kg crate are attached to the two ends of a massless string that passes over a massless frictionless pulley. The system is released from rest. Without performing a calculation, rate, smallest to largest, the magnitudes of the tension in the string and the weights of box and crate, respectively. Calculate the acceleration of the system and the tension in the string

Answer 1

Answer with Explanation:

We are given that

$m_1=20 kg$

$m_2=30 kg$

We have to find the acceleration of the system and the tension in the string.

$30g-T=30a$...(1)

$T-20g=20a$

$T=20a+20g$...(2)

Using equation (2) in equation (1)

$30g-(20a+20g)=30a$

$30g-20a-20g=30a$

$10g=30a+20a=50a$

$a=\frac{10g}{50}=\frac{10\times 9.8}{50}=1.96 m/s^2$

Where $g=9.8m/s^2$

Using the value of a in equation (2)

$T=20(a+g)=20(1.96+9.8)=235.2 N$