Question

Two objects (42.0 and 21.0 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley hangs from the ceiling. Find (a) the acceleration of the objects and (b) the tension in the string.

Answer 1

a = 3.27 m/s²

T = 275 N

Step-by-step explanation:

Given that:

Mass m₁ = 42.p0 kg

Mass m₂ = 21.0 kg

Consider both masses to be in a whole system, then:

The acceleration can be determined as:

`(m_1+m_2)a = g(m_1-m_2)`

Making acceleration the subject in the above formula;

`a =(g(m_1-m_2))/((m_1+m_2))`

`a =(9.8(42.0-21.0))/((42.0+21.0))`

`a =(9.8(21.0))/((63.0))`

`a =(205.8)/((63.0))`

a = 3.27 m/s²

in the string, the tension is calculated using the formula:

`T = (2m_1m_2g)/((m_1+m_2))`

`T = (2(42)(21)(9.81))/((42+21))`

`T = (17304.84)/(63)`

T = 274.68 N

T ≅ 275 N