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

Answer:

a = 3.27 m/s²

T = 275 N

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;

$a =\dfrac{g(m_1-m_2)}{(m_1+m_2)}$

$a =\dfrac{9.8(42.0-21.0)}{(42.0+21.0)}$

$a =\dfrac{9.8(21.0)}{(63.0)}$

$a =\dfrac{205.8}{(63.0)}$

a = 3.27 m/s²

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

$T = \dfrac{2m_1m_2g}{(m_1+m_2)}$

$T = \dfrac{2(42)(21)(9.81)}{(42+21)}$

$T = \dfrac{17304.84}{63}$

T = 274.68 N

T ≅ 275 N