Question

A cart of unknown mass is attached to a second 2.6kg mass that is suspended from the edge of a table. If the system accelerates at 3.8m/s^2. Determine the mass of the cart. Ignore friction

Answer 1

Given data:

* The mass of the object suspended from the edge of a table is 2.6 kg.

* The acceleration of the system is,

$a=3.8ms^{-2}$

Solution:

The force acting on the system is,

$F=(m_1+m_2)a$

where m_1 is the mass of the cart and m_2 is the mass of the object suspended, and a is the acceleration of the system,

The only force acting in this case is the weight of the object suspended from the edge of a tabel.

Thus, the force acting on the system is,

$F=m_2g$

where g is the acceleration due to gravity,

Substituting the known values,

$\begin{gathered} (m_1+m_2)a=m_2g \\ 3.8(m_1+2.6)=2.6\times9.8 \\ 3.8(m_1+2.6)=25.48 \\ m_1+2.6=\frac{25.48}{3.8} \\ m_1+2.6=6.7 \\ m_1=4.1\text{ kg} \end{gathered}$

Thus, the mass of the cart is 4.1 kg.