Question

Two air-track glider m1 and m2 are joined together with a light string (see figure 1 below). A constant horizontal force of 5.0N to the right is applied to mass m2.


If m_1=2.0kgand m_2=0.5kg, what is the acceleration of the glider?

Answer 1

To find the acceleration of the system consisting of the two gliders \( m_1 \) and \( m_2 \) connected by a string, we can use Newton's second law.

First, we need to calculate the total mass of the system:

\[
m_{\text{total}} = m_1 + m_2 = 2.0\, \text{kg} + 0.5\, \text{kg} = 2.5\, \text{kg}
\]

Next, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (\( F = ma \)). In this case, the net force \( F \) is the force applied to \( m_2 \), and we can set it up as follows:

\[
F = m_{\text{total}} \cdot a
\]

Substituting the values we have:

\[
5.0\, \text{N} = 2.5\, \text{kg} \cdot a
\]

Now, solve for \( a \):

\[
a = \frac{5.0\, \text{N}}{2.5\, \text{kg}} = 2.0\, \text{m/s}^2
\]

Thus, the acceleration of the glider system is:

\[
\boxed{2.0\, \text{m/s}^2}
\]