Question

Two objects are connected by a string that passes over a frictionless pulley as in Figure 5.14a, where m₁, m₂ and a₁ and a₂ are the magnitudes of the respective accelerations. Which mathematical statement is true regarding the magnitude of the acceleration a₂ of the mass m₂? (a) a₂<g (b) a₂>g (c) a₂ = g (d) a₂<a₁ (e) a₂> a₁

Short answer

The acceleration of the heavier mass is less than the gravitational acceleration, and Option (a) is correct.

Step-by-step solution

Identify the given data.

The mass of the lighter object is$m_1$

The acceleration of the lighter object is $a_1$

The mass of the heavier object is $m_2$

The acceleration of the heavier object is $a_2$

The vertical equilibrium of the objects is used to find the acceleration of the objects.

Determine the acceleration of both objects

Apply the vertical equilibrium of the lighter object.

$$\begin{gathered} m_{2}g-T=m_2{a}_2 \\ {a}_2=\frac{m_{2}g-T}{m_2} \\ {a}_2=\left(g-\frac{T}{m_2}\right) \end{gathered}$$

The above expression shows that the acceleration of the heavier mass is less than the gravitational acceleration.

Therefore, the acceleration of the heavier mass is less than the gravitational acceleration, and Option (a) is correct.