Question

Two masses are joined by a mass less string. A 33-N force applied vertically to the upper mass gives the system a constant upward acceleration of 3.5 m/s². If the string tension is 16 N, what are the two masses?

Answer 1

Lower mass: 1.20 kg, upper mass: 1.28 kg

Explanation:

In order to solve the problem, we consider the forces acting on the upper mass only first.

The upper mass is acted upon three forces:

• The applied force $F_a=33 N$, upward
• The weight of the mass itself, $m_u g$, where $m_u$ is the upper mass and $g=9.8 m/s^2$ is the acceleration of gravity, downward
• The tension in the string, $T=16 N$, downward

Therefore, the equation of the forces for the upper mass is:

$F_a - m_u g - T = m_u a$

where

$a=3.5 m/s^2$ is the acceleration (upward)

Solving for $m_u$,

$m_u = \frac{F_a-T}{a+g}=\frac{33-16}{3.5+9.8}=1.28 kg$

Now we can find the lower mass by considering the forces acting on it:

• The tension in the string, T = 16 N, upward
• The weight of the mass itself, $m_L g$, where $m_L$ is the lower mass, downward

So the equation of the forces is

$T-m_L g = m_L a$

And solving for the mass,

$m_L = \frac{T}{a+g}=\frac{16}{3.5+9.8}=1.20 kg$

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