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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?

Respuesta :

skyluke89

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

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

[tex]F_a - m_u g - T = m_u a[/tex]

where

[tex]a=3.5 m/s^2[/tex] is the acceleration (upward)

Solving for [tex]m_u[/tex],

[tex]m_u = \frac{F_a-T}{a+g}=\frac{33-16}{3.5+9.8}=1.28 kg[/tex]

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, [tex]m_L g[/tex], where [tex]m_L[/tex] is the lower mass, downward

So the equation of the forces is

[tex]T-m_L g = m_L a[/tex]

And solving for the mass,

[tex]m_L = \frac{T}{a+g}=\frac{16}{3.5+9.8}=1.20 kg[/tex]

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