Two masses are joined by a massless string. A 30-N force applied vertically to the upper mass gives the system a constant upward acceleration of 3.2 m/ s 2 . If the string tension is 18 N, what are the two masses?

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CarliReifsteck CarliReifsteck · Answer 1 · 2020-01-17T10:05:43+01:00

Answer:

The mass of both masses are 0.923 kg and 1.38 kg.

Explanation:

Given that,

Upward force = 30 N

Acceleration = 3.2 m/s²

Tension in string= 18 N

We need to calculate the mass of first mass

Using balance equation

[tex]ma=F-T-mg[/tex]

Where, m = mass

F = force

T = tension

a = acceleration

Put the value into the formula

[tex]m\times3.2=30-18-m\times9.8[/tex]

[tex]m=\dfrac{30-18}{3.2+9.8}[/tex]

[tex]m=0.923\ kg[/tex]

We need to calculate the mass of second mass

Using balance equation

[tex]ma=T-mg[/tex]

[tex]m(a+g)=T[/tex]

Put the value into the formula

[tex]m=\dfrac{18}{3.2+9.8}[/tex]

[tex]m=1.38\ kg[/tex]

Hence, The mass of both masses are 0.923 kg and 1.38 kg.