A 200N force pushes forward on the 20kg truck. The truck pulls two crates connected together by ropes, as shown. The gravitational constant is 10N/kg. Determine the acceleration of the crates and truck and the tension in each rope for one of the following sets of conditions.

Please help me! I am really confused on how to draw the diagrams and how to find the x component forms and the unknowns! I've tried working on it but ended up erasing it cause it seemed wrong.

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aristocles aristocles · Answer 1 · 2018-10-16T01:41:35+02:00

Force on left crate, right crate and truck we need to draw here

First we will write the equation for left crate

[tex]T_{left} = m*a[/tex]

[tex]T_{left} = 20*a[/tex]

Now similarly for right crate

[tex]T_{right} - T_{left} = 20*a[/tex]

now for truck

[tex]F - T_{right} = 20*a[/tex]

Now we know that F = 200 N

[tex]200 - T_{right} = 20*a[/tex]

now add all three equation

[tex]T_{left} + T_{right} - T_{left} + 200 - T{right} = 20a + 20 a + 20a[/tex]

[tex]200 = 60 a[/tex]

[tex]a = 10/3 m/s^2[/tex]

now we will find all tension using this value of acceleration

[tex]T_{left} = 20 * \frac{10}{3} = \frac{200}{3} N[/tex]

[tex]T_{right} - \frac{200}{3} = 20*\frac{10}{3}[/tex]

[tex]T_{right} = \frac{400}{3} N[/tex]