Question

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.

Answer 1

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

First we will write the equation for left crate

$T_{left} = m*a$

$T_{left} = 20*a$

Now similarly for right crate

$T_{right} - T_{left} = 20*a$

now for truck

$F - T_{right} = 20*a$

Now we know that F = 200 N

$200 - T_{right} = 20*a$

now add all three equation

$T_{left} + T_{right} - T_{left} + 200 - T{right} = 20a + 20 a + 20a$

$200 = 60 a$

$a = 10/3 m/s^2$

now we will find all tension using this value of acceleration

$T_{left} = 20 * \frac{10}{3} = \frac{200}{3} N$

$T_{right} - \frac{200}{3} = 20*\frac{10}{3}$

$T_{right} = \frac{400}{3} N$