Two children push on heavy crate that rests on a basement floor. one pushes horizontally with a force of 150 N and the other pushes in the same direction with a force of 180 N. The crate remains stationary. Show that the force of friction between the crate the floor is 330 N.

We can solve this problem by applying Newton's second law of motion, which states that the net force acting on an object is equal to the product between the mass of the object and its acceleration:

[tex]sum F = ma[/tex]

where

[tex]\sum F[/tex] is the net force

m is the mass

a is the acceleration

For the crate in this problem, we have 3 forces acting on it:

- The force applied by the 1st child, [tex]F_1 = 150 N[/tex] forward

- The force applied by the 2nd child, [tex]F_2 = 180 N[/tex]

- The force of friction, [tex]F_f[/tex], acting backward

So the net force is

[tex]\sum F = F_1 + F_2 - F_f[/tex]

We also know that the crate remains stationary, which means that its acceleration is zero:

a = 0

Therefore, we can rewrite Newton's second law as

[tex]F_1 + F_2 - F_f = 0[/tex]

From which we find

[tex]F_f = F_1+F_2 = 150 + 180 =330 N[/tex]

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