Calculating Net Force & Acceleration: Addition of Forces Explained

[Benjamin_harsh]

Homework Statement

A horizontal force of 150N is applied on a 20kg box which causes it to move to the right. What is the acceleration if the coefficient of kinetic friction is 0.25?

Relevant Equations

$\sum F_{X} = F - F_k$, $ma = F - \mu_{k}.F_k$

$\sum F_{X} = F - F_k$

(The net force, $\sum F_{X}$ is always equal to m.a)

$ma = F - \mu_{k}.F_n$

$ma = F - \mu_{k}.(mg)$ [Here $F_n = mg$ when body is on flat surface]

$20(a) = 150 - 0.25(20)(10)$

$\large a = \frac {150 - 0.25(20)(10)}{20}$

$\large a = 5\frac{m}{sec^2}$

How $\sum F_{X} = m.a$ ?

 

[PeroK]

Is there a question?

 

[Benjamin_harsh]

Is there a question?

My question: How $\sum F_{X} = m.a$?

Someone edited my title of the post.

 

[PeroK]

My question: How $\sum F_{X} = m.a$?

Someone edited my title of the post.

How not?

 

[Benjamin_harsh]

How not?

I know $F = M.A$. I never heard $\sum F_{X} = m.a$.
Please explain.

 

[PeroK]

I know $F = M.A$. I never heard $\sum F_{X} = m.a$.
Please explain.

You did all this in your OP. You can look at Newton's second law two ways.

If you assume that $F$ is the only force on an object, then you have simply $F = ma$.

But, if an object has more than one force on it (in your example there are 4 forces on the object), then the acceleration is related to the sum of the forces:

$\sum F = ma$

Sometimes, to emphasise this, we talk about the net force:

$F_{net} = \sum F = ma$

 

[Mark44]

I know $F = M.A$. I never heard $\sum F_{X} = m.a$.
Please explain.

In the first formula above, F represents the net force acting on an object, which is either the force if there is only a single force, or the sum of forces, if there are more than one force.

In your drawing, the net vertical force is zero; the upward normal force is balanced by the gravitational force. These two forces are equal in magnitude, but opposite in sign, so the block doesn't fly up or sink into the surface. In the horizontal direction, if the force acting to the right is larger in magnitude than the friction force (which acts toward the left), the horizontal forces aren't balanced, and the block will accelerate to the right.