How Friction Affects Newton's Second Law

Frictional forces are really important because they change the results of Newton's Second Law. This law says that the total force on an object equals its mass multiplied by how fast it's speeding up. We can write this as $F = ma$.

But when friction is around, it can change how this works. Friction tries to stop things from sliding or moving against each other.

1. What is Friction?

• Static Friction: This is the force you have to overcome to start moving something. It can change, but it has a maximum value. This max value is found using this formula: $F_{s, \text{max}} = \mu_s N$. Here, $\mu_s$ is a number that tells how "sticky" the surfaces are, and $N$ is the force pushing them together.

• Kinetic Friction: Once you get something moving, it feels a different force called kinetic friction. This force is usually less than static friction. We can use the formula $F_k = \mu_k N$ to find it.

2. How Does Friction Affect Movement?

When friction is present, it changes the total force on an object.

For example, if you push a box that weighs 10 kg across a floor with a friction number ($\mu_k$) of 0.3, the force that pushes down on the box (normal force, $N$) is equal to its weight. We can find this using the formula $mg$ (mass times gravity).

So, we calculate:
$N = 10 \, \text{kg} \times 9.81 \, \text{m/s}^2 \approx 98.1 \, \text{N}$

Now, to find kinetic friction ($F_k$), we do:
$F_k = 0.3 \cdot 98.1 \approx 29.43 \, \text{N}$

3. Finding the New Net Force

If we apply a force of 50 N to the box, we can figure out the new net force ($F_{net}$) like this:
$F_{net} = F_{\text{applied}} - F_k = 50 \, \text{N} - 29.43 \, \text{N} \approx 20.57 \, \text{N}$

4. Getting the Acceleration

Now, we can use Newton's second law to find out how fast the box will accelerate ($a$):
$a = \frac{F_{net}}{m} = \frac{20.57 \, \text{N}}{10 \, \text{kg}} \approx 2.06 \, \text{m/s}^2$

Conclusion

In short, friction really does change the net force acting on an object. This, in turn, affects how quickly it speeds up, as shown by the calculations we've just done using Newton's Second Law.