5.3 Will this system give a mechanical advantage? How do you know?

When two gears mesh directly, they rotate in opposite directions. If the driver gear turns clockwise, the driven gear will turn counter-clockwise.

$$\boxed{\text{Counter-clockwise}}$$

From the image:

• Driver gear (small gear) has 6 teeth.
• Driven gear (large gear) has 18 teeth.

The relationship between the number of teeth and revolutions for meshed gears is:

$$\frac{\text{Revolutions of Driver}}{\text{Revolutions of Driven}} = \frac{\text{Number of teeth on Driven}}{\text{Number of teeth on Driver}}$$

Let $R_D$ be the revolutions of the driver gear and $R_d$ be the revolutions of the driven gear.
Let $N_D$ be the number of teeth on the driver gear and $N_d$ be the number of teeth on the driven gear.
We have $N_D = 6$ and $N_d = 18$. We want to find $R_D$ when $R_d = 1$.

$$\frac{R_D}{1} = \frac{18}{6}$$ $$R_D = 3$$

The driver gear needs to turn 3 revolutions.

$$\boxed{\text{3 revolutions}}$$

The system consists of a small driver gear connected to a large driven gear. This configuration reduces the output speed but increases the output turning force (torque). The problem statement also explicitly mentions: "A small driver gear connected to a large driven gear will change a fast turning speed into a slower turning speed." and "This system gives a mechanical advantage." The reminder box defines mechanical advantage as the turning force at the output axle being greater than the turning force at the input axle. Since the driven gear is larger than the driver gear, it will produce a greater turning force.

$$\boxed{\text{Yes, this system will give a mechanical advantage.}}$$ $$\boxed{\text{This is because a smaller driver gear is connected to a larger driven gear, which results in a greater turning force (torque) at the output axle compared to the input axle.}}$$