Question

grade 8
structures & mechanical systems and control
2.2.3 will the force with which the boy has to turn the wheels be the same on both ramps, or will it be greater on one of the ramps? if yes, which one?
2.2.4 use the following terms to write four sentences to explain why it is easier for the boy to go up the one ramp than the other: input force, output force, input distance, and output distance.
2.2.5 which ramp gives the boy the greatest mechanical advantage?
2.3 axes and knives are examples of a wedge. the wedge changes a small input force into a bigger output force. they use a large input distance to give a small output distance
why does an axe make it easier to split wood?
when you cut wood with a wedge - shaped axe, a large input distance downwards causes a small output distance sideways.
figure 8: the wedge shape of the head of an axe makes it easier to cut wood.
2.3.1 is the input force greater or smaller than the output force? or are they the same?
2.3.2 does an axe give a mechanical advantage or a distance advantage?

Explanation:

2.2.3

To determine the force on ramps, we use the concept of mechanical advantage for inclined planes. The mechanical advantage (MA) of a ramp (inclined plane) is given by \( MA=\frac{\text{length of ramp (input distance)}}{\text{height of ramp (output distance)}} \). A longer ramp (gentler slope) has a higher MA. A higher MA means less input force is needed. So, the force (input force) to turn wheels (or move up) will be greater on the steeper ramp (shorter input distance relative to height) because \( \text{Input Force}=\frac{\text{Output Force (weight)}}{MA} \), and lower MA (steeper ramp) means higher input force.

1. The ramp with a longer length (input distance) and same height (output distance) has a higher mechanical advantage.
2. A higher mechanical advantage means the input force (force boy applies) is less than the output force (weight he needs to move up).
3. For the easier ramp, the input distance (length of ramp) is greater, so per the formula \( MA = \frac{\text{input distance}}{\text{output distance}} \), MA is higher.
4. With higher MA, the input force required is smaller, making it easier for the boy to go up that ramp.

Mechanical advantage (MA) of a ramp (inclined plane) is \( MA = \frac{\text{input distance (length of ramp)}}{\text{output distance (height of ramp)}} \). The ramp with the longest length (input distance) for the same height (output distance) will have the greatest MA. So, the ramp that is the longest (gentlest slope) gives the greatest mechanical advantage.

Answer:

The force will not be the same. The force will be greater on the steeper ramp (the one with a shorter length relative to its height).

2.2.4