Quiz October 2017 (GES 1)

Adding fractions is harder than multiplication!

So first things first, let's see what we can cancel

now we need a common denominator to add these two fractions together.

Once we have a common denominator, we can just add them together. This is about as good as we can get, the question doesn't specify how to write the answer, so this will do. With simplification questions, it's hard to know when to stop. I think this is good enough.

Let's write out the question and then turn that division into a multiplication using KFC (Keep Flip Change).

Next, we can cancel out like terms, and we are left with our answer:

To make this problem easier, we will split it into two triangles. First, we need to work on the blue triangle to find the hypotenuse. This is a shared edge with the red triangle. Then we can work on the red triangle

now we can use SOH CAH TOA to solve for the missing angle

The area is given by finding the area of the red and the blue triangles.
First, we need the height of the red triangle, let's use Pythagoras to solve this.

the area of a triangle is (0.5)*base*height

Ok, so we need to calculate the surface area of the sphere and the cone, the measurements are given, so its all pretty straight forwards, just remember to convert those diameters into radii (radiuses!)

So you can see that the Cone is larger!

Converting units is a big part of this test, first, let's convert RPM to rads per second for both the starting and the final velocities

First, we divide RPM by 60 to get revolutions per second

Then we can multiply by 2pi to convert from Revolutions to Radians. (For example, if we had 1 rev this would be 2pi rads)

We do this for both the initial and final velocities

Now we can find the acceleration in rads per second^2 using a SUVAT

Let's find the linear velocity of a point on the rim of this shaft flange. To calculate the linear velocity wee need to know how far the point is traveling in a second. as it is traveling in a circle, we need the circumference of the circle on which it is traveling:

Now we can convert the 1000 RPM given in the question to see how many revolutions we have a second:

If we travel 0.62832m every revolution, and we do 16.6666 revolutions every second, by multiplying these two values we can find how far a point on the rim will travel every second:

This is a very simple question. We can use F=ma to calculate the acceleration:

As this box is being pushed along a horizontal plane with no friction, all we need to solve this is a simple SUVAT:

The movement ratio is also called the velocity ratio (both these terms are used in the GES 1 test). It is the comparison between how far you have to move vs how far the load moves. I remember this as a slave pushing a lever to winch up an anchor, sorry for the example, but it stuck in my mind. The distance I have to walk around over the distance the anchor is winched up. This is effectively a simple level, its actually a circular lever

So as we are walking around in a circle, we will need the circumference, then divide this by the pitch of the screw jack. This is how much it will lift for a full turn. Just make sure you have everything in the same units, in this case, I used mm. One more thing is the large number always goes on top for these questions, so if you get mixed up, just make sure you put the largest number on top.

This gives a ratio of 680.667 to 1, but we just write it as 680.667. This means for every 680.667 mm I move, the load will be lifted 1mm.

Force ratio is a comparison of how much force can be exerted, over how much force is applied. to make this easier to remember, I think of this as the load lifted over the force applied. Again the big number always goes on top, it is a very similar layout to the previous question (but load and applied are flipped). These numbers come from actually measuring the equipment.

As we are lifting on earth, and against gravity, we find the force needed to lift the object, by converting into KG and then into Newtons, divide this but the effort, or force applied and we are done:

Efficency is a comparison between the actual advantage given by the equipment and the theoretical advantage given by the equipment.

This can be calculated by dividing the force ratio by the movement ratio.It can be given as a decimal or multiplied by 100 to convert it into a percentage. The number cannot be great than 1 (decimal) or greater than 100%, so this will help us to remember the order. The smaller number MUST go on top!