Quiz July 2017 (GES 1)

This problem is dealing with a ratio of gasses, which we will then turn into a percentage.

First we will calculate the total number of parts, we will do this by adding up the number of parts or each gas.

Then we can calculate the ratio of each gas by dividing the number of parts for each gas by the total number of parts:

We first need to draw a graph for this problem. This is easier than it sounds, as there are usually a lot of things we overlook. Be sure to include

• The x axis MUST be horizontal, and the y axis vertical.
• equal spacing on both the x axis and y axis.
• Choose appropriate spacing on each axis.

Use a ruler and square paper!
The second part of this question asks for the equation describing the data. We will use the equation y=mx+c  to solve this.

First, we will find the m value, using the points (0, 2) and (1, 5).

Then we can find the y intercept. In this graph it's easy, the c value is where the line cuts the y axis, in this case at 2.

There are 2 different ways to calculate the answer here. We can use the graph which is very easy, or we can use the equation, which may be more accurate. Here we will use the graph. First find the x value (input) then follow with a straight line up to the line, and then across to the y axis. This will be your answer:

This is a simple application of Pythagoras theorem. Ok, so we have to reverse it to find one of the "legs" but its simple enough!

A large part of this test, and the skills you require is converting units. Here we will spend some time converting between; Revolutions, Degrees and Radians.

First, we can write this out as a fraction. Then we can convert Radians into Degrees. Next 1 minute into 60 seconds. Finally, we can simplify to get the number of degrees per second.

First we will find the volume of the bearing. And then we will find the volume of the cone

We can think of this bearing, as a big external cylinder minus a small internall cylinder.

I have done the whole calculation in mm.

Next we will look at the volume of the cone

The only thing left to do is to find out how many cones we need, so we divide:

We need the cross-sectional area to calculate the stress. This question looks hard at first, but we can see that we can split that complicated shape into 2 very simple shapes. It is made from a circle, well two halves and the straight section is just a rectangle.

Lets work on each section, and the sum the areas.

Next lets find the total:

Using the above equation for stress, all we need now is the downwards force, created by the mass of the object under gravity.

As we can see the stress is below the stress limit, we can see that the column can withstand the load.

As we are given the Modulus of Elasticity, we can transpose the following equation to make strain the subject, and solve:

Remember GIGA means trillion, or 10 to the ninth power (nine zeros)

Strain has no units.

This is a nice easy question after such hard ones previously. A simple F=ma will do!

First lets draw a simple diagram. Then we need to know how much friction force is created between the box and the surface. In order to do this, we need to know the Normal force created by gravity. That is how much the mass (the weight) of the box is pushing down on the ground. The more downwards push, the more friction we will have.

The normal force (downwards force) is given by mass x 9.81

We can see that the friction created is 68.67N. Now we are pushing this box with 75N, so we need to find how much force we have left over, this will be dedicated to the acceleration.

We can see we only have 6.33N of "push" left over after we subtract the friction force. It's not much but it's something! Let's use it to do a quick F=ma calculation (again) and we now have our value for the acceleration.

First let's draw a simple diagram and get the information out of the question:

We will be using the formula for gravitational potential energy. This is the SAME as work done, so you could use that too! but as we are lifting a load, it seems appropriate to use the Gravitation potential energy. Now we can plug in our values and calculate the THEORETICAL amount of work done to lift this box. (work is the same as energy)

Work over time will give us power, so now we can calculate the theoretical power required to get this job done:

The value above the is theoretical power. The ACTUAL POWER required comes from a measurement taken from the machine, and this is given in the question. By making a comparison (dividing) between these two values we can calculate how efficient the machine is.

First lets draw a diagram

Remember the Stress formula! In order to use it, we need to know the surface area. The surface area here is the curved surface area on the outside of the round. This curved surface area used to be in contact with the metal plate, and then we punched it out. First, we need to calculate the curved surface area:

Now we know how much surface area we are dealing with, and we know the ultimate shear strength of the steel (given in the question) we can calculate the force required to punch that hole:

Ok, first of all we can turn that divide into a multiplication using KFC (Keep Flip Change)

Then we can cancel a lot of the terms.

We can combine the two square roots to make a whole

And we have our final answer.

Ok so let's start with the bracket. We are going to turn those mixed numbers to top heavy fractions:

lets use KFC (Keep Flip Change) to turn this into a multiplication

Now we can simplify this before we continue

We can finally work on the right hand side, and convert the mixed number into a top heavy fraction

At the end, we just need common denominators, and we are done! This is fine, but it could also be written as a mixed number 6 and 1/6