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Designing a children's slide, making it exciting for the children whilst exercising safety.

Extracts from this document...

Introduction

  Kelly Lam

I will be investigating into designing a children’s slide, making it exciting for the children whilst exercising safety.

In designing my slide, I will need to calculate an angle inclined to the horizontal for the slide, a height and the length of the slide, the material of what the slide will be made out of…

The co-efficient of friction is an important factor as it affects the velocity. In order to find a realistic co-efficient value, I will set up an experiment, where I will test different clothing material against different surface materials and establish the co-efficient of friction.

With the co-efficient value, I will use it to investigate into angle sizes inclined to the horizontal, as both these factors have an affect on velocity. An increase in the size of the angle should increase velocity. I will test different angles and with the use of the co-efficient of friction value, find out the acceleration, which must agree with the two main criteria of being safe yet exciting.

        However, the angle size will also have an affect on the height of the slide and height is a main safety factor. The height must not be too high in case the child falls.

Having looked as slides it appears that the height of the slide is approximately just over double the size of the children, thus approximately 2 metres.

In addition all these factors will be used in calculating the time of the journey, velocity, acceleration and where the child will land, and thus I will be able to see if the model slide is realistic by comparing my results to real life slides.

What makes a slide exciting yet safe:

  • Speed: the slide has to be at a speed, which is fast enough for a child to enjoy the ride. However, it cannot be so fast that it may become hazardous to the child.
  • Height: the height will effect the speed i.e. speed increases with height. However, the height must not become too high that it becomes dangerous.
  • Velocity as slide levels off at the end: this speed needs to decelerate at a reasonable rate for the child to get off the slide safely or a speed where the child can safely project off the slide into a sand pit.

In general, there are two variables affecting the excitement and safety; the length of the slide and angle at which the slide is horizontal from.

THEORY

In my investigation I will be looking at Newton’s second Law of motion, which states that ‘ the magnitude of the resultant force acting on the body is proportional to the rate of change of the body’s momentum and the direction of the force is the direction of the momentum change’.

F = ma

Where the resultant force acting on a particle will cause the particle to accelerate. The magnitude of the force is the product the mass of the product and the magnitude of the acceleration.

When an overall force is applied to an object, the acceleration will change. But the amount the acceleration change will be depend upon the magnitude of the force applied, the greater the force, the greater the acceleration will increase by.

Friction plays an important factor in acceleration and is defined as the resistance an object encounters in moving over another.

For example, moving an object over glass will be easier then moving it over sand paper. This is because sand paper exerts more frictional resistances.

A surface exerts a parallel force; this is the force of static friction.

If an increase force is applied to the object (A) , the frictional  force will have increased too until  a maximum frictional  force is reached and it is here when friction is said to be ‘ limiting’. Thus the object will begin to move.

Once the object begins to move, the frictional force opposing the relative motion remains a constant value (μN, where μ is the co-efficient of friction and N is the normal contact force).

The co-efficient of friction is a number, which represents the friction between two surfaces. The nature of the surface determines the co-efficient of friction, for instance glass has a low co-efficient of friction, while sand has a higher one. However, I will further investigate into the co-efficient of friction and determine a suitable one for my slide.

Gravity is acted on a child as he/she slides down the slide, which is denoted in the formula as ‘g’.

The direction of which the child travels down is considered positive; therefore the frictional force being against the direction travelled is denoted with a negative sign:

- μmg = ma

In this case the resultant force (F) is the frictional force, which consists of the coefficient of friction and gravity.

image00.png

Calculations from data collected

The purpose of the testing is to find the co-efficient of friction of each material.

In order to do so the angle must be calculated, the following formula is used given that the length opposite the angle and the hypotenuse is known:

                        Opposite

      Sin θ=        image01.png

                       Hypotenuse

To find the coefficient of static friction (μ) between the surface and the clothing, Newton’s second law is applied:

F+N+mg = 0

The above equation represents the forces at equilibrium.

F = friction force (Newton)

            N = normal contact force

           M = being the mass

        G = the gravitational pull i.e. 9.8mg/s2

F = mg sin α

N = mg cos αimage26.pngimage09.pngimage18.png

image36.png

image45.png

But as the object starts to slide F =  μ N

Substitute F and N:

                        mg sin α =  μmg cos α

μ = mg sin αimage01.png

                                       mg cos α

μ = tan α

This also illustrates that mass becomes irrelevant to friction, thus I will not be taking mass into account in my investigation.

As illustrated below the angle has an influence on acceleration.

                        mg sinθ -μN = maimage54.pngimage02.png

                   mg sinθ -μ(mg cosθ) = ma

                         g(sinθ-μ cosθ) = a

image03.pngimage04.png

image05.png

image06.png

image08.pngimage07.png

image10.png

image11.png

image12.png

Acceleration at which the child travels will eventually  fall.

 The following formula( Newton’s Second Law of Motion ) is used to find the new acceleration:

ma = - μmg  

again mass does not affect acceleration as show :

ma = - μmgimage13.png

a = - μg

as I have established, μ is 0.35 and gravity (g) is 9.8 ms-2

Assumptions:

To set up this mathematical model of the slide I must simplify the real life situation in order to be able to use the mathematical principles.

  1. Assumption: Treat the child as a particle.

This is because the position of the child on the slide will have an impact on the velocity the child will travel down the slide.

E.g.      - the child holding on to the sides of the slide

  • the position of the child’s leg i.e. placing their feet on the slide→ the shoes/ trainers worn are usually made out of material of high friction e.g. rubber. Which will increase the co-efficient of friction thus decrease velocity.
...read more.

Middle

The material used for the slide, which I will later investigate and test into that determine friction.

Variables and constants

The constants in my investigation are:

      - Gravity (g) = 9.8 m/s2

- Length of slide (S) = 3.5 metres

- Co-efficient of friction (μ) = to be calculated

The variables in my investigation are:

  • The angle at which the slide is horizontal from (θ)
  • Velocity (V)
  • Acceleration (a)

Investigation into materials

In this experiment I will investigate into different materials that could be used for the surface of the slide against clothing material wore by the children and analyse how the nature of the material affects the co-efficient of friction.

Having looked at slides from local parks and playgrounds, I have decided to base my testing on three materials; plastic, wood and metal, which seemed to be the three most common. From this test, I will collect data on each material of their friction. This will be against material clothing worn by children. For this I have researched into clothing worn by children ages 5 to 8 yrs old, through visiting children clothes store and found out that the three most commonly worn materials were denim, cotton and polyester, which I will use to test.

The purpose of this test will allow me to look at the relationship of friction between materials and find the co-efficient of friction, which tells us when the child will start to slide.

EQUIPMENT:

  • Material to represent the slide → Wood

→ Plastic

→ Metal

  • Clothing material → Denim

→ Cotton

→ Polyester

  • Ruler → use to measure the height and length
  • Textbooks → use as the mass of the child

I will collect 3 flat surface boards (representing the slide) of the material I have selected to test.

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Conclusion

In my investigation I didn’t take this factor into account, which would affect my final design. However, if the slide was use for an indoor activity, then surrounding conditions will be constant, thus seasons no longer becomes an issue.

Given more time I would further investigation into the mean height of children with the age group the slide is designed for. This extended investigation will be used to design a slide of an appropriate size, which will make the slide more realistic. I would have tested more materials.

However, the time of the journey of the slide may appear fairly short. Given more time I would investigate into the time journeys of different angles.

Conclusion

In general, I found that it was difficult to implement the two criteria of making the slide safe yet exercising safety.

It was hard to achieve the greatest amount of safety when you need to make the slide exciting as well.

Overall my findings from my experiment demonstrate that plastic and polyester has the lowest coefficient, which means that a smaller angle is required from the horizontal, for the child to over come the frictional forces. As the angle however, the acceleration increases. Looking at the equation: V2= U2 + 2aS, it is clear that velocity (V) corresponds to acceleration (a), as acceleration increase in value so will velocity. As a result the child will experience a shorter journey time.

Also when increasing force of the direction the child will travel down the slide will increase acceleration, thus acceleration is directly proportional to the resultant force applied.  

                                     F = ma

 Where m is a constant.

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image41.pngimage43.pngimage42.png

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image48.pngimage49.pngimage50.png

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...read more.

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