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.

### 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=

Hypotenuse

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