Energy Transferred = Mass x Specific Heat Capacity x Temperature Change
Where the specific heat capacity is an individual property of water the energy needed to heat the pool up from a certain temperature can be calculated.
Trampolines
This is a piece of equipment used by gymnasts in the main sports hall at the leisure centre. Its purpose is to give an elastic surface on which gymnasts jump the elastic surface allows energy to be stored this is then transferred to the gymnast propelling them back up. Advanced trampolinists are able to complete various moves in mid air such as back flips; they also land on the trampoline on different parts of their body, such as a seat drop.
The properties of the different parts of the trampolines is very important, there are four main parts to a trampoline:
- The main frame – this supports the whole structure and must be strong enough to support a large force without breaking. The position of the main frame must also mean that when jumping the trampolist does not injure them selves.
- The mats – These are positioned around the edge of the trampoline and are to ensure that should a fall occur the trampolinist would be relativity unharmed. They do this by covering hard areas such as the springs and the supporting frame and also do the opposite job to the springs and surface which is to absorb the energy of someone falling on to it.
- The springs – There are many springs on a trampoline connecting the surface material to the main frame. There job is to store energy on depression of the material and return it to the trampolinist forcing them back in to the air,
- The bed – this also possesses elastic properties as it store energy on stretching and returns to its original shape, however this does so to a lesser extent than the springs. It is also there to provide a comfortable and safe surface for the trampolinist.
Storing Energy
I will concentrate at looking at the physics properties of the springs and bed in relation to the storing of energy. The original energy with in the system is from the trampolistist by bending their knees and pushing off against the surface. When the trampolinist lands this stretches both the surface and the springs therefore storing elastic potential energy. This energy can be calculated by E = ½ kx² where k is the stiffness of the material and x is the extension.
The stiffness of the material can be calculated by Hooke’s law where the stiffness (k) is equal to the force applied (F) divided by the extension, which is the additional length of the material after a force has been applied. The stiffness of the springs and material is therefore a very important factor if they were too stiff not enough energy would be returned and where they not stiff enough this would result in injury as the material may reach the floor.
By the laws of energy conservation this energy cannot be destroyed, most of the energy is immediately returned to the person therefore pushing them back in to the air. However the material is designed so it is not 100% efficient or the person would continue bouncing indefinitely. Some energy is lost as heat and sound. The person now has kinetic energy, as they are moving up. Kinetic energy can be calculated by KE= ½ mv² where m is the mass and v the velocity. How high that person travels can be calculated by looking at the equations of motion taking in to consideration the deceleration of upward movement. Now at the top of the jump has turned this kinetic energy in to gravitational potential energy (GPE= mgh) This is then turned to kinetic energy as they fall back to the trampoline the cycle is then repeated but due to the inefficiency the trampolinist must always put in some energy if they are to reach the same height. The height the person reaches will be directly linked to the efficiency for example if it is 80% efficient the person will rise to 80% of the original height.
Stiffness
I am going to look at an example of a 60kg person falling from 5m on to the bed of a trampoline; I will use this example to make an estimate of the combined stiffness of the bed and springs.
First I need to calculate the speed at which the person hits the bed of the trampoline:
v²= u² + 2as s= 5m u=? v=0ms a= 9.81ms²
0=u² + (9.81 x 2 x 5) u²= 98.1 u=√98.1 u= 9.9ms
I have estimated through observations on my visit the depression below the person would be 0.5m so I can work out there deceleration from when they hit the bed to when they stop.
v²= u² + 2as a= -u²/2s a=-98.1/1 a=98.1
I can now work out the force exerted on the trampoline
F=ma F=60 x 98.1 F=4206N
There are 60 springs so force on 1 spring and 1/60 of bed
F=4206/60 F=98.1N
In order to work out stiffness I need to know the force and extension.
So the stiffness is-
k = F/x k= 98.1/0.5 k= 19.62 Nm
This is the stiffness of one spring and part of the bed combined, in reality most of the stiffness comes from the springs (which may only stretch up to 10cm) and less from the bed, which needs to stretch more to prevent injury. This arrangement gives the maximum dip at the centre of the trampoline where you land.
Strengths, limitations and other uses of this principal.
As I have said one limitation of this is that not all the energy is returned to the gymnast also although the physics of the equipment is important skill and fitness is required to be a successful trampolinist. Safety also limits what is possible in terms of making the best use of the energy. However without the use of these physics principles and the selection of correct materials many of the moves performed would not be possible also with out this understanding many more injuries would have occurred. Trampolines are being further developed to increase the standard with in the sport and increase safety also trampolines are being developed for use in gardens.
The social impacts of trampolining are that people meet at a club and enjoy participating in a sport. Economically trampolines also make money for the leisure centre, as they are able to hire them out to paying groups.
The principles of energy conservation used here are the same as those used in sports balls such as tennis balls, running shoes, children’s bouncy castles and bungee jump cords! It is also used in small exercise trampolines, here the efficiency is much less and material stiffer so more effort is required. Also stiffness is an important property of many materials such as floors, wires, metals e.g. in car panels and elastic bands.
