##### Investigation between the relationship of Mass and Time taken while coming down a water slide

In this experiment I am going to investigate the relationship between Mass and Speed of 5 people with different masses coming down a water slide. Firstly, I have obtained evidence by measuring the time taken for people with various different masses to come down a water slide. My prediction is that mass is independent of the time taken. We have used a digital stop watch to measure the time taken of the people coming down the slide. I am going to use several different scientific equations to try and prove my prediction. I also have to take into consideration that the slide is not a straight surface it has several different bumps but I also predict that this has no effect to the time taken as horizontal velocity is independent of vertical velocity because both of these masses are being pulled by gravity at a constant acceleration of 9.8m/sï¿½ so all objects free fall at the same rate of acceleration regardless of their mass.

I have tabulated my results according to the different Masses in kilograms from lowest to the greatest while all the attempts were measured in seconds to 2 significant figures and I have recorded Average results as well:

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Name

Mass (kg)

Attempt

1 (s)

Attempt

2 (s)

Attempt

3(s)

Attempt

4(s)

Attempt

5(s)

Average

(s)

Lian

50

7.30

7.79

7.81

7.15

7.78

7.56

Abhay

58

8.08

7.40

7.32

7.32

8.07

7.63

Omar

60

8.05

7.60

7.82

7.82

7.99

7.85

Alan

64

8.08

7.67

7.49

7.49

7.40

7.63

Calculating average velocity

We were told that the approximate distance of the slide was 74 m and by this I going to calculate the average speed by using the equation

Speed = Distance / Average time

Lian

9.78 m/s

Omar

9.42 m/s

Abhay

9.69 m/s

Alan

9.69 m/s

Calculating the height of the slide

Although we were given the length of the slide I will show how they had calculated by using Pythagoras theorem which says in a right angle triangle the sum of squares of the base and the height is equal to the square of the hypotenuse.

Xï¿½ = 55ï¿½ + 50ï¿½ I cannot be certain if this is the correct

Xï¿½ = 3025 + 2500 as the slide was not a triangle but I am

Xï¿½ = 5525 going to carry the error forward to do

X = 74.3 all calculations.

From these results I can rule out the inference, the greater the persons mass the slower a person will go down or faster! This is false because Alan has a greater mass than Omar but his average time was still smaller than Omar’s who has a smaller mass and had a larger time taken.

Back to my prediction which is in a straight that Mass is independent of time taken. To prove this I will use my equation h = ut + 1/2gtï¿½, this is the equation is used whenever an object travels at a uniform acceleration line where h = height, u = initial velocity, v = final velocity, t = time taken and g = acceleration due to gravity which is 9.8 m/sï¿½, As you can see mass does not play any role in this equation it is only acceleration that does as it is the acceleration due to gravity. My prediction is only partly correct as the results do not completely match, the time taken for the different masses have minor variation. Another possibility is this equation can only be applied on a frictionless surface with negligible air resistance so this formula can only work in theory and not practically like in this experiment.

Proof:

S = ut + 1/2 gtï¿½ where s is the distance u = initial velocity t = time g = acceleration due to gravity (9.8msï¿½)

Let us assume you throw two objects from a distance that is Constant of different masses

S = ut + 1/2 gtï¿½ = S = ut + 1/2 gtï¿½ ——-> s is the same in both of the equations

ut + 1/2 gtï¿½ = ut + 1/2 gtï¿½——–> u is always = 0 therefore ut is canceled out

1/2 gtï¿½ = 1/2 gtï¿½ ——–> g is always a constant (9.8msï¿½) therefore 1/2 g cancels out

tï¿½ = tï¿½ therefore t = t

The masses of the object play no role in how much time taken the object has to come down!

Calculating Energies:

To calculate the Gravitational Potential energy and the Kinetic energy, I have to use the two formulas GPE = mgh where m = mass and g = acceleration due to gravity which is 9.8m/sï¿½ and h is the perpendicular height of the slide = 50m and for kinetic energy the formula would be KE = 1/2 mvï¿½ where m = mass and v= average velocity.

Gravitational Potential Energies Kinetic Energy

Lian

2,391.21

Abhay

2,722.98

Omar

2,662.09

Alan

3,192.46

Lian

24,500

Abhay

28,420

Omar

29,400

Alan

31,360

The Gravitational Energy and the Kinetic Energy will not be the same because as each person went down the slide he or she encountered friction where energy is lost while energy is also lost to heat and sound.

Law of Energy: Energy can never be created or destroyed it can only be transferred or transformed. The energy lost has not been destroyed it has only been converted into heat and sound.

From these results I deduce Mass is directly proportional to GPE and KE while height is directly proportional to GPE and velocity is directly proportional to KE.

Why all my results did not match my prediction?

From the table you will notice that most of the results are different but there were cases where two people with two different masses had same results (Attempt 1 – Abhay and Omar).

If my prediction was true all of my results would have been exactly the same regardless of mass but it wasn’t. The answer to that is there are other factors that effect the time taken which are Air resistance, friction and Human error, Pushes.

Air Resistance:

All 5 of us encountered some level of air resistance on the slide; the definition of air resistance is the result of collisions of the objects leading surface with air molecules. One of the key factors that have a direct effect on air resistance is the cross sectional area of the object. An increased cross sectional area gives an increased amount of air resistance. Perhaps some of us encountered greater air resistance than others on the slide, and this is why our results vary.

Friction:

Friction is a force that opposes the movement of an object. While coming down the slide all of us would have encountered some level of friction. The slide we went down on was probably polished so that we could slide down easily but there would still be some level of friction which probably had minor changes while each person was going down the slide. A second point is that all of us had gone down the slide using different floats. Friction could have acted differently on each float depending on the material and lubrication.

Human Error:

We were using a digital stop watch which gave us results to two significant figures but there is no doubt that there will still be a minor amount of human error as the distance between the person taking the timings and the person on the slide was quite far, reaction time could have varied from person to person who took results. This would have played another role in why all the results were not the same.

Pushes: Some students were pushed down the slide while others were not the pushes create an extra force acting on the object

Variation of results:

I am now going to work with the average time taken for the 4 different masses to show you how minor the changes are.

Let’s take Lian who has a mass of 50 kg and whose average time taken was 7.56 and let’s take Alan who has a mass of 64 kg and whose average time taken was 7.63.The difference in mass is 14 kg and the difference in time taken was 0.07 seconds! Even after such a great increase in mass there has hardly been any difference in the time taken.

Let us now take Abhay with a mass of 58 kg and Omar who has a mass of 60 kg which is only a 2 kg change in the mass which is far smaller than the change with Lian and Alan. Abhay’s average time taken was 7.63 and Omar’s average time taken was 7.85, the difference in time taken was 0.22 seconds.

By using these results I can help prove my prediction saying that mass is independent to time taken.

Improvements

To improve the experiment we should have had a straight slide instead of a parabolic surface to be able to calculate the length of slide more accurately using Pythagoras’ theorem.

We could have used light gates instead of stop watches to get exact readings when students start and stop on the slide this way they could avoid any human error.

Each person could have used the same float as they can all encounter the same % of friction.

We could have used different slides to test the effect of friction on different surfaces.

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