How does height influence velocity

Rationale: When an object is at the top of a slope its position above the ground provides it with gravitational potential energy. As it moves down the slope, the object loses potential energy but as energy cannot be destroyed, it is converted into kinetic energy. Assuming that the system is 100% efficient all of the potential energy will be converted into kinetic energy at the bottom of the slope. We can use this information to predict the speed at which the object should move when it reaches the bottom of the slope.

Aim: To investigate how the velocity of an object changes when the height of the ramp it moves down is changed.

Introduction: Energy cannot be created or destroyed, it exists in many forms all around us, and we cannot sense it or feel it- it is just there. Potential energy, gravitational potential energy, elastic energy, chemical energy, nuclear energy, kinetic energy, thermal energy, electrical energy and radiant energy are examples of them.

Friction is one the most important forces that we use in everyday life. Without it we would not be able to walk or even move about. Cars would not work and you would not be able to write. Before the time of Galileo and Newton, people thought there was only one force, called a driving force. Newton discovered that there were unseen forces like friction and air resistance all around us, helping us do everything.

Therefore, when you push a car down a ramp, the forces acting on it are friction, driving force and air resistance. These are unbalanced forces as the car is moving forward meaning the driving force is greater than the air resistance and friction. As the car moves down the ramp it converts potential energy, as it is stationary on the top of the ramp, into kinetic energy as it comes down the ramp. The formula for finding out the strength of a force is Force = Mass x Acceleration. The force is measured in Newtons (N), the mass is measured in kilograms (Kg) and the acceleration is measured in metres per second per second (M/s/s). To work out the kinetic energy is Kinetic Energy = 0.5 x mass x (Velocity x velocity) or 1/2mv�. Kinetic energy, like potential energy, is measured in joules. Kinetic energy is moving energy. The formula used to find out gravitational potential energy is Gravitational potential energy = mass x gravitational field strength x height or mgh. The height is measured in metres. Gravitational potential energy is stored energy that can be turned into kinetic energy.

The Formula which we will use in the experiment is V = 2GH

This shows the speed or velocity will equal the square root of two times gravity times height. The gravity is measured in N/Kg and gravity on earth is 10 N/Kg. Here is an example of how to calculate 2GH:

If the height was 5 cm the equation is:

2 x 9.8(the gravitational pull) x 0.05m= 0.98 m/s

Friction is the force that slows down moving objects. The size of the friction force depends on the roughness of the surfaces: the rougher the surfaces, the greater the friction force. Air resistance is the force that slows down falling objects. When an object is moving forward the main resistive force is air resistance. Gravity is the force that keeps objects on the ground.

Speed is determined using the formula, Speed = Distance

Time

Distance and time can also be shown on a Distance-Time graph. If you go on a journey, the distance you have travelled can only stay the same or increase, so a Distance-time graph for the same journey cannot have a negative gradient. The graph below shows this:

Speed is measured in metres per second (M/s), distance is measured in metres (M) and time is measured in seconds (S).

Acceleration involves a change in velocity. Speeding up, slowing down and changing direction are all examples of acceleration. The formula for acceleration is Acceleration = Change in velocity

Time

Acceleration is measured in metres per second per second (M/s/s). There is also a graph for acceleration, known as a Speed-Time graph, as shown below:

The graph shows that speed can only have positive values, the steeper the gradient, the greater the acceleration that it represents and that a negative gradient is a decrease in speed.

Some factors that could influence the outcome of the investigation are how smooth or rough the ramp is, at what height we start the car from, the length of the ramp and the roughness of the wheels on the car. To overcome this we could polish the ramp before we conduct the investigation. To make the investigation a fair test we should use two stopclocks, rather than one; start all the objects use from exactly the same height and make sure that the ramp has the same texture every time we conduct the investigation. If the investigation takes more than one session to be completed, we must be sure that we have the same board next time.

Apparatus: Drawing board (for ramp)

Bricks

Black sugar paper

Metre sticks

Toy car, Tennis Ball, Golf ball, Marble, Rubber ball,

Ping-Pong ball

Stopclock

Cotton wool

Diagram:

Method:

* Firstly we collected our apparatus together.

* Then we rolled each toy or ball down the ramp.

* We recorded the time that it took to travel two metres.

* We then changed the height and repeated the experiment. We did this five times in total with different heights.

* We decided to test five heights, these were: 10cm, 25cm, 35cm, 50cm, and 60cm.

* We would test these heights ten times each so that we could have a good set of results.

Fair Test: To ensure that our investigation was a fair test we had two people recording and then took the average of the two readings, to take into account human error. Also I think we should use the same ramp just in case one is larger than the other.

Prediction:

I think that when we conduct the experiment, we will find that as the height of the ramp increases, the faster the object will go down the ramp and reach the end of the measured area. This will be because the object will go down the ramp faster due to the greater height.

To find the velocity at which it goes down the ramp, we use the equation

2GH or 2 x gravitational pull x height

EXAMPLES:

(Gravitational pull = 9.8)

* If the height is 10cm, the equation is:

2 x 9.8 x 10cm = 1.4m/s

The velocity is 1.4m/s

* If the height is 25cm, the equation is:

2 x 9.8 x 25cm = 2.21m/s

The velocity is 2.21m/s

Preliminary work

This was measured over one metre.

Ramp

Height

Car

Snooker Ball

Squash Ball

Tennis Ball

Golf

Ball

Marble

19.5 cm

2.5s

0.62s

0.635s

1.55s

1.47s

1.14s

30 cm

1.42s

0.50s

0.57s

1,105s

1.12s

1.125s

45 cm

0.96s

0.46s

0.47s

1.09s

1.0s

0.7s

We used these results to determine which object we were going to use in our real experiment. As the snooker ball was the fastest, we decided to use it.

Results

Height of Ramp-10cm

Test

1

2

3

4

5

6

7

8

9

10

Result

(cm)

1.88

1.68

1.69

1.75

1.90

1.93

1.67

1.81

1.87

1.99

Height of ramp-25cm

Test

1

2

3

4

5

6

7

8

9

10

Result

(cm)

1.02

1.01

1,05

1.07

1.09

0.97

1.11

1.04

1.02

0.99

Height of ramp-35cm

Test

1

2

3

4

5

6

7

8

9

10

Result

(cm)

0.98

0.86

0.95

0.94

0.94

0.89

0.93

1.00

0.90

0.94

Height of ramp-50cm

Test

1

2

3

4

5

6

7

8

9

10

Result

(cm)

0.79

0.94

0.93

0.94

1.00

0.91

0.91

0.95

0.88

0.96

Height of ramp-60cm

Test

1

2

3

4

5

6

7

8

9

10

Result

(cm)

0.94

0.85

0.93

0.87

0.89

0.99

0.95

0.94

0.96

0.97

Height

Av. time

Distance

Av. Speed

2GH

0.10m

1.85s

2m

1.08m/s

1.4 m/s

0.25m

1.10s

2m

2.81m/s

2.21 m/s

0.35m

0.94s

2m

2.10m/s

2.26 m/s

0.50m

0.92s

2m

2.20m/s

3.15 m/s

0.60m

0.74s

2m

2.27m/s

3.42 m/s

The following calculations show how we found each figure in the table above:

Calculations for average time:

Average time= Sum of times for specific height

10

1) Height-10cm

Time = Sum/10

1.88 + 1.68 + 1.69 + 1.75 + 1.90 + 1.93 + 1.67 + 1.81 + 1.87 + 1.99

10

Average time= 1.85 seconds

2) Height-25cm

Time = Sum/10

1.02 + 1.01 + 1.05 + 1.07 + 1.09 + 0.97 + 1.11 + 1.04 + 1.02 + 0.99

10

Average time = 1.10 seconds

3) Height- 35cm

Time = Sum/10

0.98 + 0.86 + 0.95 + 0.94 + 0.94 + 0.89 + 0.93 + 1.00 + 0.90 + 0.94

10

Average time = 0.94 seconds

4) Height- 50cm

Time = Sum/10

0.79 + 0.94 + 0.93 + 0.94 + 1.00 + 0.91 + 0.91 + 0.95 + 0.88 + 0.96

10

Average time = 0.92 seconds

5) Height- 60cm

Time = Sum/10

0.94 + 0.85 + 0.93 + 0.87 + 0.89 + 0.99 + 0.95 + 0.94 + 0.96 + 0.97

10

Average time = 0.74 seconds

Calculations for Average Speed

Speed = Distance/Average time

1) Height- 10cm

Speed =Distance/Time

2m/1.85s

Average speed = 1.08 m/s

2) Height- 25cm

Speed =Distance/Time

2m/1.10s

Average speed = 2.81 m/s

3) Height- 35cm

Speed =Distance/Time

2m/0.94s

Average speed = 2.10 m/s

4) Height- 50cm

Speed = Distance/Time

2m/0.92s

Average speed = 2.20m/s

5) Height- 60cm

Speed = Distance/Time

2m/0.74s

Average speed = 2.27 m/s

Calculations for 2GH

2GH = 2 x 9.8 (gravitational force) x height

1) Height-10cm

2GH= 2 x 9.8 x 0.1m =

2GH = 1.4 m/s

2) Height-25cm

2GH = 2 x 9.8 x 0.25m

2GH = 2.21 m/s

3) Height- 35cm

2GH= 2 x 9.8 x 0.35m

2GH= 2.26 m/s

4) Height- 50cm

2GH= 2 x 9.8 x 0.5m

2GH = 3.15 m/s

5) Height- 60cm

2GH= 2 x 9.8 x 0.6m

2GH = 3.42 m/s

Analysis

This experiment showed us that the height of the ramp does affect the velocity. The formulas that show this are:

Kinetic energy = half x mass x velocity squared

(This shows the more kinetic energy an object has the faster it is going)

Velocity = 2GH

However, our graphs show that this is wrong, but I feel that the one anomalous result that differs to this theory is wrong, and most certainly an error.

It was apparent through our results that there was a large amount of human error in our results. This was probably because of reaction time and misreading the results and figures. One mistake in an experiment could completely change the outcome of the test.

The first graph, which shows the height of the ramp vs. the velocity, is curved. As I have already stated, there was one result, which was way out of the curve, and nowhere near the rest of the results, which were very accurate. The results came out in a curved line because of the effect of squared numbers on our figures.

The second graph, which shows velocity vs. 2gh, is a straight line. There are two results that are quite a distance from the line of best fit. These could have been errors. There are three out the five results on the line of best fit, showing that our results are not quite as accurate as they could have been.

The percentage errors in our experiment are calculated by dividing average speed by the 2GH, and the times the result by one hundred.

1) Height – 10cm

Average Speed / 2GH x 100

1.08 m/s / 1.4 m/s x 100 =

77.1 % error

2) Height – 25cm

Average Speed / 2GH x 100

2.81 m/s / 2.21 m/s x 100 =

127 % error

3) Height – 35cm

Average Speed / 2GH x 100

2.10 m/s / 2.26 m/s x 100 =

92.9 % error

4) Height – 50cm

Average Speed / 2GH x 100

2.20 m/s / 3.15 m/s x 100 =

69.8 % error

5) Height – 60cm

Average Speed / 2GH x 100

2.27 m/s / 3.42 m/s x 100 =

66.3 % error

This set of data shows that our results had a lot of error in them and there are many ways in which we could have obliterated error in this experiment.

Many things could have affected our results. One of these things could have been friction. Friction is caused by two surfaces moving over each other. From the kinetic energy, it will produce different amounts of thermal, sound and sometimes even light energy. Because kinetic energy is being converted at least one of the surfaces will slow down if no more energy is being supplied. The amount of energy being converted per second depends upon the surfaces that are rubbing together. Friction can be reduced by lubricating or by polishing the surfaces. This could have changed our results, as the object we were using could have been slowed down by the ramp.

Another thing could have been air resistance, which would have slowed the object down as it came down the ramp, or when it hit the floor, and rolled across. Air resistance happens because of the particles in the air that impact against an object. More that hit the object; the more the object is slowing down. Air resistance can be reduced by streamlining the object and making it more aerodynamic, or by moving it into a vacuum, which completely eliminates air resistance.

The last thing that could have affected our results is reaction time. This is the time in which the person controlling the clocks could react. This could be obliterated by making the experiment completely computer controlled. This could be done by starting and stopping the clocks with lasers and recording the results through computers. This would eliminate the possibility of human error and our experiment would be a completely fair test.

Our prediction was correct, as we predicted that the height of the ramp would affect the velocity. Therefore the experiment was successful.

The conclusion of this experiment is that potential energy turns to kinetic energy in practice.

Evaluation:

Our experiment was successful as our prediction was correct, and we got the results we expected. There were some points that were anomalous (off the line of best fit), and they were errors, which were made when recording the results. The anomalous results found in this experiment were:

On the Graph: Height of Ramp vs. Velocity

* Height – 0.25m, Velocity – 2.6 m/s

On the Graph: 2GH vs. Velocity

* 2GH – 1.4 m/s, Velocity – 1.08 m/s

* 2GH – 2.21 m/s, Velocity – 2.81 m/s

* 2GH – 3.15 m/s, Velocity – 2.20 m/s

* 2GH – 3.42 m/s, Velocity – 2.27 m/s

The evidence that could show why these results were anomalous is that all the results where gathered and recorded by humans, not computers. The main sources of error in this experiment were human errors and the way in which we recorded the results.

To correct these errors we could use more specialist equipment, such as lasers to control the clocks, and computers to record the results. We could also do the whole experiment in a vacuum, so air resistance was obliterated and use a sheet of glass to ensure there was no friction to slow the object as it descends down the ramp. This would help to make our results more accurate.

Perhaps there were other errors in our experiment that we could not avoid, such as the object not going down the ramp in a straight line. This would have contributed to any results that might have occurred. This could be change by having a narrower ramp.

If I could do the experiment again, I would have two people recording the results, and then take the average of the two results. This would help to find the source of error easier. I feel we have enough data to form a firm conclusion and that it would not be necessary to conduct more tests. If I had access to any equiptment, I would try to make the whole experiment, computerised and have no human involvement. This would obliterate the main source of error in any experiment or investigation, which is human error. Without human error, our experiment would have been 100% accurate and correct, without any flaws or mishaps. This would help to get rid of error and give us a better, fairer set of results.

There are other experiments that we could test the hypothesis on. One experiment is the Ball and Ruler experiment. This experiment could show how air resistance affects an object falling through the air.

Apparatus

* A set of ten metre rulers

* A tennis ball

* A Stopwatch

Diagram

Method

The apparatus is set up. Ten heights are decided in advance, to obtain a wide range of results.

Then one person takes the tennis ball and drops it from the first height. This is recorded from the time the person drops the ball, to the time it hits the ground. The result is recorded and then this exercise is done a further nine times. Once all ten results have been recorded on the first height, the height is changed, and the experiment is carried out ten times.

When all the results are gathered, they should show how different heights have a different rate of air resistance. This experiment could be used to back up the first experiment and reiterated the results, as well as show their accuracy.