Lab 5/31/13

Analysis of Rocket Height and Data

Purpose: To predict the height of a rocket from a taking measurements of thrust and total time of thrust. Launch Rocket and verify predictions.

Equipment: Model Rocket, thrust engine, computer with data logger and excel software, rocket stand

1. Draw a system schema and force diagram and apply Newton's Second Law to a rocket on the launch pad.

2. Redraw the system schema and force diagram and a statement of Newton's Second Law right based on this force diagram for the moment the rocket leaves the ground.

          a. What agent is causing the upward force?

The only upward force on the rocket as it accelerates upward is the thrust force pushing on the air

          b. Do you think the thrust force is constant?  Explain

The force is not constant because the fuel is changing, with time.  The same amount of fuel isn’t being used constantly

3. As the fuel burns, is your rocket speeding up or slowing down? Which force has to be bigger for this to occur? Do you need to modify your force diagram?

Since the net force acting on the rocket is F thrust – Fg, where Fg = mg.  The net force upward is increasing because mg is decreasing due to the loss of fuel.

4. Your rocket is not a particle. Do you think you have to deal with air resistance?

Redo your system schema, force diagram and statement of Newton's Second Law to include it.

Air resistance is dependent on the velocity and the surface area.  Therefore as the rocket is speeding upwards the air resistance is increasing.  The formula to calculate the drag force on the rocket is kv^2.

5. Do you think F air is constant? If not, what does it depend on?

F air is not constant and depends on velocity. 

6. When the rocket has run out of fuel, what does direction is it still going? Is it speeding up or slowing down? Based on this what does your force diagram look like now. What is your new statement of Newton's Second Law?

The rocket is moving with an upward velocity after the rocket has fun out of fuel.  The rocket will continue upward until velocity equals zero, the rocket slows down because the net force is pointing downward. Fnet = -mg - Fair

7. How will you know when the rocket reaches its highest point?

The highest point is when the rocket seizes to move upward, this occurs when velocity is zero.

10. What specific information and measurements do we need?

Specific info: Mass of rocket, cross-sectional area of rocket, air density, force of gravity

Measured info: thrust force of rocket, time, velocity, acceleration, drag force, position

Procedure:  The rocket engine was placed securely on a stand with a force sensor attached.  The engine was then ignited and allowed to run out of fuel.  While the engine was running we used the data logger software along with the force sensor to take a measurement of the thrust force.  The data file gave us a measurement of the thrust over time.   

We then measured the mass of the rocket, which was found to be 63.2 grams.  Also the diameter of the rocket was measured in order to calculate the cross sectional-area.  We calculated the acceleration by using Newton’s second law Fnet = ma or a=Fnet/m.  In our case the calculation was

Fnet = (Fthrust – Fdrag – Fg)/m

Putting the data for thrust versus time along with the calculation for acceleration and the kinematic equations we found all the data needed to predict the height.

It was important to find the data in a specific order to get accurate results the order was time, thrust, acceleration, drag, delta r, and r.  The height found was 147 meters.

The rocket was then launched, after the rocket landed the altimeter was checked and out predictions were verified, the max height was 147meters

Lab 4 4/16/13

Human Power

Purpose: To determine the power output of a person

Equipment: Two-meter meter sticks, stopwatch, kilogram bathroom scale

Introduction:  Power is defined to be the rate at which work is done or equivalently, the rate at which energy is converted from one form to another.  In this lab the work we are performing is climbing the first and second floors of the science building, this work is then converted to gravitational potential energy. The equation used to calculate potential energy is del PE = m*g*h. PE can then be converted to Power in watts as follows: Power(watts) = del PE / del t, where m is the mass, g is the acceleration due to gravity, h is the height of the stairs, del t is change in time, and del PE is change in potential energy.

Procedure:

1.     We started the experiment by weighing ourselves using the electronic scale and data logger.  The data provided from the data logger was our weight in kilograms.  The kilogram is the SI unit for mass.

2.      The next calculation needed to do was to measure the vertical distance between the first and second floors of the science building.  This was done by using two meter long metersicks held end to end.  Figure 1 shows how the measurement was taken and what the measurement was.

3.     A person was assigned to keep track of time spent walking and or running up the stairs. 

4.     After the set up was complete the experiment was ready to begin.  One person at the time walked up and or ran up the stairs a total of two times in order to get the average time.

5.     With the times recorded the calculations were ready to be made. First we calculated our average time.  This was done as follows (T1 + T2)/2.  My average time was (5.49s – 5.2s)/2 = 5.345s.  We then used PE = m*g*h to find our potential energy.  My PE was 780.12(4.26) = 3323.311 J, where J is joules.  Converting PE to power in watts was done as follows PE/avg time, in my case it was 3323.311/5.345 = 621.76 watts. 

6.     Next, we converted our power in watts to power in horse power(hp).  We used the conversion factor 1hp/746watts.  My hp was calculated as follows 621.76watts*(1hp/746watts) = .8335 hp

7.     Our class average was calculated and discussed in class.

Questions

1.     Is it ok to use your hands and arms on the hand railing to assist you in your climb up the stairs?

Yes, because using your hands does not affect your mass or the effect gravity has on your body.  Using our hands and arms does improve the time you spend going up the stairs, but the PE calculation is for our body as a whole not just our feet.  Therefore we can conclude that in using our hands and arms we our outputting more energy, which is found when we divide by a less amount of time than if you had not used your arms.

2.     Discuss the problems with the accuracy of this experiment.

The problems involved with the accuracy of this experiment are the measurement of the stairwell.  Since the metersticks were used end to end the ends of the metersticks tend to be the most worn out since when you set them down you rest them on the ends.  An inaccurate reading of the metersticks would also play a role in accuracy.  Aside from the metersticks, the time measurement also played a role in in accuracy.  If the time was not started when we started moving up the stairs or if the time was started to late our accuracy would be affected.  Inaccurate weight measurement could have been played a role in the accuracy, for example if the reading was not zeroed before stepping on the scale.  Finally, the fact that we had to take a turn while moving up the stairs was another factor in accuracy; since we had to take more time was spent.

Conclusion:  With this lab we learned how to calculate the power output of person both in watts and in horsepower.  From this we can see that if the person is running as opposed to walking the power is going to increase significantly.  Further we can also see that if we were to climb higher our PE would increase as well, based on this observation we can conclude that PE is related to position.  The work we performed going up the stairs is what is stored as PE since we are going against the force of gravity.  Sources of error are listed in question 2.

Fig 1