Name:Partner(s):Lab #2 Gravity LabDue 6/30ObjectivesIn this lab, you will measure g, the acceleration due to gravity on Earth. You will getpractice in collecting and interpretting data and estimating uncertainty. You will also useyour measurement of g to find the Earth’s mass.1. (2 pts) Please write a hypothesis that this lab will test.Materials:• Golf ball• Stop watch with 1/100 of a second precision• String and rulers to measure heightProcedure & Results• Find a location suitable for dropping your small object. Drop from a height that ishigh enough to minimize the relative fraction of time it takes to start and stop thestopwatch but not so high that air resistance starts to affect the result (ie- the objectshould not achieve terminal velocity). One or two stories high is a good compromise.• Measure the distance the object will fall in meters.2. (1 pt) Distance in meters:• Time the object’s fall at least 20 times.3. (6 pts) Fill in the table on page 2 with your data.Astronomy 101 2 – 1 Introduction to AstronomyDrop # time (seconds)123456789101112131415161718192021222324252627282930Astronomy 101 2 – 2 Introduction to Astronomy• Find the average value of t. Use your spread in values of t to estimate your randomuncertainty:∆t =(longest time - shortest time)24. (3 pts) What is your measured value of t? (Be sure to Include units AND youruncertainty when writing this.)• Use your average value of t to calculate the Earth’s acceleration due to gravity. Forthis you will need the following relation (Galileo derived this empirically and Newtonderived it from the calculus)g =2ht2where h is the height of the fall and t is the average time of fall.• Use these uncertainties to estimate the biggest and smallest possible values you couldget for g:lowest value of g =2h(t + ∆t)2highest value of g =2h(t − ∆t)2This gives you the range of values of g that are allowed within your uncertainty.5. (3 pts) What is your measured value of g? (Be sure to include units AND youruncertainty when writing this.)Astronomy 101 2 – 3 Introduction to AstronomyAnalysis6. (2 pts) Quantitatively compare your value for g to the current best estimate for theEarth’s acceleration due to gravity (which you can find in Appendix A of your book). Con-sider your uncertainty when making the comparison.7. (3 pt) Identify all sources of error and estimate how much they could have effectedyour measurement of t. Are these errors a reasonable amount to account for your spread inmeasurements of t? In this lab you might be tempted to blame some of your uncertaintyon “human error”. Please be more specific and keep in mind that you need to be able toquantify all sources of uncertainty.8. (2 pt) Were there any other sources of error in your estimate of g besides the uncertaintyin your measurement of t?9. (2 pts) State your conclusions and relate them to your hypotheses.Astronomy 101 2 – 4 Introduction to AstronomyPhysicists have discovered that the acceleration due to gravity on a planet’s surface is relatedto the planet’s mass and radius:g =GMR2where G is the gravitational constant (equal to 6.67 × 10−11Nm2kg2), R is the planet’s radiusand M is its mass.This is simply a restatement of the gravitational law we learned in class:FGravity=GMmD2Here g = FGravity/m i.e., the gravitational acceleration at the surface of the Earth is thegravitational force on an object divided by the mass of the object. In this rewording R = Dbecause our distance from the center of mass of the Earth is the radius of the Earth.10. (3 pts) Using the radius of the Earth found in Appendix A of your text calculate theMass of the Earth using your best value of g as measured in this lab.11. (3 pts) Quantitatively compare this value to the current best estimate for the Earth’smass (also in Appendix A of the text). Consider your uncertainty in g. Does your valuematch if you include the uncertainty?12. (2 pts) How would g change if the mass of the Earth were quadrupled? How wouldFGravitychange? Hint: Rather than plugging in numbers think in terms of ratios.13. (2 pts) How would g change if the radius of the Earth were divided by three? Howwould FGravitychange? Hint: Once again, rather than plugging in numbers think in terms ofratios.Astronomy 101 2 – 5 Introduction to
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