ࡱ> { =)bjbjBrBr    !666JJJ8FJ!h:::::ggggggg$i}lg6^g::g"""v8:6:g"g""Z`:`C`\8gg0!h]m`*mp`m6`"gg x!hm : Name: ______________________________________ Date: ________________________ Student Exploration: Gravitational Force Vocabulary: force, gravity, vector Prior Knowledge Questions (Do these BEFORE using the Gizmo.) On the night of a Full Moon, Mary decides to do an experiment with gravity. At midnight, she climbs into her backyard tree house, leans out the window, and holds an acorn as high as she can. She lets go and is disappointed to see the acorn plummet back down to Earth. Why did the acorn fall to Earth instead of rising up to the Moon? ______________________ _________________________________________________________________________ Give two reasons why we feel Earths gravity more strongly than the Moons gravity. _________________________________________________________________________ _________________________________________________________________________ Gizmo Warm-up From acorns to apples, gravity causes nearly any object to fall to Earths surface. Gravity also causes the Moon to orbit Earth and Earth and the other planets to orbit the Sun. The Gravitational Force Gizmo allows you to explore the factors that influence the strength of gravitational force. To begin, turn on the Show force vector checkboxes for objects A and B. The arrows coming from each object are vectors that represent gravitational force. The length of each vector is proportional to the force on each object. Move object A around. As object A is moved, what do you notice about the direction of the two force vectors? __________________________________________________________ How do the lengths of the two vectors compare? __________________________________ Drag object A closer to object B. How does this change the gravitational force between the two objects? ______________________________________________________________ Activity A: Gravity and massGet the Gizmo ready: Turn on Show vector notation for each object. Check that each objects mass (mA and mB) is set to 10.0 105 kg. Question: How does mass affect the strength of gravitational force? Form hypothesis: How do you think the masses of objects A and B will affect the strength of the gravitational force between them? __________________________________________ _________________________________________________________________________ Predict: How do you think the gravitational force between two objects will change if the mass of each object is doubled? ____________________________________________________ Measure: Turn on Show grid. Place object A on the x axis at -20 and object B on the x axis at 20. The force on object A is now 0.0417i + 0j N. That means that the force is 0.0417 newtons in the x direction (east) and 0.0 newtons in the y direction (north). What is the magnitude of the force on object A? |FA| = _______________________ What is the magnitude of the force on object B? |FB| = _______________________ Gather data: You can change the mass of each object by clicking in the text boxes. For each mass combination listed in the table below, write magnitude of the force on object A. Leave the last two columns of the table blank for now. mA (kg)mB (kg)|FA| (N)Force factormA mB (kg2)10.0 105 kg10.0 105 kg10.0 105 kg20.0 105 kg20.0 105 kg20.0 105 kg20.0 105 kg30.0 105 kg Calculate: To determine how much the force is multiplied, divide each force by the first value, 0.0417 N. Round each value the nearest whole number and record in the Force factor column. Next, calculate the product of each pair of masses. Fill in these values in the last column. Compare these numbers to the Force factor numbers. (Activity A continued on next page) Activity A (continued from previous page) Analyze: How much does the force increase if each mass is doubled? _________________ _________________________________________________________________________ Analyze: How do the force factors compare to the products of the masses? _____________ _________________________________________________________________________ _________________________________________________________________________ Apply: What would you expect the force to be if the mass of object A was 50.0 105 kg and the mass of object B was 40.0 105 kg? ________________________________________ Check your answer with the Gizmo. Draw conclusions: How do the masses of objects affect the strength of gravitational force? _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ Summarize: Fill in the blank: The gravitational force between two objects is proportional to the _________________________ of the masses of the objects. Apply: Suppose an elephant has a mass of 1,800 kg and a person has a mass of 75 kg. If the strength of gravitational force on the person was 735 N, what would be the gravitational force on the elephant? (Assume both the person and elephant are on Earths surface.) _________________________________________________________________________ Show your work: Activity B: Gravity and distanceGet the Gizmo ready: Turn on Show distance. Set mA and mB to 10.0 105 kg. Question: How does distance affect the strength of gravitational force? Form hypothesis: How do you think the distance between objects A and B will affect the strength of the gravitational force between them? __________________________________ _________________________________________________________________________ Predict: How do you think the gravitational force between two objects will change if the distance between the objects is doubled? ________________________________________ Measure: Place object A on the x axis at -5 and object B on the x axis at 5. What is the distance between the two objects? ________________________ What is the magnitude of the force on object A? |FA| = ________________________ Gather data: For each set of locations listed below, record the distance and the force on object A. Leave the last two columns blank for now. Object AObject BDistance (m)|FA| (N)Force factor1 Distance2(-5, 0)(5, 0)(-10, 0)(10, 0)(-15, 0)(15, 0)(-20, 0)(20, 0) Interpret: How does increasing the distance affect the force? _________________________ _________________________________________________________________________ Calculate: To calculate the force factor, divide each force by the original force (0.667 N). Write each force factor with three significant digits. Next, calculate the reciprocal of the square of each distance and fill in the last column of the table. Write each of these values with three significant digits as well. (The unit of 1/distance 2 is square meters, or m2.) (Activity B continued on next page) Activity B (continued from previous page) Analyze: Compare the force factors to the 1/distance2 values in your table. What is the relationship between these values? _________________________________________________________________________ _________________________________________________________________________ Apply: What would you expect the force to be if the distance was 50 meters? ____________ Use the Gizmo to check your answer. Make a rule: Based on the measured force between objects that are 10 meters apart, how can you find the force between objects that are any distance apart? _________________________________________________________________________ _________________________________________________________________________ Summarize: Fill in the blanks: The gravitational force between two objects is proportional to the ____________________ of the distance ____________________ Challenge: In activity A, you found that the gravitational force between two objects is proportional to the product of their masses. Combine that with what you have learned in this activity to complete the universal formula for the force of gravity below. (Hint: In the equation, G is a constant.) Check your answer with your teacher.  FGravity = G  On your own: Use the Gizmo to find the value of G in the formula above. List the value and describe how you found it below. The units of G are newton meter2 kilograms2, or Nm2/kg2. Check your answer with your teacher. 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