8 labs

My_Files folder/PHSC 1011online/Chapter 3/Home Challenge Lab 3 Gravitation.htm

Home Challenge Lab 3  Newton’s Law of Gravitation

 

Essential questions that you can answer once you complete the lab:

• How do the acceleration and force due to gravity depend on the radius and mass of a planet?

• How does the mass of a falling body affect the rate at which it falls in a gravitational field?

Objectives: • see that the acceleration of an object due to gravity is independent of its mass

• determine what they would weigh on other planets

• see that the force they feel from gravity depends on the radius and the mass of the planet

  

Materials: • Several objects of different masses and sizes, such as pencils, crumpled up aluminum foil, coins, fishing weights, etc. Make sure they are not breakable! Do not use flat sheets of paper or objects with wind resistance such as balloons.

• Calculator

Pre-Activity Reading: Newton’s Law of Gravitation and the Swift Satellite

In this exercise we will study the relationship between the gravitational force on an object and its acceleration and velocity.

The following describes a satellite “Swift” that has been placed in orbit around the Earth.  Just read over the following before doing the lab to gain a better understanding of how objects remain in orbit around the Earth.

Recall that as Swift enters its orbit, it has velocity that is purely “horizontal” – that is, it is moving parallel to the curved surface of the Earth at each point. However, the force of the Earth’s gravity on Swift is “vertical” – pointed towards the center of the Earth. Why then does Swift not fall to Earth immediately? The answer is that Swift moves horizontally at just the right rate so that as it falls vertically, its motion creates a circular path around the Earth. This balance between “horizontal” and “vertical” motion is what is meant by “being in orbit.” Swift will be able to stay in orbit for many years, as long as its horizontal velocity is maintained at a high enough rate. The special relationship between the horizontal velocity and the gravitational acceleration for any body that is orbiting another more massive body was worked out by Johannes Kepler years before Sir Isaac Newton figured out the Law of Universal Gravitation.

Eventually, the cumulative effect of the small number of atmospheric molecules hitting Swift in its orbit 600 km above Earth will cause the “horizontal” motion of the satellite to slow down; its horizontal motion will no longer be able to completely counteract its vertical motion. When this happens, Swift’s orbit will start to “decay.” As Swift spirals in closer to the Earth there will be even more atmospheric drag, which will cause Swift’s orbit to decay increasingly faster. Swift will end its life plunging in through the Earth’s atmosphere, probably sometime around 2014.

The relationship between the velocity and acceleration of Swift in its orbit is shown below.

 

 

 

 

Fill in all answers to the questions below.

 You already know about gravity: it holds you down to the Earth. But there is more to gravity than that! In this activity you will investigate a few properties of gravity and see how it affects you – not just on Earth, but on other planets!

The goal of Part A is to determine the relationship between the acceleration due to gravity and the mass of an object. The goals of Part B are to determine how much you would weigh on other planets and how that weight is affected by the mass and radius of the planet.

Part A: The Fall of Objects

1) Obtain several objects of different masses and sizes, such as pencils, crumpled up aluminum foil, coins, fishing weights, etc. Make sure they are not breakable! Look over them: are they all the same size, the same weight?

Pick two of the objects that have different weights and sizes. They should be different enough that you can easily feel the difference. If they are dropped from the same height, will one hit the floor first, or will they hit at the same time? Make a prediction about this, and record it on the answer sheet below.

2) Now take the objects and hold them in front of you. Make sure the bottoms of the objects are the same height from the floor. Have another person kneel or lie down on the floor in front of you so they have a good view of where the objects will land.

Count backwards from three, and on “zero” drop the objects at the same time. Did one hit first? If so, which one? Note what happened on your sheet. Repeat the procedure at least twice more to make sure you get consistent results.

3) Was your prediction accurate? Why or why not? Can you think of any ways your experiment might have been thrown off? Explain.

4) Now find two objects that are roughly the same size, but very different weights. Repeat the experiment, and again record your prediction and the results

5) Did the results surprise you? Why or why not?

Part B: The Gravity of the Situation:

Newton’s model of gravity is one of the most important scientific models in history. It applies to apples falling from trees, baseballs soaring into the outfield, and milk being spilled on a floor. The exact same model applies to other planets in our Solar System, too!

Use the Solar System table given below to determine the value of g, the acceleration due to gravity, for each of the other planets in the Solar System. Use the equation for acceleration in the box and the values for the masses and radii of the planets listed in the table. Complete the third column of the table (simply type the correct responses on your submission) with the value for the surface gravitational acceleration for each planet (and the Moon).

 

Use this equation to solve for the second column (Acceleration) on the following chart in Part B.

 g = GM/R2

where M = mass, R = radius,

and G = 6.672 x 10-11 N m2/kg2

 

 

Part B: The Gravity of the Situation - Complete the solar system data chart (it does not have to be in chart format for your Dropbox submissions; simply type the name of the planet and the correct answers beside it on your paper):

Planet Name	Mass (kg)	Radius (m)	Acceleration (m/sec2)	*Acceleration compared to Earth(m/sec2)
Mercury	3.3 x 1023	2.4 x 106
Venus	4.9 x 1024	6.1 x 106
Earth	6.0 x 1024	6.4 x 106	9.8 m/sec2	1
Moon	7.4 x 1022	1.7 x 106
Mars	6.4 x 1023	3.4 x 106
Jupiter	1.9 x 1027	7.1 x 107
Saturn	5.7 x 1026	6.0 x 107
Uranus	8.7 x 1025	2.6 x 107
Neptune	1.0 x 1026	2.5 x 107
Pluto	1.3 x 1022	1.2 x 106

Once you complete the third column, you can see how strong (or weak) gravity is on other planets. A better way to understand this is to compare the gravity of the planets with the Earth’s. *So in the last column, divide the gravity you got for the other planets by the Earth’s gravity (for example, after you do this, you will get the Earth’s gravity = 1, since you are dividing the number you got for Earth’s gravity by itself).

a. Would you weigh more or less on Mercury than you do on Earth?

 

b. How about Jupiter?

 

c. How much would you weigh on the Moon?

 

d.What is the difference between mass and weight?