PHY_10_14_V2_DM_The law of universal gravitation

1. Newton’s Law of Gravitation

Now, work in pairs and access the applet, Gravity Lab, from the website given below:

http://www.adlerplanetarium.org/education/teachers/plans/interactives/gravity.shtml

Click on Explore Gravity and do as the applet suggests: toy with the universe!

While exploring the applet with the various masses, try and see if you can deduce what physical quantities does gravitational attraction depend on. 

1) _______________             2) ________________

Newton’s universal law of gravitation states that, for any two mass in the universe, there exists a _________________ between the two masses that is _______________ to the ______________ and ___________

_________ to the ________________________________________.

Mathematically, the above statement can be represented as:

M, m are _______ of the objects, r is the ________________________ _________and F is ________________________. The constant of proportionality, G, was determined by Newton to be 6.67 x 10^-11 Nm²kg^-2.

PROBLEM 1:

Calculate the gravitational force the Sun exerts on the Earth. Does the Earth exert the same force on the sun?

{Radius of Earth’s orbit: 1.50 x 10¹¹ m; Mass of Earth: 6.0 x 10²⁴ kg; Mass of Sun: 2.0 x 10³⁰ kg}

PROBLEM 2:

Joseph has a body mass of 100 kg and Daniel has a body mass of 70 kg. If they were standing 2.0 m apart from each other, what is the force of attraction between the two bodies?

Back to the Gravity Lab

Access the applet for Gravity Lab again and enter into Explore Gravity. Now, work with your partner to design an experiment that will allow you to plot a graph depicting the relationship between the separation distance of the two masses and their mutual gravitational attraction. (Note: Only do for 5 pairs of values). Print out the graph and attach it to the back of your worksheet.

3. Gravitational Field Strength,

Derive the above expression for g using  and Newton’s second law,

.

Note:

1)                  Gravitational field strength grows _________ when one is increasingly further away from the mass producing the gravitational field.

2)                  The expression only applies for r greater than __________________________________.

PROBLEM 3: Calculate the gravitational field strength, g, at the following heights above the Earth’s surface:

1) 100 m; 2) 1 km; 3) 10 km. (Radius of Earth: 6400 km)

What can you deduce about the gravitational field strength, g, near the Earth’s surface?

HOMEWORK TIME!!!

Do the following assignment with your partner.

In the movie Independence Day, the alien race that came to invade Earth arrived in a mothership that was 1/4 the mass of our moon. It arrived to a stop about 36,000 km above the Earth’s surface, which is about 1/10 of the distance from Earth to our moon.

Based on the information given and any other that you feel necessary, make an estimate of the gravitational attraction of the mothership on our planet. Discuss what are the effects on Earth due to the presence of such a massive object at such distances.

Was it necessary for the aliens to shoot at us at all?

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