![]() Another way to state this is that the magnitude of the field in any region is proportional to the number of lines that pass through a unit surface area, effectively a density of lines. The strength of g → g → at any point is inversely proportional to the line spacing. (The box has been added only to aid in visualization.)Īs is true for any vector field, the direction of g → g → is parallel to the field lines at any point. Note that the lines are uniformly distributed in all directions. But until Cavendish determined the value of G, the masses of all these bodies were unknown.įigure 13.8 A three-dimensional representation of the gravitational field created by mass M M. Later in this chapter, we will see that the mass of other astronomical bodies also can be determined by the period of small satellites orbiting them. The ratio of the Moon’s mass to Earth’s is the ratio of to. Earth and the Moon orbit about a common center of mass, and careful astronomical measurements can determine that location. But the mass of the Moon can actually be determined accurately without going to the Moon. The most accurate values for g and the mass of the Moon come from tracking the motion of spacecraft that have orbited the Moon. Newton attempted to measure the mass of the Moon by comparing the effect of the Sun on Earth’s ocean tides compared to that of the Moon. The average density of the Moon is actually only 3340 kg/m 3 3340 kg/m 3 and g = 1.6 m/s 2 g = 1.6 m/s 2 at the surface. (In fact, that was the ultimate purpose of Cavendish’s experiment in the first place.) The value we calculated for g of the Moon is incorrect. ![]() m 2 /kg 2 ) ( 1.1 × 10 23 kg ) ( 1.7 × 10 6 m ) 2 = 2.5 m/s 2Īs soon as Cavendish determined the value of G in 1798, the mass of Earth could be calculated.If we substitute mg for the magnitude of F → 12 F → 12 in Newton’s law of universal gravitation, m for m 1 m 1, and M E M E for m 2 m 2, we obtain the scalar equation We now know that this force is the gravitational force between the object and Earth. This weight is present regardless of whether the object is in free fall. The force causing this acceleration is called the weight of the object, and from Newton’s second law, it has the value mg. Recall that the acceleration of a free-falling object near Earth’s surface is approximately g = 9.80 m/s 2 g = 9.80 m/s 2. We also examine the gravitational effects within spherical bodies. In this section, we observe how Newton’s law of gravitation applies at the surface of a planet and how it connects with what we learned earlier about free fall. Describe how the value of g g varies due to location and Earth’s rotation.Determine the mass of an astronomical body from free-fall acceleration at its surface.Explain the connection between the constants G G and g g.Write your full formula and check with your instructor.By the end of this section, you will be able to: Determine the gravitational constant (G) that will satisfy your units G= 8. Does your lab data for mı, m2, and r does equal Fg? Also work out your units, do they equal a unit of force? 6. Combine your proportions between Mass 1 (mı), Mass 2 (m2) distance (r) into a single proportion to the Force of gravity (Fg). ![]() What is the relationship between distance and the force of gravity? What happens if you triple the distance between the objects? Half the distance between them? 4. ![]() What is the relationship (proportionality) between Mass and force? What happens to the force if you double the mass of the blue object? What happens to the force if you then triple the red object's masses? 3. ![]() Explain why varying the second mass had the same effect on the force as varying the first mass. force experiment, changing the second mass. Select a new independent and dependent variable and constant a. Select an independent and dependent variable and constant a. Quantitative It is now time to build a model. What direction are the gravitational forces acting on the objects? What is the ratio of the force on the blue object to the force on the red object? What if the mass of the blue one is twice as big as the red object? Explain. What happens to the force between the objects if Mass 2 decreases? (increases, decreases, not affected) 4. What happens to the force between the objects when mass 1 increases? (increases, decreases, not affected) Gravity Force Lab PRET = 3. How does the changing the separation of the objects affect the force between them? (increases, decreases, not affected) Omeri 2 3 4 5 6 7 8 9 10 Mass 2 Show values Mass 1 38 kg 25 kg 2. Determination of the Force of Gravity Qualitative Observations 1. ![]()
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