Find the attractive force of gravity between two objects

In summary, Cavendish was able to measure the gravitational force between two known masses, lead balls, by using Newton's Law of Universal Gravitation.
  • #1
ac7597
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6
Homework Statement
Henry Cavendish succeeded in measuring the value of the constant "G" way back in the late 1700s. His method was to put two known masses at a known distance and measure the attractive force between them; then he could use Newton's Law of Universal Gravitation to find "G".
The basic idea was to put a big sphere of a dense material next to a small sphere of dense material. Cavendish chose lead. He made one big ball with radius 5.6 inches, and one small ball with radius 1.9 inches. He then placed them next to each other, with a gap of just 0.5 inches between their closest surfaces.

How large was the attractive force of gravity between these two balls?
Relevant Equations
F=G(mass1)(mass2)/(radius)^2
G=6.67 * 10 ^(-11)
Homework Statement: Henry Cavendish succeeded in measuring the value of the constant "G" way back in the late 1700s. His method was to put two known masses at a known distance and measure the attractive force between them; then he could use Newton's Law of Universal Gravitation to find "G".
The basic idea was to put a big sphere of a dense material next to a small sphere of dense material. Cavendish chose lead. He made one big ball with radius 5.6 inches, and one small ball with radius 1.9 inches. He then placed them next to each other, with a gap of just 0.5 inches between their closest surfaces.

How large was the attractive force of gravity between these two balls?
Homework Equations: F=G(mass1)(mass2)/(radius)^2
G=6.67 * 10 ^(-11)

total radius=((5.6in)+(1.9in)+(0.5in))(0.0254m) = 0.203m

(mass1)(9.8m/s^2)=(6.67 * 10 ^(-11) ) (mass1)(mass2)/( (5.6in)(0.0254 m) )^2
mass2=2.97 * 10^(9) kg

(mass2)(9.8m/s^2)=(6.67 * 10 ^(-11) ) (mass1)(mass2)/( (1.9in)(0.0254 m) )^2
mass1=342.2 * 10^(6) kg

F=(6.67 * 10 ^(-11) )(342.2 * 10^(6)) (2.97 * 10^(9)) / (0.203m)^2
F=1.645 * 10^(9) N
Apparently this incorrect. I don't know why.
 
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  • #2
The problem is your determination of m1 and m2. Why are you using 9.8 m/sec^2? Show us your work in determining these masses.

AM
 
  • #3
Do I need to find the mass of both objects? Can I somehow cancel them out of the equation?
 
  • #4
ac7597 said:
Do I need to find the mass of both objects? Can I somehow cancel them out of the equation?

If force depends on the masses, then how could the masses cancel out?
 
  • #5
The density of lead does not appear in your calculations anywhere. You appear to be determining the mass of the balls by assuming that the acceleration of each ball toward the other is 9.8 m/sec^2. That is not correct. You have the mass of a lead ball of radius 1.9 inches at 342 million kilograms!

AM
 
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  • #6
This the correct force=1.18 * 10^(-6) N ?
 
  • #7
ac7597 said:
This the correct force=1.18 * 10^(-6) N ?
You should show us how you arrived at that answer.

AM
 
  • #8
The top portion is for this question
 

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  • #9
Your method is correct. If you use 11.34 g/cc for the density of lead the answer should work out to 1.18 e-6 N.

AM
 

Related to Find the attractive force of gravity between two objects

1. What is the equation for calculating the attractive force of gravity between two objects?

The equation for calculating the attractive force of gravity between two objects is F = G * (m₁*m₂)/r², where F is the force of gravity, G is the gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between them.

2. How does the distance between two objects affect the gravitational force between them?

The gravitational force between two objects is inversely proportional to the square of the distance between them. This means that the force of gravity decreases as the distance between the objects increases.

3. What is the gravitational constant?

The gravitational constant, denoted by G, is a fundamental constant that appears in the equation for calculating the force of gravity between two objects. Its value is approximately 6.674 x 10⁻¹¹ N*m²/kg².

4. Does the mass of the objects affect the gravitational force between them?

Yes, the gravitational force between two objects is directly proportional to the product of their masses. This means that the force of gravity increases as the masses of the objects increase.

5. What are some real-life examples of the attractive force of gravity between two objects?

Some real-life examples of the attractive force of gravity between two objects include the Earth's gravitational pull on objects on its surface, the Moon's gravitational pull on the Earth causing tides, and the gravitational pull between the Sun and planets in our solar system.

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