# Mass and force inversely proportional relationship

### An experimental verification of Newton's second law

acceleration equals to the force applied divided by mass You can also see the inverse relation between m and a by solving F=ma for one or. The inverse-square law, in physics, is any physical law stating that a specified physical quantity The inverse-square law generally applies when some force, energy, or other conserved quantity is evenly proportional to the product of their masses and inversely proportional to the square of their separation distance . Patterns and Relationships in. Physics all about RELATIONSHIPS and how things change. inversely proportional to the mass if the FORCE is constant.

As in all such legends, this is almost certainly not true in its details, but the story contains elements of what actually happened. What Really Happened with the Apple? Probably the more correct version of the story is that Newton, upon observing an apple fall from a tree, began to think along the following lines: The apple is accelerated, since its velocity changes from zero as it is hanging on the tree and moves toward the ground.

Thus, by Newton's 2nd Law there must be a force that acts on the apple to cause this acceleration. Let's call this force "gravity", and the associated acceleration the "acceleration due to gravity". Then imagine the apple tree is twice as high. Again, we expect the apple to be accelerated toward the ground, so this suggests that this force that we call gravity reaches to the top of the tallest apple tree. Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an orbit around the earth.

Newton knew that the force which caused the apple's acceleration gravity must be dependent upon the mass of the apple. And since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration Newton's third lawthat force must also depend upon the mass of the earth.

So for Newton, the force of gravity acting between the earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance which separates the centers of the earth and the object. The constant of proportionality G is known as the universal gravitational constant. It is termed a "universal constant" because it is thought to be the same at all places and all times, and thus universally characterizes the intrinsic strength of the gravitational force.

The numerical value of G is very small, which is basically the reason for the force of gravity to be the weakest force of the nature. For the value of "G", refer to your text book.

But Newton's law of universal gravitation extends gravity beyond earth. Newton's law of universal gravitation is about the universality of gravity. Newton's place in the Gravity Hall of Fame is not due to his discovery of gravity, but rather due to his discovery that gravitation is universal.

ALL objects attract each other with a force of gravitational attraction. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance which separates their centers. Weight and the Gravitational Force We have seen that in the Universal Law of Gravitation the crucial quantity is mass. In popular language mass and weight are often used to mean the same thing; in reality they are related but quite different things.

What we commonly call weight is really just the gravitational force exerted on an object of a certain mass. We can illustrate by choosing the Earth as one of the two masses in the previous illustration of the Law of Gravitation: Thus, the weight of an object of mass m at the surface of the Earth is obtained by multiplying the mass m by the acceleration due to gravity, g, at the surface of the Earth.

The acceleration due to gravity is approximately the product of the universal gravitational constant G and the mass of the Earth M, divided by the radius of the Earth, r, squared. We assume the Earth to be spherical and neglect the radius of the object relative to the radius of the Earth in this discussion. Mass and Weight Mass is a measure of how much material is in an object, but weight is a measure of the gravitational force exerted on that material in a gravitational field; thus, mass and weight are proportional to each other, with the acceleration due to gravity as the proportionality constant.

It follows that mass is constant for an object actually this is not quite true as described by the Relativity Theorybut weight depends on the location of the object. For example, if we transported the preceding object of mass m to the surface of the Moon, the gravitational acceleration would change because the radius and mass of the Moon both differ from those of the Earth. Thus, our object has mass m both on the surface of the Earth and on the surface of the Moon, but it will weigh much less on the surface of the Moon because the gravitational acceleration there is a factor of 6 less than at the surface of the Earth.

Using Equations as a Guide to Thinking The inverse square law proposed by Newton suggests that the force of gravity acting between any two objects is inversely proportional to the square of the separation distance between the object's centers. Altering the separation distance r results in an alteration in the force of gravity acting between the objects.

Since the two quantities are inversely proportional, an increase in one quantity results in a decrease in the value of the other quantity. That is, an increase in the separation distance causes a decrease in the force of gravity and a decrease in the separation distance causes an increase in the force of gravity.

### Force, Mass, Acceleration | Zona Land Education

Furthermore, the factor by which the force of gravity is changed is the square of the factor by which the separation distance is changed. So if the separation distance is doubled increased by a factor of 2then the force of gravity is decreased by a factor of four 2 raised to the second power.

And if the separation distance r is tripled increased by a factor of 3then the force of gravity is decreased by a factor of nine 3 raised to the second power. Thinking of the force-distance relationship in this way involves using a mathematical relationship as a guide to thinking about how an alteration in one variable effects the other variable.

Equations can be more than merely recipes for algebraic problem-solving; they can be "guides to thinking. Observe how the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance of separation. In the above figure, the figure on the left hand side indicates the effect of "mass" if the diatnce between the two objects remains fixed at a given value "d".

The right hand figure shows the effect of changing the distance while keeping the mass constant, and the last part of it shows the effect of changing both the distance and the mass. Check your understanding of the inverse square law as a guide to thinking by answering the following questions below.

## The Mighty F = ma

Check Your Understanding 1. Suppose that two objects attract each other with a force of 16 units like 16 N or 16 lb. If the distance between the two objects is doubled, what is the new force of attraction between the two objects? If the distance is increased by a factor of 2, then distance squared will increase by a factor of 4. Therefore, the force of gravity becomes 4 units. Suppose the distance in question 1 is tripled. What happens to the forces between the two objects?

Again using inverse square law, we get distance squared to go up by a factor of 9. The force decreases by a factor of 9 and becomes 1. If you wanted to make a profit in buying gold by weight at one altitude and selling it at another altitude for the same price per weight, should you buy or sell at the higher altitude location?

What kind of scale must you use for this work? To profit, buy at a high altitude and sell at a low altitude. Explanation is left to the student.

Check Your Understanding 4. Your weight is nothing but force of gravity between the earth and you as an object with a mass m. As shown in the above graph, changing one of the masses results in change in force of gravity.

- Newton's Second Law
- Inverse-square law
- Planetary and Satellite Motion

The planet Jupiter is more than times as massive as Earth, so it might seem that a body on the surface of Jupiter would weigh times as much as on Earth. But it so happens a body would scarcely weigh three times as much on the surface of Jupiter as it would on the surface of the Earth. Explain why this is so. The effect of greater mass of Jupiter is partly off set by its larger radius which is about 10 times the radius of the earth.

This means the object is times farther from the center of the Jupiter compared to the earth.

Inverse of the distance brings a factor of to the denominator and as a result, the force increases by a factor of due to the mass, but decreases by a factor of due to the distance squared. Comparing the values in rows 1 and 2, it can be seen that a doubling of the net force results in a doubling of the acceleration if mass is held constant.

Similarly, comparing the values in rows 2 and 4 demonstrates that a halving of the net force results in a halving of the acceleration if mass is held constant. Acceleration is directly proportional to net force.

Furthermore, the qualitative relationship between mass and acceleration can be seen by a comparison of the numerical values in the above table. Observe from rows 2 and 3 that a doubling of the mass results in a halving of the acceleration if force is held constant. And similarly, rows 4 and 5 show that a halving of the mass results in a doubling of the acceleration if force is held constant.

Acceleration is inversely proportional to mass. Whatever alteration is made of the net force, the same change will occur with the acceleration. Double, triple or quadruple the net force, and the acceleration will do the same. On the other hand, whatever alteration is made of the mass, the opposite or inverse change will occur with the acceleration. Double, triple or quadruple the mass, and the acceleration will be one-half, one-third or one-fourth its original value. The Direction of the Net Force and Acceleration As stated abovethe direction of the net force is in the same direction as the acceleration.

Thus, if the direction of the acceleration is known, then the direction of the net force is also known. Consider the two oil drop diagrams below for an acceleration of a car.