PS-5.9 Explain the relationship between mass and weight by using the formula FW = mag
Drop a ball and it falls towards the surface of the Earth. This might seem like a really simple statement, but it is an important concept when understanding the idea of weight. Isaac Newton stated that objects fall towards the Earth because of a mutual gravitational attraction between both the Earth and the object. He also determined that the gravitational force is proportional to the masses of the Earth and object. In other words, the more massive an object, like the ball is, the greater the gravitational force of attraction. If the ball, or any other object, is supported by your hand, it is not free to fall. The attractive gravitational force between the object and the Earth is felt by your hand and is referred to as weight. Weight is simply a measure of the attractive force that exists between any object and the Earth or any other massive body you or an object may be on. Mass and weight are not the same!
Near the surface of the Earth, the attractive force of gravity causes all objects to accelerate downward with an acceleration of 9.8m/s2. Of course, you know that if you drop a hammer and a feather, the hammer and the feather will not have the same downward acceleration. You would expect the hammer to hit the ground first, and you would be correct. However, take away air resistance and they will have the same acceleration, and they will both hit the ground at the same time. This was clearly illustrated in 1971 when Commander David Scott of the Apollo 15 crew dropped a hammer and feather while on the Moon. In the absence of air resistance both the hammer and feather did hit the surface at the same time.
One common misconception students have is that there is no gravity on the Moon. Obviously, since the hammer and the feather fell towards the Moon's surface, there must be gravity on the Moon and this why they have weight. The Moon has less mass than the Earth does, so the acceleration due to gravity is less on the moon than on the Earth. With an acceleration due to gravity of 1.66m/s2, objects on the Moon's surface weigh only 1/6 as much as they do on the Earth, but they certainly do have weight! An objects weight may differ from place to place depending on the value of the acceleration due to gravity, but the mass of an object remains constant. Mass is not effected by location, weight is. A 75 kilogram person will have a weight of 735N on the Earth and a weight of 123.5N on the Moon. However, this person's 75kg mass will be the same on both the Earth and the Moon.
Since weight is a force it must be mathematically defined by Newton's Second Law of motion that states F=ma. Since we are discussing a force of weight we can use "Fw" as the force symbol in the equation. We use the symbol "ag" to represent the acceleration due to gravity. Thus, when calculating an objects weight the equation F=ma becomes Fw=mag. Here are two example problems.
Example #1: What is the weight of a 75kg person on the Earth?
Example #2: What is the weight of a 75kg person standing on the surface of the Moon?