![]() ![]() The mass of an object remains constant regardless of where the object is and is, therefore, an intrinsic property of an object. The words mass and weight are frequently used interchangeably, but even though mass is often expressed by measuring the weight of an object using a spring scale, they are not equivalent. While these are conceptually distinct, there have not been conclusive, unambiguous experiments that have demonstrated significant differences between gravitational and inertial mass. Active gravitational mass is the measure of how much gravitational force an object exerts, while passive gravitational mass is the measure of the gravitational force exerted on an object within a known gravitational field. There exist other common definitions of mass including active gravitational mass and passive gravitational mass. While many different units are used to describe mass throughout the world, the standard unit of mass under the International System of Units (SI) is the kilogram (kg). An inflated balloon, for example, would have significantly less mass than a golf ball made of silver. The amount of mass that an object has is often correlated with its size, but objects with larger volumes do not always have more mass. ![]() ![]() In classical physics, matter is any substance that has mass and volume. Matter, however, is somewhat loosely defined in science, and cannot be precisely measured. It is most commonly measured as inertial mass, involving an object's resistance to acceleration given some net force. In 1 s an object falls 5 m without air resistance.Mass is typically defined as the amount of matter within an object. If the initial speed is great enough, the projectile goes into orbit. The range is larger than predicted by the range equation given earlier because the projectile has farther to fall than it would on level ground, as shown in (Figure), which is based on a drawing in Newton’s Principia. If, however, the range is large, Earth curves away below the projectile and the acceleration resulting from gravity changes direction along the path. When we speak of the range of a projectile on level ground, we assume R is very small compared with the circumference of Earth. (Figure) illustrates the notation for displacement, where we define \overset. In other cases we may choose a different set of axes. It is not required that we use this choice of axes it is simply convenient in the case of gravitational acceleration. (This choice of axes is the most sensible because acceleration resulting from gravity is vertical thus, there is no acceleration along the horizontal axis when air resistance is negligible.) As is customary, we call the horizontal axis the x-axis and the vertical axis the y-axis. The key to analyzing two-dimensional projectile motion is to break it into two motions: one along the horizontal axis and the other along the vertical. We discussed this fact in Displacement and Velocity Vectors, where we saw that vertical and horizontal motions are independent. The most important fact to remember here is that motions along perpendicular axes are independent and thus can be analyzed separately. In this section, we consider two-dimensional projectile motion, and our treatment neglects the effects of air resistance. The motion of falling objects as discussed in Motion Along a Straight Line is a simple one-dimensional type of projectile motion in which there is no horizontal movement. Such objects are called projectiles and their path is called a trajectory. Some examples include meteors as they enter Earth’s atmosphere, fireworks, and the motion of any ball in sports. The applications of projectile motion in physics and engineering are numerous. Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration as a result of gravity. Calculate the trajectory of a projectile.Find the time of flight and impact velocity of a projectile that lands at a different height from that of launch.Calculate the range, time of flight, and maximum height of a projectile that is launched and impacts a flat, horizontal surface.Use one-dimensional motion in perpendicular directions to analyze projectile motion.By the end of this section, you will be able to: ![]()
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