Laws of Motion Weight and Apparent Weight Force

Laws of Motion Weight and Apparent Weight

Force of Gravity Forces cause acceleration. If there is an acceleration of gravity, then there must be a force of gravity that causes it. The force of gravity is long range force acting between masses. All masses are surrounded by gravity fields. Imagine an isolated mass. The ability of this 1 st mass to generate a force of gravity on other masses can be determined at every point in space surrounding this mass. The mathematical field of gravity values is known as the gravity field. When a 2 nd mass (an object) is positioned at a specific point in the gravity field of the 1 st mass (the agent), then the 2 nd mass will experience a force of gravity equal to the mass of the object (2 nd mass) multiplied by the gravity field of the agent (1 st mass). The gravity field, g , has the same magnitude and direction as the acceleration of gravity. There is a conceptual difference between them, but they are mathematically the same.

Weight is another term for the force of gravity. Mass and Weight People in the United States often have difficulty distinguishing mass and weight. This may be due to the fact that we are never taught the units for mass in the SILLY system, which is the really awful measurement system used only by the United States, Liberia, and Myanmar. What are the units of mass in the silly system is? Slugs People in the United States often say they need to lose weight. If you want to lose weight move to the equator or go to the moon. Either of these will reduce the force of gravity acting on you. What people really want is to lose some of the excess mater that they are composed of. They really want to lose MASS not weight. Losing mass will indirectly reduce your weight, but changing weight does not solely depending on changing mass. Let’s see if you know the difference between mass and weight.

Example 1 Complete the table below. 60 kg object Mass on Earth Weight on Earth Mass on Moon where gravity is 1/6 th of Earth. Weight on Moon where gravity is 1/6 th of Earth. 120 N object

g’s Many quantities have a variety of units. Example: Length can be expressed in centimeters, kilometer, inches, yards, miles, astronomical units, light years, etc. This is also true for acceleration. While we will always work in m/s 2 your calculus class tend to work in ft/s 2 (Seriously. The highest level of instruction in high school mathematics uses the silly system. You have to be kidding me. No wonder we run with Liberia and Myanmar. ) An alternate unit of acceleration used in physics is g’s. 1 g = 9. 8 m/s 2 (One “g” is one Earth gravity) If you are know the acceleration in m/s 2 , and need the acceleration in g’s , divide the acceleration in m/s 2 by 9. 8 If you are know the acceleration in g’s , and need the acceleration in m/s 2 , multiply the acceleration in g’s by 9. 8

How Do Humans Feel Motion? Acceleration Examples: • Seasickness. • Vibration of a car. • • Pit of the stomach feeling when an elevator moves downward. The heavy, light, and side to side feeling on a roller coaster ride. What about constant velocity? Humans can only sense changes in velocity. We have not sensation of motion when velocity is constant. This means that humans CANNOT distinguish the difference between being at rest of moving at constant. Example: You feel stationary at this moment. However, the Earth is turning and moving through space. Yet you have no sensation of this motion. But, I can feel motion when I drive a car at constant velocity. What you actually are detecting is the vibration of the car due to the engine and road. Vibrations involve continuous changes in speed and direction, and it is this acceleration that you feel.

How Do Humans Feel Weight? You actually CANNOT feel your weight. An object cannot create a force on itself. An external agent is needed to create a force on an object. When you feel a force, it is the push of the agent that you feel. However, gravity is NOT a contact force. You CANNOT feel gravity pushing you. Yet I know that I have weight. After all I get tired of standing, and if I exercise I get tired of lugging all my weight around. When you are standing, sitting, or lying down you are in contact with a surface. Your weight pulls you down into that surface and according to Newton’s 3 rd law, the surface pushes back. The normal force of the surface pushing back on you is a contact force that you are capable of sensing. Humans sense the normal force of the surfaces they are into contact with, and this is what your senses interpret as your weight. However, normal forces and weight are not always equal. This means that humans can be tricked into feeling heavier and lighter.

Apparent Weight You CANNOT feel your own weight. An object cannot create a force on itself. When you feel a force, you are actually feeling the push of an agent (external object doing the pushing). Gravity is NOT a contact force. How can you feel a force that does not physically touch you? When you are standing, sitting, or lying down you are in contact with a surface. Your weight pulls you down into that surface, and according to Newton’s 3 rd law the surface pushes back. The normal force of the surface pushing against you is a contact force, which you are capable of sensing. When you are stationary the normal force acting upward is equal to your weight pulling downward. What you feel and describe as your weight is actually your brain’s interpretation of the normal force. However, normal force and weight are not always equal. This means that humans can be tricked into feeling heavier and lighter. The appearance of a weight that is different from our actual weight is known as apparent weight.

Calculating Apparent Weight Apparent weight differs from real weight when object are accelerating. There are two main ways to determine apparent weight. 1. If the acceleration of an object is given and is different than 9. 8 m/s 2, simply multiply the objects mass by the acceleration. Example: An 80 kg astronaut experiences 5. 0 g’s of acceleration during a spacecraft launch. What is their apparent weight? w apparent = Fg apparent = ma = (80)(5 9. 8) = 3920 N 2. If the object is in contact with a surface, then solve for the normal force. w apparent = Fg apparent = N Example: An elevator ride. See the next few slides.

Vertical Motion and Apparent Weight The free body diagram for a person in contact with a surface that is accelerating vertically is the same for both upward and downward motion. Exception: When ropes are involved, tension replaces normal force as the variable that equals apparent weight (rope swings, climbing ropes, etc. ) This means that the sum of forces is also the same, as are most of the steps in solving for the normal force. The problem will differentiate when it is time to substitute values for acceleration. N Moving up (+) and speeding up (+): +a Moving up (+) and slowing ( ): a Moving down ( ) and speeding up (+): a Fg Moving down ( ) and slowing ( ): +a Constant Velocity or Stationary a=0

Elevators (or, vertical motion and apparent weight) Leaves 1 st floor accelerating upward at 2. 0 m/s 2 Moving upward at a constant velocity of 3. 0 m/s Nearing 10 th floor and decelerating at 2. 0 m/s 2 Stopped at the 10 th floor. Assess Acceleration upward, ΣF = ma Constant velocity upward, ΣF = 0 Decelerating upward, ΣF = ma Stationary, ΣF = 0 Diagram The diagram is the same for all four scenarios Up, slowing: + a a=0 ΣF Solve N Fg Sum of forces is the same The problem does not differentiate until the numerical substitution of acceleration. Up, faster: + + a a=0

Elevators (or, vertical motion and apparent weight) Leaves 10 th floor accelerating down at 2. 0 m/s 2 Moving down at a constant velocity of 3. 0 m/s Nearing 1 st floor and decelerating at 2. 0 m/s 2 Stopped at the 1 st floor. Assess Acceleration down, ΣF = ma Constant velocity down, ΣF = 0 Decelerating down, ΣF = ma Stationary, ΣF = 0 Diagram The diagram is the same for all four scenarios Down, slower: a a=0 ΣF Solve N Fg Sum of forces is the same The problem does not differentiate until the numerical substitution of acceleration. Down, faster: + a a=0

Apparent Weightlessness Astronauts in space experience weightlessness. However, they possess mass and are pulled to Earth by the force of gravity. Therefore, they have weight. Even though they are in space, they are still very close to Earth. Surprisingly, the pull of gravity acting on astronauts orbiting Earth is just slightly lower than it is on Earth. So why do they experience a feeling of weightlessness? When in orbit the astronauts and their spacecraft, are actually falling toward Earth. Everything is in free fall together. Since they are falling at the same rate as the spacecraft the surfaces in the ship cannot create a contact force on the astronauts. With no normal forces to give the astronauts a sensation of weight they feel weightless, despite having an actual weight nearly the same as on Earth. If the spacecraft is continually falling, what prevents it from crashing into Earth? When a spacecraft has the correct orbital speed its tangential velocity combines with the vertical free fall to create a projectile motion effect that matches the curvature of Earth. The spacecraft circles Earth, continually falling but never changing height. You don’t need to go into space. Any amusement park ride that causes you to lose contact with the surfaces that you would normally be touching will make you feel temporarily weightless.