Chapter 4 4-4 everyday forces

Objectives Explain the difference between mass and weight. Find the direction and magnitude of normal forces. Describe air resistance as a form of friction. Use coefficients of friction to calculate frictional force.

Mass and weight The mass of an object is a fundamental property of the object; a numerical measure of its inertia; a fundamental measure of the amount of matter in the object. Definitions of mass often seem circular because it is such a fundamental quantity that it is hard to define in terms of something else. All mechanical quantities can be defined in terms of mass, length, and time. The usual symbol for mass is m and its SI unit is the kilogram. While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass. The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton. Density is mass/volume.

Weight The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton. For an object in free fall, so that gravity is the only force acting on it, then the expression for weight follows from Newton's second law.

Weight formula

What is Weight? The gravitational force (Fg) exerted on an object by Earth is a vector quantity, directed toward the center of Earth. The magnitude of this force (Fg) is a scalar quantity called weight.

Weight Weight changes with the location of an object in the universe.

Weight Calculating weight at any location: Fg = mag ag = free-fall acceleration at that location Calculating weight on Earth's surface: ag = g = 9.81 m/s2 Fg = mg = m(9.81 m/s2)

Normal Force The normal force acts on a surface in a direction perpendicular to the surface. The normal force is not always opposite in direction to the force due to gravity.

Normal Force In the absence of other forces, the normal force is equal and opposite to the component of gravitational force that is perpendicular to the contact surface. In this example, Fn = mg cos

Friction Static friction is a force that resists the initiation of sliding motion between two surfaces that are in contact and at rest. Kinetic friction is the force that opposes the movement of two surfaces that are in contact and are sliding over each other. Kinetic friction is always less than the maximum static friction.

Coefficient of friction The quantity that expresses the dependence of frictional forces on the particular surfaces in contact is called the coefficient of friction, . Coefficient of kinetic friction: Mk=Fk/Fn

Coefficient of friction

Coefficient A student attaches a rope to a 20.0 kg box of books. He pulls with a force of 90.0 N at an angle of 30.0° with the horizontal. The coefficient of kinetic friction between the box and the sidewalk is 0.500. Find the acceleration of the box.

Coefficient 1. Define Given: Unknown: Diagram: m = 20.0 kg k = 0.500 Fapplied = 90.0 N at  = 30.0° Unknown: a = ? Diagram:

continue 2. Plan Choose a convenient coordinate system, and find the x and y components of all forces. Fapplied,y = (90.0 N)(sin 30.0º) = 45.0 N (upward) Fapplied,x = (90.0 N)(cos 30.0º) = 77.9 N (to the right)

Continue . Calculate A. To apply the condition of equilibrium in the vertical direction, you need to account for all of the forces in the y direction: Fg, Fn, and Fapplied,y. You know Fapplied,y and can use the box’s mass to find Fg. Fapplied,y = 45.0 N Fg = (20.0 kg)(9.81 m/s2) = 196 N Next, apply the equilibrium condition, Fy = 0, and solve for Fn. Fy = Fn + Fapplied,y – Fg = 0 Fn + 45.0 N – 196 N = 0 Fn = –45.0 N + 196 N = 151 N

continue Fk = mkFn = (0.500)(151 N) = 75.5 N

Air resistance Air resistance is a form of friction. Whenever an object moves through a fluid medium, such as air or water, the fluid provides a resistance to the object’s motion. For a falling object, when the upward force of air resistance balances the downward gravitational force, the net force on the object is zero. The object continues to move downward with a constant maximum speed, called the terminal speed

Fundamental Forces There are four fundamental forces: Electromagnetic force Gravitational force Strong nuclear force Weak nuclear force The four fundamental forces are all field forces.

Homework Special project coming up !! Presentation on Newton’s Laws Do a research presentation How is the man behind Newton’s laws A brief history on newton’s laws What are examples of newton’s laws

Closure Today we saw about everyday forces Next class we are going to learn about work and energy