A Few Good Questions…

Which has more inertia? Bull elephant, Stampy, sleeping. A small mouse, Speedy, running at 95% the speed of light. Bull elephant, Stampy, stampeding. (d) Both (a) and (c).

(d) Both (a) and (c). Mass is the measure of inertia.

If a car moves with constant velocity, which of the following must be true? No forces act on the car. No unbalanced forces act on the car.

(b) No unbalanced forces act on the car. According to Newton’s Second Law of Motion, unbalanced forces cause accelerations.

If you threw a ball into frictionless space, away from any gravitational forces, the force needed to keep the ball moving is… Equal to the weight of the ball. The same force use to throw it. Zero, because no force is needed.

(c) Zero, because no force is needed. According to Newton’s First Law of Motion, an object in motion will remain in motion unless acted upon by an unbalanced force. In space, if the ball encounters no unbalanced forces, it will continue in constant velocity motion.

Which of Newton’s Laws best explains this animation? First Law Second Law Third Law

(a) First Law A body in motion will remain in motion unless acted upon by an unbalanced force

Which of the following is synonymous with F ? Unbalanced force. Summation of forces. Net force. (d) All of the above.

(d) All of the above. The summation of forces IS the unbalanced force, which is the same as the net force, all of which constitute the force that doesn’t cancel… that is left over. F

If a net force of 20 N acts on a 5 kg object, what it its acceleration? 4 m/s2 9.8 m/s2 100 m/s2

20 N = (5 kg) (a) and therefore, a = 4 m/s2 According to Newton’s Second Law of Motion, the net force is equal to the mass times the acceleration. 20 N = (5 kg) (a) and therefore, a = 4 m/s2

Identify the Reaction Force: Ball hits bat with equal but opposite force. Ball hits bat with less force. Ball hits bat with more force.

(a) Ball hits bat with equal but opposite force. Newton’s Third Law states that for every action, there is an equal but opposite reaction.

Identify the Reaction Force: Earth pulls on dinosaur. Dinosaur pulls up on earth with equal force. Dinosaur pulls up on earth with less force. Dinosaur pulls up on earth with more force.

(a) Dinosaur pulls up on earth with equal force. Newton’s Third Law states that for every action, there is an equal but opposite reaction.

Objectives for Everyday Forces Explain the difference between mass and weight. Find the direction and magnitude of normal forces. Use coefficients of friction to calculate frictional forces. Sketch appropriate forces on free-body diagrams. Use free-body diagrams and apply Newton’s Laws to solve problems.

Mass vs. Weight The mass of an object is the amount of matter contained by the object… that mass doesn’t change, regardless of the position of the object within the universe.

I can lose weight without losing mass… by jumping Mass vs. Weight The weight of an object is the magnitude of the force of gravity acting on an object. Weight changes based on an object’s position in the earth’s gravitational field. The earth’s gravitational field is strongest closest to sea level. I can lose weight without losing mass… by jumping

How to Figure Weight W = mg m is mass of object (in kg) g is 9.8 m/s2 The weight of an object near the surface of the earth may be calculated using: W = mg m is mass of object (in kg) g is 9.8 m/s2

Weight On a free-body diagram, the weight of an object is always represented with a force vector pointing straight down from the center of mass, towards the center of the earth. mg

Which Weighs More? A 25-kg dog in deep space. A 25-kg dog on Earth at sea level. A 25-kg dog on the moon. A 25-kg dog on Mount Everest. (e) They all weigh the same.

(b) A 25-kg dog on Earth at sea level. The weight of an object (or pup) is the gravitational force exerted on that object, which varies with its position.

Which has more mass? A 25-kg dog in deep space. A 25-kg dog on Earth at sea level. A 25-kg dog on the moon. A 25-kg dog on Mount Everest. (e) They all have the same mass.

(e) They all have the same mass. Mass is the amount of matter in an object (or pup). This value does not change with the position of the object.

How Much Does a 25-kg Dog Weigh on Earth? About 250 N About 25 kg About 25 N

(a) About 250 N The weight of an object on earth is equal to the mass of the object times the acceleration due to gravity. W = mg W = (25 kg)(9.8 m/s2)

The Normal Force A Normal Force (FN) is a force exerted by one object on another in a direction perpendicular to the surface of contact. The normal force is not necessarily opposite the weight of an object. FN mg

Friction Friction is a force that opposes the relative motion of two surfaces in contact. Friction is really a macroscopic effect caused by a complex combination of forces at a microscopic level, when two surfaces are in contact.

Static vs. Kinetic Friction Static friction is the resistive force that opposes the relative motion of two contacting surfaces that are at rest with respect to each other. Kinetic friction is the resistive force that opposes the motion of two contacting surfaces that are moving across one another.

Static vs. Kinetic Friction Kinetic friction (Fk) is less than static friction (Fs). This means that it will take a greater force to overcome static friction when trying to move a stationary object than it would to overcome kinetic friction when moving the same object once it’s in motion.

The Normal Force and Friction The force of friction is proportional to the normal force. Ff  FN The proportionality constant is called the coefficient of friction (), and the value for the coefficient depends on the surfaces in contact.

Coefficient of Friction There are separate coefficients of friction for static (s) and kinetic friction (k) and these values may be found experimentally. s=Fs,max/FN k=Fk/FN There is a table of values for some coefficients of friction on page 144 of the text book.

s=Fs,max/FN… Whaaaaaa??? Imagine there is a huge truck in the middle of the floor, and you need to move it and you don’t have the keys (did I mention the tires are flat?). You try to push it, but it doesn’t budge. How does the force you apply compare to the static frictional force? Fs

A Little Help, Please So you go and get a few buddies, and they help you try to push it (off your parents’ best oriental rug). The truck still doesn’t move. Fs

Come on, Conan Finally, you convince your big gorilla of a brother to help you and your friends push the truck off the rug. Hooray!!! It works, and you were able to move the truck. The force you applied just as the truck began to move was just a hair more than the maximum static frictional force, Fs,max. Fs

Static and Kinetic Friction Friction Force Applied Force Fs,max=sFN Fs = F Static Region Kinetic Region Fk=kFN

Kinetic friction Static friction No friction A group of students is pushing a car with four flat tires out of the road with a horizontal force of 1225 N, but the car doesn’t move. What type of friction exists between the tires and the road? Kinetic friction Static friction No friction

(b) Static friction Since the car is NOT moving, the friction is static.

A group of students is pushing a car with four flat tires out of the road with a horizontal force of 1225 N, but the car doesn’t move. Which of the following is true? Ff > 1225 N Ff = 1225 N Ff < 1225 N

(b) Ff = 1225 N Since the car is NOT moving, the forces acting on it must be balanced:

Tension Tension, as it applies to forces, is typically the force that is transmitted through a rope, string, chain, etc., that is taut. Tension forces are always represented as forces parallel to the rope(s), and always pull away from objects. For example, this box is suspended from the ceiling by two ropes: T1 T2 mg

Drawing Free-Body Diagrams Isolate the object(s) under consideration, and draw a simple shape representing each object. Draw and label all external forces acting on the object(s). Gravitational forces are always straight down, toward the center of the earth. Normal forces are always perpendicular to the surfaces in contact. Frictional forces are always drawn in the direction opposing motion, parallel to the surfaces in contact. Tensile forces are always drawn away from the objects.

Examples Two boxes are pushed across a frictionless surface by force F: m1 m2 F m1 F FN1 F21 m2 F12 FN2 m1g m2g

Examples A box is pulled up a ramp by a force F: F F mg Ff FN

How to Solve Problems Draw an appropriate free-body diagram, correctly labeling all forces acting on the object. Establish a convenient coordinate system. The direction of the object’s motion should be aligned with an axis. Resolve all forces into components parallel and perpendicular to the object’s motion. Write equations using Newton’s Second Law for each dimension. The sum of the forces perpendicular to the object’s motion should = 0. Solve for unknown variables.

Example Given: m=25 kg W = mg = (25 kg)(9.8m/s2)= 245 N A 25-kg chair initially at rest requires a 365 N horizontal force to set it in motion. Once the chair is in motion, a 327 N horizontal force is required to keep it in motion at constant velocity. Find s. Find k. Given: m=25 kg W = mg = (25 kg)(9.8m/s2)= 245 N Fy = 0 = 245 N - FN FN =245 N Fx = 0 = 365 N - Fs.max Fs,max= 365 N s= Fs,max /FN = 356 N/245 N = 1.45 365 N Friction FN = 245 N mg = 245 N