Honors Physics Chapter 4 Forces

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Four Fundamental (Basic) Forces in Nature Gravitational Force Electromagnetic Force Strong (Nuclear) Force Weak (Nuclear) Force

Gravitational Force Gravity (Gravitational force Earth pulling on objects around it), weight: W, Fg On surface of Earth, gravity is always straight downward, with a magnitude of Gravitational force always exist, but value of g is different at different location. On surface of earth, g = 9.8 m/s2. Higher elevation, smaller g. Higher latitude, larger g.

Electromagnetic Force All other forces we encounter in daily life are electromagnetic force in nature. Electric force: F Magnetic force: F Tension (pull, string): T Push: F Normal (support): FN or N (not to be confused with Newton, the unit of force) Friction: ƒ (ƒs or ƒk) Air resistance, air drag: Fd

Strong (Nuclear) Force Holds protons and neutrons within the nucleus Exist in very short distance only (fm,  10-15 m) Stable nucleus

Weak (Nuclear) Force Also holds protons and neutrons within the nucleus Also very short range (fm,  10-15 m) Not strong enough. Protons and neutrons can sometimes escape  Nuclear reaction Unstable nucleus

Relative Strength of Forces Electromagnetic Gravitational Weak Strong Weakest Strongest

Force at Distance Contact force: Field force / Distant force: Force giver and receiver must be in contact Tension, push, normal force, friction, … Field force / Distant force: Force giver and receiver do not have to be in contact Gravity, electric force, magnetic force, …

Unification of Forces Electromagnetic and weak forces have been unified into one force: Electroweak force It is believed that all four forces are different aspects of a single force. Grand Unification Theories (GUTs) and Supersymmetric theories Not yet sucessful

Newton’s First Law of Motion Law of Inertia An object with no net force acting on it remains at rest or moves with constant velocity in a straight line. No net force is needed to keep a motion/velocity. A net force is needed to change a motion/velocity. Net force = 0  Object at Equilibrium. A special case of Second Law of Motion.

Newton’s Second Law of Motion The acceleration of a body is directly proportional to the net force on it and inversely proportional to its mass. Unit of Force: F = ma  [F] = [m] [a] = kg = Newton = N

Example: Together a motorbike and rider have a mass of 275 kg. The motorbike is slowed down with an acceleration of –4.50 m/s2. What is the net force on the motorbike? Describe the direction of the force and the meaning of the negative sign. The negative sign indicates that the force is opposite to the direction of motion.

Practice: A car, mass 1225 kg, traveling at 105 km/h, slows to a stop in 53 m. What is the size and direction of the force that acted on the car? What provided the force? “-”: direction of force is opposite to velocity Road surface is providing the force as friction.

Newton’s Third Law of Motion When one object exerts a force on a second object, the second object also exerts a force on the first object that is equal in magnitude but opposite in direction. Action-reaction forces always exist together. Action and reaction forces are of the same kind of fundamental force--both are electromagnetic, or both are gravitational. Action and reaction forces act on two different objects and therefore do not cancel out each other when only one object is considered.

Action and Reaction Forces In general, the force acting on the object under consideration is the action force, and the other is the reaction. Action Action force: ground supporting the box, Fgb Reaction Reaction force: box pushing on the ground, Fbg Force between box and ground:

How To Find Reaction Force Identify the force giver and receiver of the force. Reversing the order of force giver and receiver, you will get the reaction force. Example: Action force: a  b Reaction force: b  a

Example on Action-Reaction box table

Example (2) Force Diagram, Free-Body Diagram N: normal force, force table supporting the box forces on box Wb: weight of box, force Earth pulling on box Are N and W a pair of action and reaction force? No 2 different objects same fundamental force

Example (3) forces on table Ngt: normal force of ground supporting table forces on table N: Force of box pushing on table N Wt: weight of table, gravitational force Earth pulling on table

Example (4) forces on earth Wt: reaction force to weight of table, gravitational force table pulling on Earth Wt Wb: reaction force to weight of box, force box pulling on Earth Wb forces on earth Ntg: force of table pushing on ground (Earth), reaction force of Ngt.

Example (5) N Ngt Wb Wt N Wt Wb Ntg Action and reaction forces always exist in pairs and act on different objects.

What is mass? Mass is an intrinsic property of an object. It does not change. It does not depend on the object’s position, velocity, acceleration, temperature, or … Two methods to measure mass: two kinds of mass Inertial mass: m = F / a Gravitational mass: comparing gravitational force on the object whose mass to be measured to gravitational force on an object of known mass

Tension Tension is along the line. Tension points away from the object. T

Normal Force (N or FN) Fapp N N N Normal force points from surface to object. Normal force is always perpendicular to the surface in contact. (Normal = perpendicular) If there is no tendency for the object to go into the surface, there is no normal force. No contact, no normal force. Fapp N N N

Weight and Apparent Weight Weight is force of gravity of Earth pulling on the object. N Apparent weight is the reading on the apparatus. T Apparent weight is the normal force the scale exerting on the object Apparent weight is the tension the spring exerting on the object Apparent weight does not have to be the same as the weight.

Free-Body Diagram (Force Diagram) Draw all the forces acting on the object of consideration. Ignore all forces the object acting on other objects (reaction forces) Draw all forces starting from center of the object for simplicity. (frictional force normally is drawn at surface of contact.) T N f W

b) Define upward as the positive direction. Example: A person of 50 kg stands on a scale on the floor of an elevator that is accelerating upward at 2.0 m/s2. a) What is the weight of the person? b) What is the apparent weight of the person? (What is the reading on the scale?) + N=? b) Define upward as the positive direction. “-” because W is in the negative direction. W=mg Diagram: 2nd Law:

Define upward as the positive direction. + T Example: 106-32 You are helping to repair a roof by loading equipment into a bucket that workers hoist to the rooftop. If the rope is guaranteed not to break as long as the tension does not exceed 450 N and you fill the bucket until it has a mass of 42 kg, what is the greatest acceleration that the workers can give the bucket as they pull it to the roof? Define upward as the positive direction. + T Diagram: 2nd Law: W=mg

Practice 113-68 A 873-kg dragster, starting from rest, attains a speed of 26.3 m/s (58.9 mph) in 0.59 s. a) Find the average acceleration of the dragster during this time interval. B) What is the magnitude of the average net force on the dragster during this time? C) Assume that the driver has a mass of 68 kg. What horizontal force does the seat exert on the driver? + v N Fseat ? W

Example: 115-92 Two blocks, one of mass 5.0 kg and the other of mass 3.0 kg, are tied together with a massless rope as in Figure 4-24. This rope is strung over a massless, resistance-free pulley. The blocks are released from rest. Find a) the tension in the rope, and b) the acceleration of the blocks. + T T 3 + 5 Wb Let downward = + for ma = 5 kg, and upward = + for mb = 3 kg. Then two masses will have the same acceleration, a = ?. And the tensions will be the same, T = ? Wa ma: mb:

Another Approach: 115-92 Two blocks, one of mass 5 Another Approach: 115-92 Two blocks, one of mass 5.0 kg and the other of mass 3.0 kg, are tied together with a massless rope as in Figure 4-24. This rope is strung over a massless, resistance-free pulley. The blocks are released from rest. Find a) the tension in the rope, and b) the acceleration of the blocks. + 3 T Wb 5 + Take the two masses as a single system. Let clockwise as the positive direction of the motions. Wa Then the net force accelerating the system is: And this net force is acceleration a total mass of So the acceleration of the system is Then we apply Newton’s second law on one of the mass to find the tension. Let downward = + for 5kg. Then

Let right = +, m1 = 5.0 kg, m2 = 3.0 kg, F = 16.0 N Practice: Two blocks, 3.0kg and 5.0kg, are connected by a light string and pulled with a force of 16.0N along a frictionless surface. Find (a) the acceleration of the blocks, and (b) the tension between the blocks. + N1 N2 T T F 16.0N 3.0kg 5.0kg W2 W1 Let right = +, m1 = 5.0 kg, m2 = 3.0 kg, F = 16.0 N Consider only forces in the horizontal direction. m1: m2: