Announcements :Announcements Homework for tomorrow… (Ch. 4, Probs 12 & 24 ) Office hours… MTWRF 11-noon


Chapter 4 :Chapter 4 The Laws of Motion


Previously… :Previously… Chapter 2 & 3 - Kinematics Motion w/ constant acceleration Free fall (1D) Projectile motion (2D) Chapter 4 - Dynamics Newton’s 3 Laws Applications of Newton’s laws Today…


Section 4.1:Forces :Section 4.1:Forces Classical Dynamics is the study of motion and of physical concepts (i.e. relationship between force and mass) Force is a vector quantity two kinds: contact force field force “Action at a distance”


Sir Isaac Newton :Sir Isaac Newton – British Physicist 1642 – 1727 Formulated basic laws of Mechanics Universal Law of Gravitation Calculus Light and Optics


Section 4.2:Newton’s 1st Law :Section 4.2:Newton’s 1st Law “An object moves with a velocity that is constant in magnitude and direction, unless acted on by a nonzero net force.” Mathematically:


What causes/affects motion? :What causes/affects motion? (Inertial) Mass A measure of the resistance of an object to changes in it’s motion due to a force Force(s) Cause a change in motion (i.e. acceleration) Kinematics -> Dynamics


Section 4.3:Newton’s 2nd Law :Section 4.3:Newton’s 2nd Law “The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to the mass.” Mathematically:


Units of ‘Force’ :Units of ‘Force’ Definition: “1 Newton” Intuition: The weight of an apple


Question 1: True or False? :Question 1: True or False? It is possible to have motion in the absence of a force True! If a body has no acceleration, then no net force is acting on it. True! If only a single force acts on a body, it must accelerate. True! It is possible for a body to “round a curve” without a net force acting on it. False! If a net force is acting on an object in the y-direction, then the object will move only in the y-direction False!


Quiz Question 1: :Quiz Question 1: Two forces are shown acting on an object. For the object not to accelerate, a 3rd force must be applied to the object that has a magnitude equal to: 1N 3N 4N 5N 7N 3N 4N


Quiz Question 2 :Quiz Question 2 Three blocks (A,B,C), each having mass M, are connected by strings as shown. Block C is pulled to the right by a force F that causes the entire system to move to the right at constant velocity. The net force acting on block B is: 0 F/3 F/2 2F/3 F A B C F


Newton’s Universal Law of Gravitation :Newton’s Universal Law of Gravitation Every massive particle in the Universe attracts every other massive particle with a force given by where


Gravity Problem: :Gravity Problem: A massive object is dropped from an elevation of 50 m above the Earth’s surface. What is the acceleration of this object? Given: Strategy: Use


Weight :Weight The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object Weight: is a force special case of 2nd law is not an inherent property of an object


Section 4.4:Newton’s 3rd Law :Section 4.4:Newton’s 3rd Law In Newton’s own words… “To every action there is always opposed an equal and opposite reaction.” Mathematically:


Quiz Question 3 :Quiz Question 3 A young physics professor drags a plastic box across the floor at a constant speed in a straight line. The magnitude of the force he exerts on the box is _______ the force the box exerts on him. a little less than a lot less than a little more than a lot more than the same as


Quiz Question 4 :Quiz Question 4 A young physics professor drags a plastic box across the floor at increasing speed in a straight line. The magnitude of the force he exerts on the box is _______ the force the box exerts on him. a little less than a lot less than a little more than a lot more than the same as


Quiz Question 5 :Quiz Question 5 A large truck collides head-on with a small compact car. During the collision, the truck exerts a greater amount of force on the car than a smaller amount of force on the car than the same amount of force on the car as the car exerts on the truck.


Quiz Question 6 :Quiz Question 6 A large truck collides head-on with a small compact car. During the collision, the truck has a larger acceleration than the car. a smaller acceleration than the car. the same acceleration as the car.


Demo :Demo When the fan is turned on, why does the cart accelerate? When the sail is added, why does it not?


Section 4.4:Newton’s 3rd Law :Section 4.4:Newton’s 3rd Law How to solve “F=ma” problems… Pick a body Draw force diagram Choose a coordinate system Break forces into components


Some particular forces… :Some particular forces… Gravitational force ( ) Normal force ( ) Tension force ( ) Frictional force ( )


Normal Force: Question :Normal Force: Question An object of mass m rests on the table. What is the force of the table on the object? (What is the ‘normal force’, ? )


Tension :Tension Comment: The magnitude of the force exerted on a rope is the same at all points on the rope


Quiz Question 7: :Quiz Question 7: The figure below shows 2 equal 100 lb. weights connected by a light string and supported by a pulley. The tension in the string is: 0 lbs 50 lbs 100 lbs 200 lbs It is impossible to know from the data given m1


Quiz Question 8 :Quiz Question 8 Consider the two situations shown in which there is no acceleration. In both cases the men pull with a force of magnitude F. Is the reading on the scale in part (i) of the figure greater than less than equal to the reading in (ii)?


Problem 1: :Problem 1: What is the acceleration of mass down the inclined plane? What is the Normal force? (In this problem, friction is negligible)


Problem 2: :Problem 2: An object of mass m = 100 kg is being accelerated upward into the air at a rate of 5 m/s2 . What is the tension in the cable? a


Section 4.6:Forces of Friction :Section 4.6:Forces of Friction Frictional Force… … is proportional to the normal force … points in the direction to resist the motion … two types - static & kinetic


Static & Kinetic Friction :Static & Kinetic Friction Static Friction depends on materials is the coefficient of static friction


Static & Kinetic Friction :Static & Kinetic Friction Kinetic Friction depends on materials is the coefficient of kinetic friction Which is larger or ?


Some Coefficients of Friction :Some Coefficients of Friction


Quiz Question 9 :Quiz Question 9 You are pulling a wooden block across the table at constant speed. You decide to turn the block on end, reducing by half the surface area in contact with the table. In the new orientation, to pull the same block across the table at the same speed, the force that you apply must be about four times as great twice as great equally great half as great one-fourth as great as the force required required before you changed the crate’s orientation.


Problem 3: :Problem 3: How much force must a person apply to the box on the ground such that the box moves with v = 3 m/s? Given: µk = .3, µs = .5 m = 100 kg v


Problem 4: Eraser on Incline :Problem 4: Eraser on Incline The angle of the inclined plane is slowly increased. In terms of the coefficient of friction, at what angle does the eraser slip? (In this problem, the frictional force is non-negligible) 