Newton’s Second Law © 2015 Pearson Education, Inc.

Newton’s Second Law A force causes an object to accelerate.
The acceleration a is directly proportional to the force F and inversely proportional to the mass m: The direction of the acceleration is the same as the direction of the force: © 2015 Pearson Education, Inc.

Newton’s Second Law (Written with the Σ)
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Section 4.3

Solving Newton’s Second Law Problems
Read the problem at least once Draw a picture of the system Identify the object of primary interest Indicate forces with arrows Label each force Use labels that bring to mind the physical quantity involved Section 4.5

Solving Newton’s Second Law Problems, cont
Draw a free body diagram If additional objects are involved, draw separate free body diagrams for each object Choose a convenient coordinate system for each object Apply Newton’s Second Law The x- and y-components should be taken from the vector equation and written separately Solve for the unknown(s) Section 4.5

Equilibrium An object either at rest or moving with a constant velocity is said to be in equilibrium The net force acting on the object is zero (since the acceleration is zero) Section 4.5

Equilibrium cont. Easier to work with the equation in terms of its components: This could be extended to three dimensions A zero net force does not mean the object is not moving, but that it is not accelerating Section 4.5

Equilibrium Example – Free Body Diagrams
Section 4.5

Inclined Planes Choose the coordinate system with x along the incline and y perpendicular to the incline Replace the force of gravity with its components Section 4.5

Multiple Objects – Example
When you have more than one object, the problem-solving strategy is applied to each object Draw free body diagrams for each object Apply Newton’s Laws to each object Solve the equations Section 4.5

Multiple Objects – Example, cont.
Section 4.5

Some Notes About Forces
Forces cause changes in motion Motion can occur in the absence of forces All the forces acting on an object are added as vectors to find the net force acting on the object m is not a force itself Newton’s Second Law is a vector equation Next 4 Slides Review of the relationships between mass/ inertia Force/mass/acceleration Section 4.3

Exercise, Newton’s 2nd Law
A woman is straining to lift a large crate, without success. It is too heavy. We denote the forces on the crate as follows: P is the upward force being exerted on the crate by the person C is the contact force on the crate by the floor, and W is the weight (force of the earth on the crate). Which of following relationships between these forces is true, while the person is trying unsuccessfully to lift the crate? (Note: force up is positive & down is negative) P + C < W P + C > W P = C P + C = W

(Newton’s Second Law F=ma or a=F/m)
Mass We have an idea of what mass is from everyday life. In physics: Mass is a quantity that specifies how much inertia an object has (i.e. a scalar that relates force to acceleration) (Newton’s Second Law F=ma or a=F/m) Mass is an inherent property of an object. Mass and weight are different quantities; weight is usually the magnitude of a gravitational (non-contact) force.

Inertia and Mass The tendency of an object to resist any attempt to change its velocity is called Inertia Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity (acceleration) If mass is constant then 𝑎∝𝐹 If force constant  𝑎∝ 1 𝐹 |a| m Mass is an inherent property of an object Mass is independent of the object’s surroundings Mass is independent of the method used to measure it Mass is a scalar quantity The SI unit of mass is kg

Exercise Newton’s 2nd Law
An object is moving to the right, and experiencing a net force that is directed to the right. The magnitude of the force is decreasing with time (read this text carefully). The speed of the object is increasing decreasing constant in time Not enough information to decide

Question 1 A constant force causes an object to accelerate at 4 m/s2. What is the acceleration of an object with twice the mass that experiences the same force? 1 m/s2 2 m/s2 4 m/s2 8 m/s2 16 m/s2 Answer: B © 2015 Pearson Education, Inc.

Question 1 A constant force causes an object to accelerate at 4 m/s2. What is the acceleration of an object with twice the mass that experiences the same force? 1 m/s2 2 m/s2 4 m/s2 8 m/s2 16 m/s2 © 2015 Pearson Education, Inc.

Newton’s Laws Law 1: An object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame. Law 2: For any object, FNET = F = ma Law 3: Forces occur in pairs: FA , B = - FB , A (For every action there is an equal and opposite reaction.) Read: Force of B on A

Newton’s Third Law: If object 1 exerts a force on object 2 (F2,1 ) then object 2 exerts an equal and opposite force on object 1 (F1,2) F1,2 = -F2,1 For every “action” there is an equal and opposite “reaction” IMPORTANT: Newton’s 3rd law concerns force pairs which act on two different objects (not on the same object) !

Push Me and I Push Back!!! SCHWINN: Read the cartoon and then insert the picture of the two people pulling on the same rope. Ask the question what happens in the Green Shirted man decides not to pull back on the rope?

What is the relationship between these forces?
Push me and I push back! For example, with the palm of your hand, push on a book, desk or table. You are exerting a force on the object you are pushing. At the same time, you can feel a force on your hand. There seems to be two forces: the one your hand exerted on the object, and another force on your hand. What is the relationship between these forces? ANSWER: THEY ARE EQUAL IN MAGNETUDE AND OPPOSITEDLY DIRECTED! This is true whether or not a big object is pushing a smaller object or whether the objects are stationary or moving. WHEN EVER TWO OBJECTS TOUCH THEY HAVE TO FOLLOW THIS SIMPLE RULE!

The man weighs 700 N. The force exerted by the table on the man is:
a) Larger than 700 N b) Equal to 700 N c) Smaller than 700 N d) There is no force. ANSWER: EXACTLY 700 N

A hand pushes on a balloon against a wall with a force of 10 N
A hand pushes on a balloon against a wall with a force of 10 N. The force exerted by the balloon on the hand is: a) Larger than 10 N b) Equal to 10 N c) Smaller than 10 N d) There is no force. ANSWER Exactly 10 Newton’s

A building is being torn down. The wrecking ball smashes through a wall. Does the ball put a larger force on the wall than the wall puts on the wrecking ball? Explain your answer. THE BALL AND THE WALL EXPERIENCE THE SAME EXACT FORCE… HOWEVER the EFFECT OF THE FORCE ON EACH OBJECT RESULTS IN A DIFFERENCE IN ACCELERATION. WHY? THE INDIVIDUAL BRICKS IN THE WALL HAVE A MUCH SMALLER MASS so the ACCELERATION (Resulting effect) is greater than the resulting ACCELERATION (Change in motion) of the Ball which has a much GREATER MASS (or Inertia). THE FORCES ARE EQUAL but the EFFECT of the FORCES on specific object can BE (Often times are) Different!

Imagine that you hold the two force probes, one probe in each hand
Imagine that you hold the two force probes, one probe in each hand. You will notice that each force probe has a hook on it. Connect the two force probes together and pull as seen in the following figure. You can experimentally do this by connecting your fingers together with somebody else. Try having them pull on you with out pulling back. What happens if somebody doesn’t resist the effort force of pulling?

The friction that prevents slipping is static friction.
Runners and Rockets In order for you to walk, the floor needs to have friction so that your foot sticks to the floor as you straighten your leg, moving your body forward. The friction that prevents slipping is static friction. The static friction has to point in the forward direction to prevent your foot from slipping. © 2015 Pearson Education, Inc.

QuickCheck 4.16 10-year-old Sarah stands on a skateboard. Her older brother Jack starts pushing her backward and she starts speeding up. The force of Jack on Sarah is Greater than the force of Sarah on Jack. Equal to the force of Sarah on Jack. Less than the force of Sarah on Jack. Answer: B © 2015 Pearson Education, Inc.

QuickCheck 4.16 10-year-old Sarah stands on a skateboard. Her older brother Jack starts pushing her backward and she starts speeding up. The force of Jack on Sarah is Greater than the force of Sarah on Jack. Equal to the force of Sarah on Jack. Less than the force of Sarah on Jack. © 2015 Pearson Education, Inc.

Exercise Newton’s Third Law
A fly is deformed by hitting the windshield of a speeding bus.  v The force exerted by the bus on the fly is, greater than equal to less than that exerted by the fly on the bus.

A fly is deformed by hitting the windshield of a speeding bus.  v The force exerted by the bus on the fly is, B. equal to that exerted by the fly on the bus.

Exercise 2 Newton’s Third Law
Same scenario but now we examine the accelerations A fly is deformed by hitting the windshield of a speeding bus.  v The magnitude of the acceleration, due to this collision, of the bus is greater than equal to less than that of the fly.

Exercise 3 Newton’s 3rd Law
Two blocks are being pushed by a finger on a horizontal frictionless floor. How many action-reaction force pairs are present in this exercise? a b 2 4 6 Something else

a b 6 Exercise 3 Solution: Fa,f Ff,a Fb,a Fa,b FE,a Fa,E FE,b Fb,E
Fg,a Fa,g Fg,b Fb,g 6

Mass and Weight Mass and weight are not the same thing.
Mass is a quantity that describes an object’s inertia, its tendency to resist being accelerated. Weight is the gravitational force exerted on an object by a planet: w = –mg © 2015 Pearson Education, Inc.

Apparent Weight The weight of an object is the force of gravity on that object. Your sensation of weight is due to contact forces supporting you. Let’s define your apparent weight wapp in terms of the force you feel: © 2015 Pearson Education, Inc.

Apparent Weight The only forces acting on the man are the upward normal force of the floor and the downward weight force: n = w + ma wapp = w + ma Thus wapp > w and the man feels heavier than normal. © 2015 Pearson Education, Inc.

Example 5.8 Apparent weight in an elevator
Anjay’s mass is 70 kg. He is standing on a scale in an elevator that is moving at 5.0 m/s. As the elevator stops, the scale reads 750 N. Before it stopped, was the elevator moving up or down? How long did the elevator take to come to rest? The scale reading as the elevator comes to rest, 750 N, is Anjay’s apparent weight. Anjay’s actual weight is w = mg = (70 kg)(9.80 m/s2) = 686 N © 2015 Pearson Education, Inc.

Example 5.8 Apparent weight in an elevator (cont.)
The vertical component of Newton’s second law for Anjay’s motion is Fy = n  w = may n is the normal force, which is the scale force on Anjay, N. w is his weight, 686 N. We can thus solve for ay: © 2015 Pearson Education, Inc.

The acceleration is positive and so is directed upward, exactly as we assumed—a good check on our work. The elevator is slowing down, but the acceleration is directed upward. This means that the elevator was moving downward, with a negative velocity, before it stopped. © 2015 Pearson Education, Inc.

To find the stopping time, we can use the kinematic equation (vy)f = (vy)i + ay Δt The elevator is initially moving downward, so (vy)i =  5.0 m/s, and it then comes to a halt, so (vy)f = 0. We know the acceleration, so the time interval is © 2015 Pearson Education, Inc.

assess Think back to your experiences riding elevators. If the elevator is moving downward and then comes to rest, you “feel heavy.” This gives us confidence that our analysis of the motion is correct. And 5.0 m/s is a pretty fast elevator: At this speed, the elevator will be passing more than one floor per second. If you’ve been in a fast elevator in a tall building, you know that 5.5 s is reasonable for the time it takes for the elevator to slow to a stop. © 2015 Pearson Education, Inc.

Weightlessness A person in free fall has zero apparent weight.
“Weightless” does not mean “no weight.” An object that is weightless has no apparent weight. © 2015 Pearson Education, Inc.