Chapter 3-1

Force, Mass, and Acceleration Newton’s Second Law 3.1 Force, Mass, and Acceleration Newton’s first law of motion: the motion of an object changes only if an unbalanced force acts on the object Coming up… Newton’s second law of motion: describes how the forces exerted on an object, its mass, and its acceleration are related.

Force and Acceleration Newton’s Second Law 3.1 Force and Acceleration Q: Which has a greater force? 1.) throwing a ball gently OR 2.) throwing a ball really hard? WHY?

Force and Acceleration Newton’s Second Law 3.1 Force and Acceleration A: The hard-thrown ball: it has a greater change in velocity, and the change occurs over a shorter period of time…

Force and Acceleration Newton’s Second Law 3.1 Force and Acceleration Remember: acceleration is the change in velocity divided by the time it takes for the change to occur. So, a hard-thrown ball ALSO has a greater acceleration than a gently thrown ball (because it has a greater velocity over a shorter period of time)

Newton’s Second Law 3.1 Mass and Acceleration Q: If you throw a softball and a baseball as hard as you can, why don’t they have the same speed? A: because of their masses

*Force, mass, and acceleration are related. Newton’s Second Law 3.1 Mass and Acceleration Q: If it took the same amount of time to throw both balls, which would have less acceleration? A: the softball because the acceleration of an object depends on its mass as well as the force exerted on it. *Force, mass, and acceleration are related.

Notice…

Newton’s Second Law 3.1 Newton’s Second Law Newton’s second law of motion: the acceleration of an object is in the same direction as the net force on the object, and it can be calculated from the following equation:

Calculating Net Force with the Second Law Newton’s Second Law 3.1 Calculating Net Force with the Second Law Or, more simply,… F = force (units = Newtons) m = mass (units = kilograms) a = acceleration (units = m/s)

Practice Problems 1. You’re helping your friend move. You choose a 30 kg box and push it down a moving ramp at an acceleration of 2 m/s/s. With what force did you push it? A: F = ma F = (30)(2) F = 60 N

2. A ball is thrown and accelerates at a rate of 15 m/s/s 2. A ball is thrown and accelerates at a rate of 15 m/s/s. The ball has a mass of .1 kg. What is the force? A: F = ma F = (.1)(15) F = 1.5 N

You can also solve for variables OTHER THAN force… 3 You can also solve for variables OTHER THAN force… 3. A force of 50 N is applied to a box. The box has a mass of 10 kg. What is the acceleration? A: F = ma 50 = 10a 10 10 a = 5 m/s/s

Finally…

Suppose you give a skateboard a push with your hand… Newton’s Second Law 3.1 Suppose you give a skateboard a push with your hand… According to Newton’s first law of motion, if the net force acting on a moving object is zero, it will continue to move in a straight line with constant speed. Does the skateboard keep moving with constant speed after it leaves your hand? Why or why not?

Newton’s Second Law 3.1 Remember: when an object slows down, it is still accelerating (speeding up, slowing down, or changing direction) By Newton’s second law, if the skateboard is accelerating, there must be a net force acting on it… which force is it?

Newton’s Second Law 3.1 Friction Friction: the force that opposes the sliding motion of two surfaces that are touching each other. The amount of friction between two surfaces depends on two factors: 1. the kinds of surfaces 2. the force pressing the surfaces together

Newton’s Second Law 3.1 What causes friction? a “smooth” surface is not really smooth… it has microscopic “bumps” on it if two surfaces are in contact, welding, or sticking, occurs where the bumps touch each other 3. these microwelds (bumps sticking) are the source of friction

Newton’s Second Law 3.1 Sticking Together The larger the force pushing the two surfaces together, the stronger these microwelds (or the “sticking”) will be, because more of the surface bumps will come into contact. To move one surface over the other, a force must be applied to break the microwelds.

If the box doesn’t move, then it has zero acceleration. Newton’s Second Law 3.1 Suppose you have filled a cardboard box with books and want to move it. It’s too heavy to lift, so you start pushing on it, but it doesn’t budge. If the box doesn’t move, then it has zero acceleration.

Newton’s Second Law 3.1 Newton’s second law says that if the acceleration is zero, then the net force on the box is zero. Therefore: another force that cancels your push must be acting on the box…

Newton’s Second Law 3.1 Static Friction That force is the friction due to the microwelds that have formed between the bottom of the box and the floor. Static friction: the frictional force that prevents two surfaces from sliding past each other.

You ask a friend to help you move the box… Newton’s Second Law 3.1 You ask a friend to help you move the box… Pushing together, the box moves. Together you and your friend have exerted enough force to break the microwelds between the floor and the bottom of the box.

Newton’s Second Law 3.1 Sliding Friction If you stop pushing, the box quickly comes to a stop. This is because as the box slides across the floor, another forcesliding frictionopposes the motion of the box. Sliding friction: the force that opposes the motion of two surfaces sliding past each other.

Newton’s Second Law 3.1 As a wheel rolls over a surface, the wheel digs into the surface, causing both the wheel and the surface to be deformed.

Newton’s Second Law 3.1 Rolling Friction Static friction acts over the deformed area where the wheel and surface are in contact, producing a frictional force called rolling friction. Rolling friction: the frictional force between a rolling object and the surface on which it rolls

So, the three types of friction are: 1. static friction 2 So, the three types of friction are: 1. static friction 2. sliding friction 3. rolling friction

Newton’s Second Law 3.1 Air Resistance 1. When an object falls toward Earth, it is pulled downward by the force of gravity. 2. BUT… a friction-like force called air resistance opposes the motion of objects that move through the air. 3. Air resistance causes objects to fall with different accelerations and different speeds.

Q: Why does the elephant hit the ground first Q: Why does the elephant hit the ground first? Does it have a greater acceleration? A: No… it’s the same… the acceleration of gravity (9.8 m/s/s). BUT air resistance DOES depend on the size and shape of an object. The elephant also has a faster terminal velocity.

Newton’s Second Law 3.1 Air Resistance 4. Air resistance acts in the opposite direction to the motion of an object through air. 5. If the object is falling downward, air resistance acts upward on the object. 6. The size of the air resistance force also depends on the size, shape, and speed of an object.

Newton’s Second Law 3.1 Air Resistance The amount of air resistance on an object depends on the speed, size, and shape of the object. Air resistance, not the object’s mass, is why feathers, leaves, and pieces of paper fall more slowly than pennies, acorns, and apples.

Newton’s Second Law 3.1 Terminal Velocity

Newton’s Second Law 3.1 Terminal Velocity terminal velocity: the highest speed a falling object will reach. depends on the: size shape mass of a falling object

Section Check 3.1 Question 1 Newton’s second law of motion states that _________ of an object is in the same direction as the net force on the object. A. acceleration B. momentum C. speed D. velocity

Section Check 3.1 Answer The answer is A. Acceleration can be calculated by dividing the net force in newtons by the mass in kilograms.

Question 2 3.1 The unit of force is __________. A. joule B. lux Section Check 3.1 Question 2 The unit of force is __________. A. joule B. lux C. newton D. watt

Section Check 3.1 Answer The answer is C. One newton = 1 kg · m/s2

Question 3 Answer 3.1 What causes friction? Section Check 3.1 Question 3 What causes friction? Answer Friction results from the sticking together (microwelds) of two surfaces that are in contact.

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Start 3-2

Gravity 3.2 What is gravity? Gravity: an attractive force between any two objects that depends on the masses of the objects and the distance between them.

Earth’s Gravitational Acceleration Gravity 3.2 Earth’s Gravitational Acceleration 1. free fall: when all forces except gravity acting on a falling object can be ignored (objects appear to be weightless) 2. Close to Earth’s surface, the acceleration of a falling object in free fall is about 9.8 m/s2. 3. This acceleration is given the symbol g and is sometimes called the acceleration of gravity…and again, it’s 9.8 m/s2

Earth’s Gravitational Acceleration Gravity 3.2 Earth’s Gravitational Acceleration By Newton’s second law of motion, the force of Earth’s gravity on a falling object is: Force = the object’s mass X the acceleration of gravity on Earth (F = ma or, in this case, F = mg).

Weight (N) = mass (kg) x acceleration of gravity (m/s/s) 3.2 Weight Weight: the gravitational force exerted on an object; it changes if gravity changes Because the weight of an object on Earth is equal to the force of Earth’s gravity on the object, weight can be calculated from this equation: Weight (N) = mass (kg) x acceleration of gravity (m/s/s) OR W = mg

Gravity 3.2 Weight and Mass 1. Weight and mass are not the same. Weight can change… mass doesn’t. 2. Weight is a force and mass is a measure of the amount of matter an object contains. 3. Weight and mass are related. Weight increases as mass increases.

Examples of Weight Problems: A boy “weighs” 150 lbs. when he steps on a scale. How many Newtons does he weigh? A: 150 lbs. = 68 kg 2.2 W = mg (a = g = acceleration of gravity) W = (68)(9.8) W = 666.4 N

2. Now calculate your weight in Newtons 2. Now calculate your weight in Newtons. Remember to first convert your “weight” in pounds to kilograms. Ex: 130 lbs. = 59 kg 2.2 W = mg W = (59)(9.8) W = 578.2 N

Gravity 3.2 Weight and Mass The table shows how various weights on Earth would be different on the Moon and some of the planets.

Gravity 3.2 Projectile Motion projectiles: follow a curved path due to the Earth’s gravity Examples: 1.) a thrown ball 2.) a bullet shot from a gun 3.) a thrown dart 4.) an archer’s arrow *all aim above target*

What is happening to the rolling (or thrown) ball? Gravity 3.2 What is happening to the rolling (or thrown) ball? Gravity exerts an unbalanced force on the ball, changing the direction of its path from only forward to forward and downward. The result of these 2 motions: the ball appears to travel in a curved path

Gravity 3.2 Centripetal Force Centripetal force: the net force exerted toward the center of a curved path Anything that moves in a circle is doing so because a centripetal force is accelerating it toward the center.

Gravity 3.2 Example #1: a car rounds a curve on a highway… the centripetal force is the frictional force, or the traction, between the tires and the road surface. Example #2: people on many amusement park rides (gravitron, yo-yo, etc.)

Gravity 3.2 Example #3: Earth’s gravity exerts a centripetal force on the Moon that keeps it moving in a nearly circular orbit.

Gravity 3.2 Example #4: an object tied to a string whirling around your head…the string exerts a centripetal force on the object that keeps it moving in a circular path

Section Check 3.2 Question 1 Gravity is an attractive force between any two objects and depends on __________. Answer Gravity is an attractive force between any two objects and depends on the masses of the objects and the distance between them.

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Start 3-3

The Third Law of Motion 3.3 Newton’s Third Law Newton’s Third Law of Motion: for every action force, there is an equal and opposite reaction force Example #1: Jumping on a trampoline… you apply downward force as the trampoline exerts an equal upward force on you

Example #2: a male skater pulling upward on a female skater as she pulls downward on him Example #3: kickback occurs when a gun is fired Example #4: Jet or rocket propulsion due to compressed gas release

The rocket exerts a force on gas molecules, pushing them backwards The rocket exerts a force on gas molecules, pushing them backwards. The gas molecules exert a force on the rocket, pushing it forward.

What is happening here?

Action and Reaction Forces Don’t Cancel The Third Law of Motion 3.3 Action and Reaction Forces Don’t Cancel According to Newton’s Third Law, action and reaction forces act on different objects. 2. Therefore, even though the forces are equal, they are not balanced because they act on different objects.

The Third Law of Motion 3.3 Example: a swimmer “acts” on the water and the “reaction” of the water pushes the swimmer forward Thus, a net force, or unbalanced force, acts on the swimmer so a change in his or her motion occurs.

The Third Law of Motion 3.3 Momentum 1. A moving object has a property called momentum that is related to how much force is needed to change its motion. 2. momentum (kg m/s) = mass (kg) x velocity (m/s)

p = mv p = momentum (kg m/s) m = mass (kg) v = velocity (m/s) Note: momentum (units = kg m/s) has a direction because velocity has a direction

Law of Conservation of Momentum The Third Law of Motion 3.3 Law of Conservation of Momentum 1. The momentum of an object doesn’t change unless its mass, velocity, or both change. 2. Momentum, however, can be transferred from one object to another. 3. The law of conservation of momentum: states that if a group of objects exerts forces only on each other, their total momentum doesn’t change.

The Third Law of Motion 3.3 When Objects Collide The results of a collision depend on the momentum of each object. When the first puck hits the second puck from behind, it gives the second puck momentum in the same direction.

The Third Law of Motion 3.3 When Objects Collide If the pucks are speeding toward each other with the same speed, the total momentum is zero.

Practice Problems: What is the momentum of a car with a mass of 1300 kg traveling at a velocity of 28 m/s? Answer: p=mv p=(1300)(28) p=36,400 kg m/s

2. A baseball thrown by a pitcher has a momentum of 6. 0 kg m/s 2. A baseball thrown by a pitcher has a momentum of 6.0 kg m/s. If the baseball’s mass is .15 kg, what is the baseball’s velocity? Answer: p=mv 6.0=(.15)v v=40 m/s

3. What is the mass of a person walking with a velocity of 0 3. What is the mass of a person walking with a velocity of 0.8 m/s if their momentum is 52.0 kg m/s. Answer: p=mv 52=0.8m m=65 kg

Question 1 Answer 3.3 According to Newton’s third law of motion, Section Check 3.3 Question 1 According to Newton’s third law of motion, what happens when one object exerts a force on a second object? Answer According to Newton’s law, the second object exerts a force on the first that is equal in strength and opposite in direction.

Section Check 3.3 Question 2 The momentum of an object is the product of its __________ and __________. A. mass, acceleration B. mass, velocity C. mass, weight D. net force, velocity

Answer 3.3 The correct answer is B. An object’s momentum Section Check 3.3 Answer The correct answer is B. An object’s momentum is the product of its mass and velocity, and is given the symbol p.

Section Check 3.3 Question 3 When two objects collide, what happens to their momentum?

Section Check 3.3 Answer According to the law of conservation of momentum, if the objects in a collision exert forces only on each other, their total momentum doesn’t change, even when momentum is transferred from one object to another.

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