Chapter 5 Newton’s Second Law of Motion-- Force and Acceleration

Chapter 5

Newton’s Second Law of Motion--Force and Acceleration

Force Causes Acceleration

In order to make an object at rest move, it must accelerate Suppose you hit a hockey puck

• as it is struck it experiences acceleration, but as it travels off at constant velocity (assuming no friction) the puck is not accelerating

• if the puck is struck again, then it accelerates again; the force the puck is hit with causes the acceleration

Acceleration depends on net force• to increase acceleration—increase net force• double acceleration—double the force

Force ~ Acceleration • directly proportional

Mass Resists Acceleration

Acceleration depends on massto decrease acceleration—increase massto increase acceleration—decrease massdouble the mass = ½ the acceleration

Acceleration ~ 1/mass • inversely proportional

Newton’s Second Law

Newton was the first to realize that acceleration produced when something is moved is determined by two things

• how hard or fast the object is pushed• the mass of the object

Newton’s 2nd Law The acceleration of an object is directly

proportional to the net force acting on the object and is inversely proportional to the object’s mass


Second Law Video


a = F/m or F = ma

1. Robert and Laura are studying across from each other at a wide table. Laura slides a 2.2 kg book toward Robert. If the net force acting on the book is 1.6 N to the right, what is the book’s acceleration?

A = F/m = 1.6N / 2.2kg = .73m/s2


2. An applied force of 50 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance.)

3. Rose is sledding down an ice-covered hill inclined at an angle of 15.0° with the horizontal. If Rose and the sled have a combined mass of 54.0 kg, what is the force pulling them down the hill?

Newton’s 2nd Law & Kinematics

1. A 4.60 kg sled is pulled across a smooth ice surface. The force acting on the sled is of magnitude 6.20 N and points in a direction 35.0° above the horizontal. If the sled starts at rest, what is its velocity after being pulled for 1.15 s?

1. V = 1.265 m/s2. The fire alarm goes off, and a 97 kg fireman

slides 3.0 m down a pole to the ground floor. Suppose the fireman starts from rest, slides with a constant acceleration, and reaches the ground floor in 1.2 s. What was the force exerted by the pole on the fireman?

1. F = 201.76N

Friction

Acts on materials that are in contact with each other Always acts in a direction to oppose motion Depends on type of surfaces

• Rubber against concrete produces more friction than steel against steel

Occurs in liquids and gases• Air resistance, running in water

When friction is present an object can still move at a constant velocity

• The friction force must balance outside force—net force would be zero (no acceleration)

Friction

Does friction act on an object at rest?• No, there must be movement

Suppose a biker cruises with a constant velocity but the thrust from his pedaling is 10 N. What is the acceleration of the bike?

• 0 m/s2; the bike is moving at a constant speed

What is the force of air resistance (friction) acting on the bike?

• 10 N in the direction opposite the motion of the bike; these forces must balance or the bike would be accelerating

Friction Types of Friction

Static • The resistance force that must be overcome to start

an object in motion Kinetic/Sliding

• The resistance force between two surfaces already in motion

Rolling• The resistance force between a surface and a

rolling object Fluid

• The resistance force between and object and a fluid/gas (air resistance)

Sliding Friction

Ffriction = µFnormal

µ = the coefficient of sliding friction (has no units)

1. Ben is walking through the school cafeteria but does not realize that the person in front of him has just spilled his glass of chocolate milk. As Ben, who weighs 420 N, steps in the milk, the coefficient of sliding friction between Ben and the floor is suddenly reduced to 0.040. What is the sliding force of friction between Ben and the slippery floor?

Friction

2. While redecorating her apartment, Kelly slowly pushes an 82 kg china cabinet across the wooden dining room floor, which resists motion with a force of 320 N. What is the coefficient of sliding friction between the china cabinet and the floor?

3. A rightward force is applied to a 10-kg object to move it across a rough surface at constant velocity. The coefficient of friction, µ, between the object and the surface is 0.2. Use the diagram to determine the gravitational force, normal force, applied force, frictional force, and net force.

(Neglect air resistance.)

Applying Force—Pressure

Pressure – the amount of force per unit areaP = F/A

• Units are Pascal’s (Pa) = N/m2

• We usually use kPa Suppose you are standing on the ground. Do

you exert more pressure when you stand on both feet or stand on one foot?

• The force, your weight, is the same in both cases. Two feet have more area than one foot, therefore, there will be more pressure exerted if you are standing on one foot.

Pressure

1. Brooke comes home from school and puts her books down on the kitchen table. The books have a combined weight of 25 N and the area in contact is 0.19 m by 0.24 m. What pressure do the books apply on the table?

2. A full coffee mug has a mass of 0.60 kg and an empty mug has a mass of 0.30 kg. a.) Which mug, the full or empty one, applies a greater pressure on the table? b.) If the full mug applies a pressure of 1200 N/m2, what is the area of the circular ring of coffee left on the table by the bottom of the mug?

Free Fall Explained

Do heavy objects always fall faster than light objects?

• Only in the presence of air resistance

Newton’s Second Law (F = ma)• Mass is only a factor in the force; not in the

acceleration• A heavier object will strike the ground with a

much greater force than a lighter object, but they will have the same acceleration and drop time

Falling & Air Resistance

Air resistance obviously affects the amount of time it takes an object to drop.

Think of an elephant and a feather; if we dropped both off the school, which would land first?

Without air resistance, they land at the same time

With air resistance, the elephant lands first

http://www.physicsclassroom.com/mmedia/newtlaws/efar.gif

http://www.physicsclassroom.com/mmedia/newtlaws/efff.gif


For the elephant: • net force is only slightly decreased by the air

resistance because the elephant has a large weight (downward force)

For the feather: • the net force is greatly decreased by the air

resistance because the feather has a small weight (downward force)


Does the elephant or the feather experience a greater force due to air resistance? Air resistance of a falling body depends on

1.How big the body is2.How fast the body is falling

Air resistance is the result of an object plowing through a layer of air and colliding with air molecules.

• The more air molecules which an object collides with, the greater the air resistance force. Subsequently, the amount of air resistance is dependent upon the speed of the falling object and the surface area of the falling object.

• Based on surface area alone, it is safe to assume that (for the same speed) the ELEPHANT would encounter more air resistance than the feather.


Why does the elephant fall faster if it experiences more air resistance than the feather?

• Objects accelerate when forces are unbalanced• The feather has a smaller force of gravity,

therefore its air resistance (even though it is smaller than the elephant’s) equals its force of gravity much faster than for the elephant.

• When these forces are equal, the feather has stopped accelerating and therefore reached its terminal speed.


Terminal Speed – the speed reached when the acceleration stops

Terminal Velocity – the terminal speed with its direction Ping pong ball = 9 m/s; baseball = 20 m/s

When the force of air resistance of a falling object is equal to the object’s weight, what will the net force be?

What will the acceleration be? Does this mean that the object stops falling?


With air resistance, Newton’s Second Law becomes

a = Fnet/m = (weight – air resistance)/m

a = (mg – R)/m = g – R/m

R = resistance force

This is actually a much simplified version of the formula so we won’t be doing actual air resistance problems.


1. A skydiver jumps. As she falls faster through the air, does air resistance increase, decrease, or remain the same?

2. Does net force increase or decrease?

3. As she falls faster and faster does her acceleration increase, decrease, or remain the same?

4. How can a skydiver control his/her velocity?


For each case, use the diagram to find the net force and the acceleration of the skydiver.

Documents

Chapter 5 Newton’s Second Law of Motion-- Force and Acceleration