Unit 4 FORCES AND THE LAWS OF MOTION

4-1 Forces

• Force: A push or pull exerted on an object

• Forces cause a change in velocity (acceleration)

*cause a stationary object to move

*cause a moving object to stop

*cause an object to change direction

• SI Unit for Force is the Newton• Newton: amount of force that will

accelerate a 1 kg mass by 1 m/s2

1 N = 1 kg·m/s2

• Forces can act through contact or at a distance.

• Contact forces: result from physical contact between 2 objects (kicking a ball)

• Field forces: do not involve physical contact (example: gravity, magnetism)

• Force is a vector quantity. (has magnitude and direction)

• Force diagram: shows all forces in a situation (objects are treated as points)

• Free-body diagram: shows only forces on a single object of interest.

A force diagram (a) shows all forces acting in a situation

A free body diagram (b) shows only those forces acting on an object of interest (the car)

4-2 Newton’s First Law of Motion

4-2 Newton’s First Law

• Newton’s First Law (Law of Inertia)

• An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless the object experiences a net external force.

• Inertia: The tendency of an object to maintain its state of motion. (that is, a constant speed in a straight line)*If net external force is zero, then acceleration is

zero.

• External force: a single force that acts on an object.• Net external force: vector sum of all the forces

acting on an object.• An object’s acceleration is the same as if the net

external force were the only force acting on the object.

• Mass is a measure of inertia.– (The greater the mass, the less the body accelerates under an applied

force.)

• Objects in motion tend to stay in motion.

• Objects that are at rest or moving constantly tend to stay at rest and are at equilibrium. (net force must be zero)

If no seat belt, no force to hold person when car collision occurs.

Practice Problem 1• Steve is pulling a wagon with a force of 100 N directed at an angle of +40 to the horizontal.

a. Draw a free body diagram showing all the forces

b. Find the x and y components of this force (using trig).

Practice Problem 2• A box is pulled to the right with a force of

150 N, to the left with a force of 225 N, upward with a force of 520 N and downward with a force of 321 N.

a. Draw a free body diagram showing the forces

b. Find the net external force in the x direction

c. Find the net external force in the y direction

d. Find the magnitude and direction of the net external force on the box

4-3 Newton’s Second and Third Laws

• Newton’s Second Law:

• The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the object’s mass.

• Newton’s Third Law:

• For every action there is an equal and opposite reaction.

• When two forces interact with one another, the forces they mutually exert are called an action-reaction pair

• Field forces also exist in pairs.

Practice Problem 3• A 6.0 kg object undergoes an acceleration of 2.0 m/s2

a) What is the magnitude of the net external force acting on it?

b) If the same force is applied to a 4.0 kg object, what will be the acceleration?

Practice Problem 4• Identify the action-reaction pairs in the following situations

– Person takes a step– Snowball hits someone in the back– Baseball player catches a ball– Gust of wind strikes a window

4-4 Everyday Forces• Weight (Fw or Fg): force acting on a mass toward center of Earth due to gravity.

• Normal force (FN): a force exerted by one object on another in a direction perpendicular to the surface of contact.

• Mass is a measure of the amount of matter in an object

• Weight is a measure of the force of gravity on an object.

• Because weight is a measure of force, we use Newtons to measure weight in Physics.

Converting Mass to Weight

Remember: F=ma. • Therefore, to convert mass (kg) to weight

(Newtons), one must multiply the mass of an object by 9.8 m/s2.

• To convert weight to mass, one must divide the weight of an object by 9.8 m/s2.

Converting Mass to WeightPractice Problem 5: A dog weighs 195 Newtons. What is its mass in kg?• 195 Newtons / 9.81 m/s2 = 19.9 kg

Practice Problem 6: Susan has a mass of 50.0 kg. What is her weight in Newtons?• 50.0 kg x 9.81 m/s2 = 491 Newtons.

Tension and Compression• Tension is the magnitude of the pulling force exerted by a

string or rope on another object, and is the opposite of Compression

• When two objects connected by a rope are pulling in opposite directions, the pulling forces are added to determine tension

• Practice Problem 7. If RJ and Billy are playing tug of war with a rope and each is pulling with a force of 2000 Newtons, what is the tension on the rope?

• 2000 N + 2000 N = 4000 N

Friction

• Force of friction (Ff): force that opposes motion.

• Caused by the attractive forces of two surfaces in contact

• Friction is necessary for life because we depend on it to hold things together.

• Static friction: resistive force that keeps an object from moving when object is at rest.

• Kinetic friction: resistive force that opposes an object that is moving (slows it down)

• Frictional forces (Ff) are proportional to normal force FN. (heavier an object is, the greater the friction)

• Friction depends on the surface.

• The coefficient of friction is a ratio of forces.

µk = coefficient of kinetic friction

Fk = kinetic force

FN = normal forcen

kk F

F

Coefficient of Static Friction: Is the ratio of the maximum value of the force of static friction to the normal force

µs = coefficient of static friction

Fs = static force

FN = normal forcen

ss F

F max,

Practice Problem 8

• A 50 kg crate at rest on a horizontal floor requires a 150 N horizontal force to set it in motion. What is the coefficient of static friction between the crate and the floor?

31.0491

150

/81.950

1502

max,

N

N

smkg

N

F

F

n

ss

• Air resistance is a form of friction.

• Free-falling objects experience air resistance.

• If air resistance = weight of object then the object reaches terminal velocity

• When an object is at terminal velocity, there is: no net force, no acceleration, The object is at maximum constant velocity.