Unit 3

Newton’s Laws of Motion

Aristotle vs Galileo• What enables an object to

move?• Galileo…What enables an

object to continue moving?• Force = • Net force =

Newton’s First Law of Motion

Newton’s 1st Law is often called the law of inertia.

Mass

Mass is not weight.

Mass is the measure

Weight can

Why do all objects fall at the same rate? (|a|=g=9.8m/s2)

• Aristotle felt heavy things fell faster than lighter ones. However, without air resistance, a light object falls the same as a heavy object…

Newton’s Third Law of Motion

Weight & the Force of Gravity:

Weight

Weight or the force of gravity

Normal Force (FN)A normal force (FN)

Tension Force (FT)

Tension forces exist in cables, ropes, wires, strings, etc. The tension force pulls on an object where the direction of the tension is always away from the surface of the object to which the ‘rope’ is attached.

FT

m

m

Force Body Diagrams (FBD)

In order to solve problems involving forces, we need to draw an FBD.

Draw all forces acting on a box that is being dragged to the right across a very smooth floor.

v

Newton’s 2nd Law of Motion

Example1

A Mazda Miata has a mass of 1080kg and can go from zero to 26.8m/s (0 to 60 mph) in 7.9s.  What magnitude of net force acts on the car?

A crane lowers a cable with a 1306kg car with an acceleration of 0.73 m/s2.  The car starts 20.0m above the ground with an initial speed of zero.

Example 2

a) What is the tension in the cable?

b) How much time will it take the car to reach the ground?

Example 3

A person stands on a bathroom scale in an elevator at rest on the ground floor of a building.  The scale reads 836N.  As the elevator begins to move upward, the scale reading briefly increases to 935N but then returns to 836N after reaching a constant speed. 

b) If the elevator was moving at 3.0m/s upwards and then uniformly decelerated to rest in 4.7s, determine the scale reading.

a) Determine the acceleration of the elevator.

A 35.0 kg lawn mower is pushed across a level lawn in a direction of 0.0. The force exerted on the handle is 100 N @ 310.0. Assume friction is negligible.

Example4

(a) Determine the acceleration of the mower.

(b) Determine the normal force acting on the lawn mower.

Bird in a box

A bird sits on a sensitive scale inside a large cardboard box.

Falling appleForce of gravity is the action force for a falling apple.

True or False: The Earth accelerates towards apple as apple falls towards ground.

Equilibrium

Object is in equilibrium or is balanced when ΣF=0 in a particular direction.

Determine the weight of the hanging picture.

Force of Friction (Ff)On a microscopic scale, most surfaces are rough.

Force of friction tends to oppose the motion of objects

Two Types of Friction:

1) Static Friction (Ffs)

2) Kinetic Friction (Ffk )

Friction depends on two things:

1) The normal force

2) The coefficient of friction (μ)

In the case of static friction, there is a maximum value at which the static friction force will resist motion between surfaces.

Nsfs FF This means that if you push a table with 50N of force where maximum static friction is 75N, the table won’t break free. You need to push with just a smidge over 75N.

The static frictional force increases as the applied force increases, until it reaches its maximum.

What minimum amount of force is needed to start to make a 250N crate move across a floor if the coefficient of static friction is 0.65?

Example1

A traveler pulls a suitcase of mass 8.00kg across a level surface by pulling on the handle with 20.0N at an angle of 50.0° relative to horizontal.  Coefficient of kinetic friction against the suitcase is μk = 0.100.Determine the acceleration of the suitcase. 

Example2

Example3

A physics book is sent sliding across a lab table with a speed of 4.3m/s. If it takes the book 1.6m to stop, determine the value of the coefficient of kinetic friction.

Terminal VelocityConsider a skydiver who steps off a hovering helicopter at high altitude. NOW consider the effect of air resistance (friction) during the fall.

As the skydiver continues to fall, describe what happens to their speed and acceleration? Why?

Initially at t=0, what is the acceleration and velocity of the skydiver?

Initially at t=0, what forces act on the skydiver?

As the skydiver begins to fall, what happens to the force of air resistance on skydiver?

Eventually what happens to the speed of the skydiver?

System of Bodies:

Multiple bodies connected together is called a system where all bodies MUST accelerate at the same value.

Assume mA = 1kg, mB = 3kg, mC = 4kg and the surface on which they sit to be smooth. If block C is pulled with a force F equal to 15N, determine:

a) The acceleration of the system.

b) The tension in each string btw A & B and btw B & C.

Example2 Block m2 (5.0kg) sits on rough surface where us= 0.65. Determine the minimum value of m1 to accelerate the system. Assume a frictionless & negligible mass pulley.

If m1 = 6.0kg, determine the tension in the string if uk = 0.30.

Example3

Assume a frictionless & negligible mass pulley. If the system is released from rest, determine the speed of the 5kg mass after it has fallen for 1.3s.

b) Determine the tension in the string.

Inclines

y

x

Consider a block that slides down a frictionless incline.

θ

Since the surface of the incline does not lie along x or y, we rotate our x-y axis to meet our needs.

Draw the force of gravity vector

A skier moves down a ski slope angled at 30o.

If the length of the slope is 50m, determine the time it takes to reach the bottom if the skier starts from rest. Ignore friction.

Example

A block of mass 2kg is projected up a rough incline (uk = 0.40) at 6.2m/s where the angle of the incline is 25o.

Example 2

a) Determine the distance along the incline it slides before coming to rest.

b) Determine the acceleration of the block on the way down the incline.

Example 3

Determine the minimum value of m1 if us = 0.70,θ = 30o, and m2 = 3.0kg so that the system will start to accelerate when m1 is released.

If m1 is 4kg, determine the tension in the string if uk = 0.35.