Unit 2

1D Vectors &

Newton’s Laws of Motion

A. Vectors and Scalars

B. Addition of Vectors & RESULTANT

In one dimension, simple addition and subtraction is all that is needed.

RESULTANT VECTOR

Aristotle vs Galileo

FORCES

NET FORCE

D. TYPES OF FORCES

1) Force of Gravity (Weight)

2) Normal Force (Support Force)

If the box weighed less, what would happen to the normal force acting on the box?

3) Tension Force

4) Friction Force

E. NEWTON’S LAWS

Newton’s 1st Law of Motion

Also called the law of inertia.

Mass

- Without gravity, how can we distinguish between a 1kg and a 2kg mass?

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

Newton’s 3rd Law of Motion

Explain the movement of a rocket using the 3rd Law.

Question: A loaded school bus hits a bug and kills it. Which body receives the greater force of impact, bug or bus?

Who pulls harder on the rope?

Who wins the tug of war?

Force Body Diagrams (FBD) using vectors

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

A box is dragged by a rope towards the right on a smooth floor. Draw the force vectors on the box.

Newton’s 2nd Law of Motion

Constant velocity equates to what in regards to Fnet?

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

Example 1

a) What is the tension in the cable? Draw FBD

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

Example 2A 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.

Example 3: A force of 75N pushes on 2 boxes as shown. The mass of b1 is 20kg and the mass of b2 is 35kg. Surface is smooth.

a) Determine the acceleration of the two boxes.

b) Determine the net force on b2.

c) Determine the net force on b1 . Why is it different?

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:

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

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 where we say you just have to equal maximum static to break free.

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

A person crosstrains by pushing a 950N man (who sits

on a 45N metal box). The box is pushed with a force of 335N at a constant acceleration. If the coefficient of kinetic friction is 0.30, determine the speed of the box after 3.0s if it starts from rest.

Example1

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 and the coefficient of kinetic friction is 0.40?

Example2

Example2A physics book is pushed and released across a table. The book is sent sliding 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.

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

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

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

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

e) Eventually what happens to the speed of the skydiver?

2D Vectors/Forces

Vectors & Components

Any vector pointing at an angle other than multiples of 90o can be broken down into components.

The components form the legs of a right triangle.

If a force, F, acts at an angle, θ, it can be resolved into perpendicular components and can be found using trigonometric functions.

Adding Vectors by Components

Use the Pythagorean Theorem and Right Triangle Trig to solve for resultant and θ.

Know your quadrants. (+) angle is moving CCW

(-) angles mean moving CW

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.

Example 4

(a) Determine the acceleration of the mower.

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

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. 

Example5

Suppose a 3-kg block is being pushed against a wall by a force F = 75N acting at an angle of 30º to the horizontal. Determine the acceleration of the block if the coefficient of kinetic friction is 0.10.

Example6

F

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 can rotate our x-y axis to meet our needs.

Draw the force vector, Fg , on the box

y

x

Resolve the force of gravity into components

θFg

θygF

xgF

θ

Fg

What is the normal force on the block equal to?

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.

Example1

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.

A man pushes a 39.0-kg crate, starting at rest, up a 30.0o incline that is 23.5m long with a force of 335N. The coefficient of sliding friction between the crate and the incline is 0.20.

Example 3

a) Calculate the magnitude of the frictional force acting on the crate.

b) What will be the speed of the crate when it reaches the top of the incline?