Equilibrium Forces and Unbalanced Forces

Topic Overview A force is a push or a pull applied to an object. A net Force (F net ) is the sum of all the forces on an object (direction determines + or -) F net = 6N to the right

Isaac Newton has 3 laws that describe the motion of object 1 st Law: Law of inertia ▫ An object at rest will stay at rest unless acted on by an outside force ▫ Inertia: The amount of mass an object has ▫ More inertia = more mass = Harder to move

Topic Overview When an object is in equilibrium, the net force equals zero Equilibrium  Fnet = 0 Objects in equilibrium can either be at rest or be moving with constant velocity Up = Down Forces Left = Right Forces

3 rd Law: Equal and Opposite ▫ For every action, there is an equal and opposite reaction. ▫ “Things push back”

Topic Overview When an object has unbalanced forces acting on it, the object will accelerate in the direction of that excess force: F net = ma This is called “Newton's Second Law”

Example Problem – Balanced Forces

Example Problem – Balanced Forces Solution

Example Problem – Unbalanced Forces

Example Problem – Unbalanced Forces - Solution

Common Mistakes Make sure you know if the object is in equilibrium or not

Circular Motion

Topic Overview An object in circular motion has a changing velocity but constant speed. This is possible because the objects speed does not change (same m/s) but the direction of its motion does change

Topic Overview The velocity of the object is always “tangent” to the path of the object. The circular force (F c ) is always directed toward the center The acceleration is always toward the center of the circle Force Velocity

Equations r is the radius of the circle

Example Problem

Example Problem - Solution

Common Mistakes Be sure to square the velocity Cross multiply when solving for “r”

Momentum/Impulse

Momentum Recap Momentum: The product of the mass and velocity of an object Equation: p = mv Units:p = kilograms meters per second (kgm/s) Momentum is a vector: When describing the momentum of an object, the direction matters.

Momentum Recap Collision: When 2 or more objects interact they can transfer momentum to each other. Conservation of Momentum: The sum of the total momentum BEFORE a collision, is the same as the sum of the total momentum AFTER a collision Momentum Before = Momentum After p 1i +p 2i + p 3i = p 1f +p 2f + p 3f

Momentum Recap To Solve Collision Problems: Step 1: Find the total momentum of each object before they interact Step 2: Set it equal to the total momentum after they collide Remember momentum is a vector, so you have to consider if the momentum is (+) or(-) when finding the total!!! Initial = Final 0 = -1.2 (v) + (1.8)(2) Initial = Final (1)(6)+ 0 = ( ) v

Impulse An outside force will cause a change in the momentum of an object. This is called an impulse. IMPULSE: A change in momentum F net  t =  p = m  v Units = Ns

Impulse To find the impulse under a force vs. time graph, you would find the area under the line. I = Ft

Example Problem - 1

Example Problem 1- Solution

Kinematics

Topic Overview Kinematics is what we use to describe the motion of an object. We use terms such as displacement, distance, velocity, speed, acceleration, and time to describe the movement of objects.

Topic Overview Distance (m): The total meters covered by an object (odometer) Displacement (m): The difference between the start and end points.

Topic Overview Velocity (m/s): How fast the car is moving is a (+) and (–) indicate direction Acceleration (m/s 2 ) Acceleration is a change in velocity If an object is accelerating, it is either speeding up or slowing down

Topic Overview Some objects have constant velocity Again this means that acceleration = 0 The equation for constant velocity is: x = vt If you are given an average velocity (v ave ), it is the same thing as constant velocity: x = v ave t

Topic Overview Some objects have constant acceleration This means they are speeding up or slowing down The equations for constant acceleration: a = (v f -v i ) / t  x = v i t + ½ at 2 v f 2 = v i 2 + 2a  x

Topic Overview To solve problems with constant acceleration, make a table! ViVi Initial velocity VfVf Final velocity aAcceleration xDistance ttime Reminder: If an object is “at rest” Velocity = 0

Topic Overview One example of a “constant acceleration problem” is a falling object (an object traveling through the air) All falling objects accelerate at 9.8m/s 2 due to gravity They also start with Zero initial velocity ViVi 0m/s VfVf a9.8m/s 2 x t

Example Problem A stone is dropped from a bridge approximately 45 meters above the surface of a river. Approximately how many seconds does the stone take to reach the water's surface? ViVi 0m/s VfVf a9.8m/s 2 x45 t? Reminder: Choose the equation that does not have the “blocked off” variable. In this case, choose the equation that does not have vf a = (v f -v i ) / t  x = v i t + ½ at 2 v f 2 = v i 2 + 2a  x

Example Problem - Solution

Graphs

Topic Overview The motion of an object can be represented by three types of graphs. 1) Displacement vs. Time graphs Tells you where the object is The slope (steepness) is the velocity In the graph above A is faster than B X (m) Time (s) A B

Topic Overview 1) Displacement vs. Time graphs X (m) Time (s) X (m) Time (s) X (m) Time (s) Not moving because the position does not change Constant velocity because the slope does not change (linear) Accelerating because it is a curve

Topic Overview 2) Velocity vs Time graphs Tells you how fast the object is moving Area under curve = Displacement Slope of the line = Velocity v (m/s) (s) 0

Topic Overview 2) Velocity vs. Time graphs Constant speed because the value for velocity does not change Speeding up because the value of the velocity is moving away from zero v (m/s) (s) 0 v (m/s) (s) 0 v (m/s) (s) 0 Slowing down because the value of the velocity is moving toward zero

Topic Overview 3) Acceleration vs. time Tells you the acceleration of the object Area under curve = Velocity a (m/s 2 ) (s) 0

Topic Overview 3) Acceleration vs. Time graphs This object has positive acceleration No acceleration. This means the object has a constant speed a (m/s 2 ) (s) 0 a (m/s 2 ) (s) 0 This object has negative acceleration a (m/s 2 ) (s) 0

Example Question-1

Example Question-1 Solution

Example Question-2

Example Question-2 Solution

Projectile Motion

Topic Overview Objects that travel in both the horizontal and vertical direction are called “projectiles”. These problems involve cars rolling off cliffs, objects flying through the air, and other things like that.

Topic Overview ▫ An object traveling through the air will: ▫ ACCELERATE in the VERTICAL DIRECTION  Because it is pulled down by gravity ▫ Have CONSTANT VELOCITY in the HORIZONTAL  Because there is no gravity ▫ Because they are different, we do calculations in the horizontal (x) and vertical (y)_ SEPARATELY.

Acceleration Velocity Horizontal Velocity Vertical -9.8m/s 2 Constant Increasing Zero Launch Angle Projectile Motion The time for an object to fall is determined by drop height ONLY (horizontal velocity has no effect)

Projectile Motion Horizontal Constant Velocity  x = vt Vertical Accelerating a = (v f -v i ) / t  x = v i t + ½ at 2 v f 2 = v i 2 + 2a  x TIME=TIME The key to solving projectile motion problems is to solve the horizontal and vertical parts SEPARATELY. Time is the only thing that is the same!

Example 1 A bullet is shot at 200m/s from a rifle that is 2.5m above the ground. How far downrange will the bullet reach before hitting the ground? vivi 0 vfvf a -9.8 x 2.5 t ?? Step 1: Find the time. In this case we have to use the vertical height to find the time. (acceleration) t = 0.72s Step 2: Use the time to find out the distance in the other direction (in this case the horizontal direction) x = vt x = 200 (0.72) x = 150m  x = v i t + ½ at 2

Energy and Power

Energy is the ability to CHANGE an object. These types of energy are a result of a CHANGE in……. Work:FORCE Kinetic Energy:VELOCITY Potential Energy: HEIGHT Elastic Energy:SHAPE

Conservation of Energy In a system, the TOTAL MECHANICAL ENERGY never changes Energy can switch forms, but it cannot be created or destroyed. KINETIC POTENTIAL ELASTIC WORK

Conservation of Energy Mathematically speaking that looks like this TME Initial=TME Final KE + PE + EE + W = KE + PE + EE + W

Energy: Joules (J) Work:W = Fd Kinetic Energy:KE = ½mv 2 Potential Energy: PE = mgh Elastic Energy:EE = ½kx 2

Examples A ball is dropped from a height of 12m, what is the velocity of the ball when it hits the ground? Potential Energy  Kinetic Energy Since all of the energy is transferred, we cans set them equal to each other PE = KE m(9.8)(12) = ½(m)v 2  mass cancels m/s = v

Examples A ball is dropped from a height of 12m, what is the velocity of the ball when it hits the ground? Potential Energy  Kinetic Energy Since all of the energy is transferred, we can set them equal to each other PE = KE m(9.8)(12) = ½(m)v 2  mass cancels m/s = v

Examples A force of 50N pushes horizontally on a 5kg object for a distance of 2m. What is the final velocity of the object? Work  Kinetic Energy Since all of the energy is transferred, we can set them equal to each other Work = KE (50)(2) = ½(5)v m/s = v

Examples No matter type of energy transfer, the set up is the same. Even if there is more than one type of energy present TME Initial=TME Final KE + PE + EE + W = KE + PE + EE + W

POWER Power = Energy/ time P = E/t On your equation sheet it lists “Energy” as Work for the top of the fraction. But you can put any type of energy on the top part of this equation.

AP ONLY: Torque

AP ONLY: Oscillations

AP ONLY: Gravitation