Chapter FOUR: Forces in One Dimension 4.1 Force and Motion force: a push or pull exerted on an object forces cause objects to: speed up slow down change direction = change in velocity therefore, a force causes an acceleration force is a vector 1
when considering force problems, the object of interest = the system everything that acts on the system = the external world ex: book on table Contact forces and Field forces external world physically touches the system exerted by external world without physical contact Ex: Kyle shoves Mrs. Stowell out the window Ex: gravity pulls the flower pot to Earth agent: the cause of the force 2
Free body diagrams sketch the situation identify the system identify the contact forces and the directions they push/pull identify the field forces and the directions they push/pull Flower pot is sitting on a shelf system = flower pot contact forces: shelf pushing up field force: gravity pulling down agent: earth's mass agent: shelf simplify to F shelf F Earth's mass length of vector arrows indicate magnitude = length = constant velocity draw free body diagram of: skydiver free falls out of a helicopter (ignore air resistance) Oct 28 1:10 PM 3
draw free body diagram of: skydiver free falls and accelerates toward the ground (DO factor in air resistance) Oct 28 1:10 PM draw free body diagram of: skydiver opens chute and falls at a constant velocity toward the ground Oct 28 1:10 PM 4
draw the free body diagram of: crate is being pulled at a constant velocity to the right as friction opposes the motion Oct 28 1:10 PM Force and Acceleration restated: a force causes a CHANGE in velocity ( an acceleration ) F = ma F = labeled in Newtons m = kilograms a = m/s 2 it is a linear relationship : the greater the force exerted, the larger the acceleration of the object larger mass = larger force necessary to cause the same acceleration 5
Combining Forces force = vector ex: you and your friend push on a table x F 1 = 100N F 2 = 75N + x 100N + 75N = 25 N positive (direction) Combining Forces ex: you and your friend push on a table F 1 = 100N F 2 = 75 N + x 100N + 75N = 175 N 6
Combining Forces ex: you and your friend push on a table F 1 = 100N F 2 = 100 N + x 100N + 100N = 0 N no net force = no acceleration clarification: doesn't mean no velocity Newton's Second Law F = ma m = F/a a = F/m label for force? label for mass? label for acceleration? 1 Newton = 1 kg m /s 2 solving problems: draw diagram identify all forces find net force use Newton's second Law use previous formulas to find v, d, or t 7
ex: What force is required to accelerate a 6.0 kg bowling ball at +2.0 m/s 2? ex: What is the acceleration of a 35 kg mass that has a force of 270 N applied to it horizontally? 8
Ex: What is the acceleration of a 125 kg mass when three different forces are exerted on it? The object was at rest and achieved a speed of 10.0 m/s. The first force is 10.0 N east, the second is 30.0 N east, and the third is 15.0 N west. How far did the object travel by the time it reached 10.0 m/s? Newton's First Law an object at motion will stay in motion and an object at rest will stay at rest unless an unbalanced force acts upon it aka "Law of Inertia" so...what is the motion of an object with no net force acting upon it? nothing changes if there is NO NET force 9
Some types of forces: table 4 2 on page 94 you'll see these abbreviations in free body diagrams ex: F g instead of F Earth's mass inertia: tendency of an object to resist a change in its motion NOT a force as mass of object increases = inertia increases equilibrium: when net force on object = 0 object is either: 1) at rest 2) moving at a constant velocity 10
4.2 Using Newton's Laws F = ma Weight is a force F g = mg It is the mass of an object being pulled on by Earth's gravitational field Fg and g are both straight downward toward center of the Earth gravity is pulling down on objects even when they aren't falling scales you have mass gravity pulls down on that mass you have weight when you stand on the scale, your weight is a downward force are you accelerating? (are you speeding up? slowing down? changing direction? ) so the scale must be pushing up on you with force equal in magnitude to your weight F sp F g 11
Felicia, a ballet dancer, has a mass of 45.0 kg. a) what is Felicia's weight on Earth? b) what is Felicia's mass on Jupiter where acceleration due to gravity is 25.0 m/s 2? c) what is Felicia's mass on Jupiter where acceleration due to gravity is 25.0 m/s 2?. A space ship has a mass of 9000 kg. The space ship is launched from Earth and lands on a distant planet where it has a weight of 390000 N. What is the acceleration of gravity on this planet? 12
Arnold needs to lift a 35.0 kg rock. If he exerts an upward force of 502 N on the rock, what is the rock's acceleration? The elevator in the new office building warns that it can safely lift 300 kg at one time. If John (850 N), Betty (530 N), Robert (740 N) and Alice (610 N) all get in the elevator at once, can the elevator safely carry them up to the third floor? 13
A giant crane in Washington DC was tested by lifting a load with a mass of 2.232 x 10 3 kg. Find the force needed to lift the load with an acceleration of 2.20 m/s 2. If friction exerts a force of 15.0 N and a crate of 105 kg is accelerated to the right at a rate of 0.652 m/s 2, what is the force pushing the crate to the right? 14
Apparent Weight observed when an object experiences a vertical acceleration elevator: at constant velocity ( no acceleration) scale will read your actual weight accelerating upward stronger upward force than the downward gravity force scale will read that you are heavier than your actual wt. accelerating downward scale will read less than your actual weight cable breaks: you and elevator room are in free fall only acceleration is g you will appear weightless on the scale. You are in an elevator standing on a balance scale such as the kind you find in a doctor's office. You notice that the scale reads many kilograms less than you really weigh. a. Is the elevator moving at constant velocity or is it accelerating? b. What is the direction of the acceleration? 15
Drag force and terminal velocity So far, we've ignored air resistance In reality, when an object moves through any fluid (liquid/gas) the fluid exerts a force opposing the motion the magnitude of the drag force depends on: the speed the object is moving faster object speed = greater drag force slower object speed = smaller drag force the size and shape of the object that is moving sheet of paper has a greater drag force than a spherical ball properties of the fluid temperature and viscosity. When drag force EQUALS the force of gravity ( Fg = mg), the object is in equilibrium object falls, and accelerates due to "g" F air F air F air (initial velocity is small, so drag force is small) as velocity increases, so does the drag force F g F g F g if the object falls long enough, it speeds up until drag force has increased to = "g" then it no longer accelerates = constant velocity = TERMINAL VELOCITY. 16
4.3 Interaction Forces Forces exist in pairs example: two people wearing ice skates ( to reduce friction ) one person pushes the other, but both will move Grandma Jedidiah James F JJ on grandma F grandma on JJ opposite directions, but equal magnitude they act on EACH OTHER: so, JJ is the agent when Grandma is the system Grandma is the agent when JJ is the system. Newton's Third Law: For every force, there is an equal and opposite force F A on B = F B on A Force of Grandma on JJ = Force of JJ on Grandma in opposite direction 17
equal and opposite = interaction pair F floor on lady F lady on floor = F floor on lady F lady on floor Fg Fg is always present interaction pair if Earth exerts a downward force on the person the person also exerts an upward force on earth the FORCES are equal and opposite but Earth's mass is so large compared to the person... it makes the acceleration of the Earth very small 18
Forces of Ropes and Strings Tension: force exerted by rope/string. Tension is distributed equally throughout the length of the rope/string F T Tension in the string would equal the weight of the bucket F g #32, page 106 19
You are fishing and catch a fish with a mass of 2.0 kg. If the fishing line can withstand a maximum tension of 30.0 N, what is the maximum acceleration you can give the fish as you reel it in? The Normal Force : the perpendicular contact force exerted by a surface on another object any two objects in contact with each other exert a force on each other F table on box F box on table the surface that the object makes contact with is the table (horizontal) so the normal force is perpendicular to and away from the surface F n F n = the force of the table on the box 20
F n often equals F g in magnitude ex: 10kg this crate is in equilibrium (0 m/s, no acceleration) Fn = Fg Fg = 10kg ( 9.8m/s 2 ) = 98 N but not always... what is the normal force? What if a little kid tried to lift it with a force of 10 N upward? It isn't enough force to move the box, but it is still exerted on the box. F kid = 10 N 10kg Fg = 10kg ( 9.8m/s 2 ) = 98 N still in equilibrium, so up forces have to balance with down forces What is the normal force? What if something pushed down on the box with 5 N of force. 10kg Fg Fg = 10kg ( 9.8m/s 2 ) = 98 N F push What is the normal force? F kid = 10 N 10kg Fg = 10kg ( 9.8m/s 2 ) = 98 N still in equilibrium, so up forces have to balance with down forces What is the normal force? 21
A 12.0 kg block sits on a table. A 10.0 kg block sits on top of the 12.0 kg block. If there is nothing on top of the 10.0 kg block, what is the force that the table exerts on the 12.0 kg block? 22