May the Force Be With You A lesson on dynamics and forces By, Christina Germak Danielle Rosenberg Ali Larcombe

What are we trying to accomplish? To model why objects move To model forces To connect motion to forces What is mass? How are mass, force, and acceleration related? To begin solving problems To gain an understanding of Newton’s 3 Laws of Motion

How to make a Free-Body Diagram Start with a dot to represent the object that the forces are acting on (This is where the mass should be). Draw arrows from the dot to show the direction of the forces acting on it.  The upward arrow represents the force of the surface on the object, or whatever is exerting an upward force on the object (the normal force).  The downward arrow always represents the force of the Earth on the object (gravity).  The arrows in the x direction represent other outside forces, such as friction, or a push or pull. If all arrows in the x or y direction are equal in length, the net force is zero, and the object is traveling at a constant speed. If one arrow is bigger than the other in either direction, there is a net force.  Net Force- The difference of forces in two opposite directions. If the difference is 0, there is no net force.  If the arrow in the negative direction or positive direction is bigger than the arrow in the opposite direction, the object is accelerating.

Constant motion or acceleration? How do you interpret these free-body diagrams? Constant motion- The two upward forces add up to the downward force (gravity), which means the net force is zero. The object could be in motion or at rest. Constant motion- The net force is zero in the x direction and the y direction. The object could be in motion or at rest. Acceleration in the positive or negative x direction- The arrow to the left (negative direction) is bigger than the arrow to the right. The object could be slowing down to the right, or speeding up to the left. Acceleration in the positive or negative x direction- The arrow to the right (positive direction) is bigger than the arrow to the left. The object could be speeding up to the right, or slowing down to the left. Constant motion- The two arrows are the same size (net force = 0). The object could be in motion or at rest. Acceleration in the positive or negative y direction- The upward arrow (positive direction) is bigger than the downward arrow. The object could be speeding up to the north, or slowing down to the south. Acceleration in the negative or positive y direction- The downward arrow (negative direction) is bigger than the upward arrow. The object could be speeding up to the south, or slowing down to the north.

Try a Problem Tina and Danielle are pulling Ali, who weighs 45 kg, in a wagon by a string (in the positive x direction), across the street at a constant speed. (45 kg includes the mass of the wagon). Draw a free-body diagram to model this scenario. Ali and wagon = 45 kg

Limitations of Free-Body Diagrams Can you tell which of these free-body diagrams represent an object that is moving down? Did you say only this one? The real answer is that ALL of these free-body diagrams could represent an object that is traveling downwards. Free-body diagrams only represent the magnitude of the forces that are acting on the object. For example, if the top arrow is larger than the bottom arrow, it does not mean it is only moving up. It could also be slowing down in the negative direction. If the arrows are equal to each other, it does not only mean it is in motion, because if an object has a constant speed of 0 m/s, it has the same free-body diagram as an object that is traveling at a constant speed of 10 m/s.

How to make a Motion Diagram Start off with t = 0 to represent that no time has passed (for the first dot). Have each proceeding dot represent a certain amount of time. If the object is traveling at a constant speed, draw the dots equally apart from each other. If the object is accelerating, draw each dot a little farther apart than the last one. If the object is decelerating, draw each dot a little closer to the last one. Depending on the direction of motion, the motion diagram will go to the left, right, up, or down. Velocity vectors show the direction of the object and acceleration vectors show the direction of acceleration (they face in the opposite direction of motion when the object is decelerating).  Acceleration vectors are all the same length when the acceleration is constant. Place them above or next to the velocity vectors.

Can you interpret these motion diagrams? t=0 Acceleration- An object is speeding up in the positive x direction. Acceleration- An object is slowing down in the positive x direction. Acceleration- An object is slowing down in the negative x direction. Constant / Accelerated Motion- An object starts out with constant motion in the positive x direction, and then slows down to a stop, and is stopped for 2 seconds. Acceleration- An object speeds up in the positive y direction. t = 0 Constant motion- An object is traveling at a constant speed in the negative y direction. = 1 second

Try a problem A car is traveling at a constant speed. He then realizes he is not going to make the green light, so he steps on the gas and accelerates through it. Draw a motion diagram to model this situation. t=0

What experiments will provide a good basis for this chapter? Roller skating experiment Bocce ball experiments (1 and 2) Fan cart experiments 2 lab experiments that show the relationship between acceleration, force, and mass The weight on the scale (in elevator and elsewhere)

Roller Skating Make sure you have the appropriate safety equipment! (helmet, wrist guards, elbow and knee pads) Make sure there is nothing on the ground you could run over and trip on (back packs, etc.). See how many ways you can get yourself to move on roller skates. Pay attention to:  what direction you exert the force, and what direction you actually move. The direction in which you exert the force is opposite to the direction in which you move.  how much of a force you exert and how fast you move. The speed at which you move depends on how much force you apply. They are directly proportional.

Bocce Ball Exp. 1 Have person 1 roll the ball at a constant speed to person 2, who is sitting 5 meters away. Halfway there, have person 3 push the ball in the direction of its original motion and observe the results before person 2 stops it by exerting a force in the opposite direction of its motion. You should observe that the speed of the ball increases in the direction of its motion after it has been pushed the first time. Make sure no body is around the bocce ball when it is rolled.

Bocce Ball Exp. 2 Have person 1 roll the ball at a constant, fast speed to person 2, who is sitting 5 meters away. Halfway there, person 3 should push the ball in the opposite direction of its original motion, and observe the results before person 2 stops it by exerting a force in the opposite direction of its motion. The ball should slow down in the original direction of its motion, after it has been pushed the first time. t=0 Make sure no body is around the bocce ball when it is rolled.

Fan Cart Scenario 1 There are 2 connected fan carts, A and B. A is on the left and B is on the right. The positive direction is to the right, and the negative direction is to the left. Turn on fan A, and observe the motion of the two carts. You should observe that the two carts accelerate in the positive direction. Be careful not to put your fingers, or any part of your body near the fan! If you have long hair, make sure to tie it back.

Fan Cart Scenario 2 There are 2 connected fan carts, A and B. A is on the left and B is on the right. The positive direction is to the right, and the negative direction is to the left. Turn on fan B, and observe the motion of the two carts. You should observe that the two carts accelerate in the negative direction. Be careful not to put your fingers, or any part of your body near the fan! If you have long hair, make sure to tie it back.

Fan Cart Scenario 3 There are 2 connected fan carts, A and B. A is on the left and B is on the right. The positive direction is to the right, and the negative direction is to the left. Turn on fan A and fan B, and observe the motion of the two carts. You should observe that the two carts do not move. t=0 Be careful not to put your fingers, or any part of your body near the fan! If you have long hair, make sure to tie it back.

Mass is Constant You will need a small cart, a spring scale, 1500 grams, a meter stick, and a stop watch. Measure 1 meter from the start point to the end point. Put the 1500 grams onto the cart and attach the spring scale to the cart as well. Place the cart at the start point and start the stop watch as some one pulls the spring scale with a constant force until the end point, where you stop the watch. Do this, increasing the force by 10 N each trial. Find the acceleration of each trial and see how the force is related to the acceleration. You should find that acceleration and force are directly proportional. Force (N)Time (s)Acceleration (m/s/s) Due to human error, results may vary. Make sure you are wearing closed-toed shoes!

Force is Constant You will need different masses, a meter stick, a small cart and hanger (pulley), and stopwatch. The cart is connected to a pulley which has a constant mass at the end of it resulting in a constant force Load different masses onto the cart and set it down on the lab table See what happens to the acceleration when more mass is added to the cart You should find that mass and acceleration are inversely proportional. Mass (g)Time (s)Acceleration (m/s/s) Due to human error, results may vary. Make sure you are wearing closed-toed shoes!

From the last two experiments, it can be seen that acceleration is directly proportional to the net force, and inversely proportional to the mass. From this, we can derive this equation, which represents Newton’s Second Law.

Scale in Elevator Place a 100 gram weight on a scale in an elevator, and hit the up button in the elevator. What do you notice about the reading on the scale as the elevator speeds up? When it stays at a constant speed? When it slows to a stop? When the elevator is accelerating upward you should notice that the force on the scale increases (the reading on the scale should increase over 100 g). When the elevator stays at a constant speed, the force on the scale remains constant (it should read the final mass that it increased to from the previous scenario). When the elevator slows down while traveling upward, the force should decrease (it should slowly decrease to 100 g).

Weight on Scale 1 Take a 100 gram mass and place it on the scale. First, attach a string to the side of the mass and pull upward in a diagonal direction while sliding it across the surface of the scale. What do you notice happens to the force on the scale? You should notice that the force on the scale decreases because the force of you pulling on the mass alleviates some of the force on the scale. 100 g Fstring scale

Weight on Scale 2 Take that same 100 gram mass and place it on the scale. Using your finger, press down on a corner of the mass in a downward diagonal direction and push the mass across the surface of the scale. What do you notice happens to the force on the scale as you push it across? You should notice that the force on the scale increases as you push it down and across the surface of the scale. 100 g Fstring scale

First Law (Law of Inertia) An object at rest will stay at rest, and an object in motion will stay in motion, unless an unbalanced force acts upon it. An object with more mass has more inertia, which means its resistance to motion is greater than an object with less mass. Because the rock was only in the way of the skateboard, the skateboard stopped, but the skateboarder continued his motion in the positive x direction.

Skateboard before hitting rock Fsurface skateboard Fearth skateboard Skateboard after hitting rock Fsurface skateboard Fearth skateboard Frock skateboard The force of the rock on the skateboard is an unbalanced force (the net force is no longer 0 N), and caused the skateboard to stop moving. First Law (Law of Inertia)

Second Law ( ) The Net force on an object is directly proportional to the acceleration of the object and is indirectly proportional to the mass of the object. Because the ball has less mass than the wall, it accelerates more.

Second Law ( ) Fperson wall Fperson ball The amount of force exerted on the wall by the person and the ball by the person is the same. However, if you look at Newton’s 2 nd law equation, if the mass increases, the acceleration will decrease, since they are inversely proportional. This is why the wall does not move, and the ball does. Fearth wall Fearth ball (wall) (ball)

Third Law For every force, there is an equal and opposite force. The rocket’s engine pushes on the ground with the same force as the ground pushes back on the rocket, causing it to launch.

Third Law Fground rocket (rocket) Frocket ground (ground) The amount of force exerted on the ground by the rocket is the same as the amount of force exerted on the rocket by the ground.

Environmental Examples There are several examples of Newton’s 3 Laws in your everyday life.  1 st Law: Imagine you are playing in a soccer game, and you kick the ball at the goal, and think it is going to go in. However, the goalie blocks it and keeps it from continuing in its original path of motion, so you don’t score a goal.  2 nd Law: If you go to the grocery store and you grab an empty cart, you will notice that it is really easy to push around and go fast with. Once the cart starts to get full you should notice that it gets harder to push and is harder to accelerate.  3 rd Law: If you see a car driving down the highway and a truck is coming in the other direction, on the wrong side of the road, and they collide, the car will exert the same amount of force on the truck as the truck will exert on the car, even though the truck is bigger.

Exemplary Problem 2 Elevator problem  A 50 kg person stands on a scale in an elevator. What does the scale read when: A) The elevator is at rest? B) The elevator is going up at a constant speed of 6 m/s? C) The elevator is going down at a constant speed of 6 m/s? D) The elevator is accelerating upward at 6 m/s/s? E) The elevator is accelerating downward at 6 m/s/s?

Answer 1 A, B, and C) 490 N = Fearth person = Felevator person Because scenarios A, B, and C are all traveling a constant speed / at rest, the force of the elevator on the person will remain the same. Felevator person Fearthperson D) 300 N = Felevator person N Felevator person = 790 N E) -300 N = Felevator person N Felevator person = 190 N

Exemplary Problem 2 What is the acceleration of a pulley system with two masses attached to each end, one weighing 45 kg and 15 kg? 45 kg15 kg

F45kg 15kg F15kgearth Answer N = Fearth 45 kg 147 N = Fearth 15 kg a = +/ m/s/s Step 1 Step 2 Step 3

Exemplary Problem 3 Remember this problem? Tina and Danielle are pulling Ali, who weighs 45 kg in a wagon by a string (in the positive x direction), across the street at a constant speed. Draw a free-body diagram to model this scenario. (45 kg includes mass of wagon) Now, Ali is accelerating. The force of Tina and Danielle on Ali is 12 N, and the force of friction on Ali is 7 N. Find the acceleration of Ali.

Answer 3 a= 0.1 m/s/s Fsurface Ali 12 N Fearth Ali 7 N

Exemplary Problem 4 A 50 kg man fell out of a plane and is hurtling towards the ground. What is the force of the earth on the man as he accelerates downward?

(air resistance negligible) Fearthperson 490 N 50kg Answer 4

Chapter 8 Summary We model why objects move using free- body diagrams and motion diagrams.  Objects move because of the forces that act upon them. We model forces using free-body diagrams.  Net Force is the difference of forces that are acting on an object in opposite directions. There is no net force if the object is moving at a constant speed or motionless.

Chapter 8 Summary  Mass is the amount of inertia an object has, or how much it resists a change in motion. Weight is the amount of force with which an object pushes down on the Earth.  Mass is inversely proportional to acceleration. Force is directly proportional to acceleration.

Chapter 8 Summary Newton’s 3 Laws of Motion model how and why objects move.  First Law (Law of Inertia): An object at rest will stay at rest, and an object in motion will stay in motion, unless an unbalanced force acts upon it. An object with more mass has more inertia, which means it will resist motion more.  Second Law ( ): The Net force is directly proportional to the acceleration of an object and indirectly proportional to the mass of an object.  Third Law: For every force, there is an equal and opposite force.

Practice Problems 1. An object sits on a frictionless surface. There is a 20 N force being applied to the object in the right direction and its acceleration is at 2 m/s/s. What is its mass? 2. A 25 kg mass pulled along a frictionless surface by a horizontal force of 150 N will have what acceleration?

Practice Problems 3. A shopper in a supermarket pushes a loaded cart with a horizontal force of 15 N. The cart has a mass of 40kg.  a. What is the resulting force? Ignore friction.  b. What will the resulting force if shopper places their 30N child in the cart before they begin to push it? 4.A 35 kg block is pulled along a frictionless horizontal surface by a string The string is pulled by a 110 N force. What is the acceleration of the block?

5. A professional wrestler pushes his small son on a sled from behind along a horizontal surface. a. As they accelerate from rest, which force is larger: the force of the boy on the wrestler or the force of the wrestler on the boy? b. Once they are traveling at a constant velocity, which force is larger: the force of the wrestler on his son, or the force of the surface, due to friction on the boy? c. As they slow down what is the larger force: the force of the wrestler on his son, or the force of the surface, due to friction on the boy? 6. What force is required to accelerate an object having a mass of 3 kg at 10 m/s/s? 7. What is the mass of an object which is accelerated at 15 m/s/s due to a force of 70 N? 8.A rope is lifting a heavy bucket with a force of 20N and it is accelerating upward at 5 m/s/s. What is the mass of the bucket? Practice Problems

9. Amanda is pulling a 50 kg cart with a force of 10N across a carpet with friction of 7N. How much is it accelerating? 10. There is a frictionless pulley with a 5.5 kg mass and a 6.5 kg mass attached on either end. What will the acceleration of this system be? 11. You are pulling your suitcase, with a mass of 20 kg, across a carpet to the right (there is a force of friction of 6 N to the left). The suitcase is moving at a constant speed. Draw a free-body diagram for this situation, and what is the force of you that is pulling the suitcase? 12. A man standing on a scale in an elevator usually weighs 850 N but the scale he is standing on reads 15 N. He is traveling upward to the 50 th floor. What is his acceleration? 13. A man in an elevator weighs 75 kg. He is accelerating downwards at 5 m/s/s. What is the force of the elevator on the man? Practice Problems

1.) 10 kg 2.) 6 kg

3.)  A.) m/s/s  B.) 0.35 m/s/s  4.) 3.14 m/s/s

5.)  A.) The force of the wrestler on the son is the same as the force of the son on the wrestler.  B.) Fwrestler son  C.) Fwrestler son 6.) 30 N

7.) 4.67 kg 8.) 4 kg

9.) 0.06 m/s/s 10.) 0.82 m/s/s

11.) 6 N 12.) m/s/s 13.) 360 N Fearth you Fsurface you 6 N? 15 N 850 N ? 735 N 75 kg ?

Works Cited htm htm help/net-force.php help/net-force.php