Free Body Diagrams in Physics

Introduction to free-body diagrams 1

Free-body diagrams used to correctly apply the 2nd law 1. Identify a single object. Draw a point as an idealization of the object. 2. Think of a force that acts on it. Ask yourself: What gives rise to this force? If you can answer that question, then draw the force. If you can t, then don t. (This ensures that you have an inertial reference frame.) 3. Repeat for all forces. Having the correct free-body diagram makes it easy to correctlyapply Newton s 2nd law 2

Simple example: Free-body diagram of a hanging yoyo The yoyo is just hang there, not moving In particular, it is not accelerating What forces act on the yoyo? T Upward force: Tension -- Comes from the string! w Weight; the force of gravity -- Comes from the earth! That s it! 3

Having the correct free-body diagram makes it easy to apply Newton s 2nd law y = = F F ma ma ma = a = Project onto the chosen coordinate system net T net T w here, 0,so w = T w 4

Having the correct free-body diagram makes it easy to apply Newton s 2nd law y = = F F ma ma ma = a = Project onto the chosen coordinate system net net T w here, 0,so = T w = 0 F net No net force, no acceleration, it s at rest. So, it just stays there! 5

Suppose the guy holding the yoyo string is in an elevator, and the elevator accelerates upwards. 0! F Does the yoyo accelerate? Yes! Therefore, net y = F ma ma = a net T w T here, 0,so = w ma + T w 6

Suppose the guy holding the yoyo string is in an elevator, and the elevator accelerates upwards. 0! F Does the yoyo accelerate? Yes! Therefore, net y = F ma ma = a net T w F here, 0,so net = w ma + T 7

Suppose the guy holding the yoyo string is in an elevator, and the elevator accelerates upwards. 0! F Does the yoyo accelerate? Yes! Therefore, net y = F ma ma = a net T w here, 0,so a = w ma + T 8

Often will see several forces acting y Here, it is useful to replace with its vector components 1F 1F 3 F x 2 F 9

Often will see several forces acting y F 1,y 3 F F x 1,x 2 F 10

One books notation (not ours) y F 1,y 1F 3 F F x 1,x 2 F 11

Forces are mysterious Where do forces come from? Ultimately, can t answer that! We can see what forces exist, and we can describe how they behave What forces exist in nature? We understand three: 1. Gravitation 2. Electromagnetism 3. Weak force 4. Strong force Maybe another: cosmological constant 12

Newtons Third Law of Motion 13

Regarding forces, Newton made the following observation: They come in pairs! They come in pairs! 14

Newtons third law of motion: Forces come in pairs! Forces come in pairs! If object A exerts a force on object B, then object B exerts a force on object A. These two forces have the same magnitude but are opposite in direction. Never forget: these two forces act on different objects! 15

Example: two people on skateboards A B Free-body diagrams: Normal force from . F F , , N B N A the ground m g m g Gravity from... B A the earth 16

Suppose they push each other A B BonA F F F AonB F , N B , N A m g m g B A = BonA F F AonB 17

Suppose they push each other The third law A B Never forget: the 3rd law pair of forces act on different objects! BonA F F F AonB F , N B , N A m g m g B A = BonA F F AonB 18

Suppose they push each other A B net A F net B F , , = net A F net B F , , 19

. m m Suppose A B Q: Which person experiences the larger net force? A A B B C Neither, the net forces have equal magnitudes. 20

. m m Suppose A B Q: Which person experiences the larger net force? A A B B C Neither, the net forces have equal magnitudes. 21

. m m Suppose A B Q: Which person experiences the larger acceleration? A A B B C Neither, both accelerations have equal magnitudes. 22

. m m Suppose A B Q: Which person experiences the larger acceleration? A A B B C Neither, both accelerations have equal magnitudes. 23

To answer use the 2nd law! net A F m net B F m = = , , a a = F ma A B net A B F = net m a a a A B 24

Another example: consider an apple on a table Free-body diagrams Apple EonA grav F , Table AonE grav F , Earth 25

Another example: consider an apple on a table Free-body diagrams T onA contact F , Apple Table AonT contact F , Earth 26

Another example: consider an apple on a table Free-body diagrams Apple Table EonT grav F , T onE grav F , Earth 27

Another example: consider an apple on a table Free-body diagrams Apple EonT contact F , Table Earth T onE contact F , 28

Another example: consider an apple on a table Free-body diagrams Apple T onA grav F , AonT grav F , Table Earth 29

Another example: consider an apple on a table Free-body diagrams Summary: 5 pairs of forces T onA contact F , Apple T onA grav F EonA grav F , , AonT grav F EonT contact F , , Table AonT contact F EonT grav F , , AonE grav F T onE grav F , , Earth T onE contact F , 30

Free-body diagrams Third law: links forces that act on different objects T onA contact F , Apple T onA grav F EonA grav F , , AonT grav F EonT contact F , , Table AonT contact F EonT grav F , , Second law: use a FBD of only one object! AonE grav F T onE grav F , , Earth T onE contact F = F ma , net 31

Newtons Laws of Motion Concept Questions 32

You are a passenger in a car and are not wearing the seatbelt. Without increasing or decreasing its speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door. Which is the correct analysis of the situation? A. Before and after the collision, there is a rightward force pushing you into the door. B. Starting at the time of the collision, the door exerts a leftward force on you. C. Both of the above. D. None of the above. 33

You are a passenger in a car and are not wearing the seatbelt. Without increasing or decreasing its speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door. Which is the correct analysis of the situation? A. Before and after the collision, there is a rightward force pushing you into the door. B. Starting at the time of the collision, the door exerts a leftward force on you. C. Both of the above. D. None of the above. 34

OUCH! OUCH! 35

Consider a car at rest. We can conclude that the downward gravitational pull of Earth on the car and the upward contact force on it are equal and opposite because A. The two forces form an interaction pair. B. The net force on the car is zero. C. Neither of the above 36

Consider a car at rest. We can conclude that the downward gravitational pull of Earth on the car and the upward contact force on it are equal and opposite because A. The two forces form an interaction pair. B. The net force on the car is zero. C. Neither of the above. 37

= F ma F net N = 0 F net = F mg mg N 38

A horse is hitched to a wagon. Which statement is correct? A. The force that the horse exerts on the wagon is greater than the force that the wagon exerts on the horse. B. The force that the horse exerts on the wagon is less than the force that the wagon exerts on the horse. C. The force that the horse exerts on the wagon is just as strong as the force that the wagon exerts on the horse. D. The answer depends on the acceleration of the horse and wagon. 39

A horse is hitched to a wagon. Which statement is correct? A. The force that the horse exerts on the wagon is greater than the force that the wagon exerts on the horse. B. The force that the horse exerts on the wagon is less than the force that the wagon exerts on the horse. C. The force that the horse exerts on the wagon is just as strong as the force that the wagon exerts on the horse. D. The answer depends on the acceleration of the horse and wagon. 40

Q4.1 Motor An elevator is being lifted at a constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft. Cable v The upward force exerted on the elevator by the cable is Elevator A. greater than the downward force of gravity. B. equal to the force of gravity. C. less than the force of gravity. D. any of the above, depending on the speed of the elevator. 41

Q4.1 Motor An elevator is being lifted at a constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft. Cable v The upward force exerted on the elevator by the cable is Elevator y A. greater than the downward force of gravity. T B. equal to the force of gravity. C. less than the force of gravity. D. any of the above, depending on the speed of the elevator. w 42

Q4.1 Motor An elevator is being lifted at a constant speed by a steel cable attached to an electric motor. There is no air resistance, nor is there any friction between the elevator and the walls of the elevator shaft. Cable v The upward force exerted on the elevator by the cable is Elevator y A. greater than the downward force of gravity. T B. equal to the force of gravity. C. less than the force of gravity. D. any of the above, depending on the speed of the elevator. w = = = 0 T w F ma 0 F net net = T w 43

Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is A. larger than B. identical to C. smaller than the downward weight of the person. 44

Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is y y A. larger than B. identical to C. smaller than F N the downward weight of the person. w 45

Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is y y A. larger than B. identical to C. smaller than F N the downward weight of the person. w = F ma 0 F net net 46

Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is y A. larger than B. identical to C. smaller than F net the downward weight of the person. = F ma 0 F net net 47

Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is y y A. larger than B. identical to C. smaller than F N the downward weight of the person. w = F ma 0 F w 0 F net N net F w N 48

Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is y y A. larger than B. identical to C. smaller than F N the downward weight of the person. w = F ma 0 F w 0 F net N net F w N 49

A ball sits at rest on a horizontal tabletop. The gravitational force on the ball (its weight) is one half of an action reaction pair. Which force is the other half? A. the force of the earth s gravity on the ball B. the upward force that the tabletop exerts on the ball C. the upward force that the ball exerts on earth D. the downward force that the ball exerts on the tabletop 50