Lecture 7: Forces & The Laws of Motion

Questions of Yesterday A ball is thrown vertically upwards in the air by a passenger on a train moving with a constant velocity. To a stationary observer outside the train, is the velocity of the ball at the top of its trajectory a) greater than b) Less than c) Equal to the velocity observed by the passenger? 2) The hang-time of a basketball player who jumps a vertical distance of 2 ft is about 2/3 second. What will the hang-time be if the player reaches the same height while jumping 4 ft horizontally? a) less than 2/3 s b) greater than 2/3 s c) equal to 2/3 s

Forces Contact Forces Field Forces Force applied to an object without direct contact Applied over a range of space Ex. Gravitational force, Electrical force, Magnetic force Force applied to an object by direct contact A physical push or pull Ex. Stretching a spring, Hitting a baseball Tug-of-war

Newton’s First Law What happens when… you push your physics book sitting on your desk? You roll a basketball across the floor? You hit a hockey puck in an ice rink? Why? An object at rest will remain at rest unless acted on by an external force. Also, an object in motion will remain in its original state of motion unless acted on by an external force.

Newton’s First Law What happens when… you push your physics book sitting on your desk? You roll a basketball across the floor? You hit a hockey puck in an ice rink? Why? An object moves with a velocity that is constant in magnitude and direction unless acted on by a nonzero net force. Net force = sum of all external forces acting on an object

Newton’s First Law An object moves with a velocity that is constant in magnitude and direction unless acted on by a nonzero net force. Why is Newton’s first law true? What makes an object resist changing its state of motion? INERTIA tendency of an object to continue in its original state of motion

Newton’s First Law An object moves with a velocity that is constant in magnitude and direction unless acted on by a nonzero net force. Which ball do you want to have a game of toss with? Why? MASS measure of object’s resistance to changes in its motion due to an external force

Newton’s Second Law The acceleration of an object is inversely proportional to its mass The acceleration of an object is directly proportional to the net force acting on it The acceleration a of an object is directly proportional to the net force acting on it and inversely proportional to its mass

F = ma Newton’s Second Law a = F/m Fx = max Fy = may Fz = maz The acceleration a of an object is directly proportional to the net force acting on it and inversely proportional to its mass a = F/m SI Unit of force = Newton 1 N = 1 kg*m/s2 F = ma F and a are vectors! Vector equation! Fx = max Fy = may Fz = maz

greater than, less than, or equal to F1? Newton’s Second Law F = ma If an object is accelerating does that mean that there has to be a net force on it? If an object is not accelerating does that mean that no forces are acting on it? I apply a force F1 to my physics book to push it across the desk with a velocity of 10 m/s. If instead I want to push the book at a velocity of 20 m/s is the force I need to apply greater than, less than, or equal to F1?

Gravitational Force Force of attraction between any two objects in the Universe. Gravitational force causes…. Objects in free fall near the Earth’s surface to accelerate towards the Earth the moon to orbit the earth & the planets to orbit the sun An astronaut to be able to jump higher on the Moon than on Earth

Gravitational Force Fg = G m1m2 r2 Newton’s Law of Gravitational Force m1,m2= mass of objects attracting each other r = distance between the objects Universal gravitational constant = G = 6.67*10-11 N*m2/kg2

Weight Fg = G w = mg MEm RE2 Fg = m*(9.8m/s2) = mg What is the magnitude of the gravitational force acting on object with mass m near Earth’s surface? ME = 5.98*1024 RE = 6.38*106 Fg = G MEm RE2 Fg = m*(9.8m/s2) = mg Weight Magnitude of gravitational force acting on an object near Earth’s surface w = mg

Forces in nature always exist in pairs! Newton’s Third Law Forces in nature always exist in pairs! If object 1 and object 2 interact, the force F12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F21 exerted by object 2 on object 1 For every force there is an equal and opposite reaction force F12 = -F21 Action-reaction force pairs always act on different objects!

Newton’s Third Law F12 = -F21 If a Mack Truck and Honda Civic have a head-on collision, upon which vehicle is the impact force greater? Which vehicle experiences the greater acceleration?

Is there a nonzero net force on a freely falling object? Newton’s Third Law F12 = -F21 Is there a nonzero net force on a freely falling object? Why? What force(s) acts on the object during free fall? What exerts this force on the object? What is the corresponding reaction force? What does it act on?

Newton’s Third Law F12 = -F21 m2a2 = -m1a1 m0a0 = -MEaE FE0 = -F0E Why doesn’t the Earth accelerate towards us as we accelerate towards it? F12 = -F21 m2a2 = -m1a1 m0a0 = -MEaE FE0 = -F0E aE = -(m0a0 )/ME m0 << ME aE ≈ 0

Normal Force Fg N Is there a nonzero net force acting on the block? What about the gravitational force? N Fg

Normal Force Fg N Fg’ N’ Normal Force force exerted by surface on object in contact with the surface N Are N and Fg action-reaction pairs? Why? Fg N’ Fg’ Is the magnitude of N greater than, less than, or equal to Fg?

Free Body Diagrams Fg N Fg’ N’ Diagram of a single object with all the forces acting ON it N DO NOT INCLUDE: -Forces that the object exerts on other objects or the Earth -Other objects that the object is in contact with Fg N’ Fg’

Tennis ball undergoing projectile motion Free Body Diagrams Tennis ball undergoing projectile motion Fg

Free Body Diagrams FA Fg Tennis ball while a tennis player is serving it. The player swings the racket at a 30o angle with the horizontal when in contact with the ball. FA 30o Fg Is the ball accelerating? How do you know? In what direction is it accelerating?

Free Body Diagrams A block sliding down a frictionless inclined plane. q N Fg q Is the block accelerating? In what direction?

Free Body Diagrams Fg N Fgy Fgx Fgx = Fgsinq Fgy = Fgcosq A block sliding down a frictionless inclined plane. N Fgy + y + x - x - y Fg q q Fgx Fgx = Fgsinq Fgy = Fgcosq Choose coordinate system to be in direction of incline plane!

Questions of the Day You must apply a force F1 to begin pushing a crate from rest across the floor, you must apply a force F2 to keep the crate moving at a constant velocity once its in motion. Which statement is true? a) F1 = F2 b) F1 > F2 c) F1 < F2 2) When do action and reaction pairs of forces not cancel one another out? a) when one of the objects is accelerating b) when both objects are accelerating c) never