PHYSICS 149: Lecture 5 Chapter.5 Newton s Third Law.6 Gravitational Forces.7 Contact Forces: Normal Force and Friction 1
Newton s Third Law All forces come in pairs Third law forces involve TWO OBJECTS. The two forces are: the force object one exerts on object two the force object two exerts on object one Three ways to state t the 3rd law: Forces on each other are equal and opposite For every action there is an equal and opposite reaction You can t push on something without it pushing back on you
Newton s Third Law of Motion In an interaction between two objects, each object exerts a force on the other. These two forces are equal in magnitude and opposite in direction. To every action, there is always opposed an equal reaction. Forces always come in equal but opposite actionreaction pair. Note that these two forces act on different objects; they do not cancel in any way. Don t forget that forces always exist in pairs. 3
Free Body Diagram (FBD) A simplified sketch of a single object with force vectors drawn to represent every force acting on that object. (It must not include any forces that act on other objects.) FBD is useful to find the net force acting on an object. 4
Internal and External Forces Internal Forces: Forces which act on one part of an object by another part of the same object External Forces: Forces which act on an object by some other object. Net force on a system = vector sum of internal forces + vector sum of external forces But, vector sum of internal forces is zero because, from Newton s third law, internal forces will occur in equal and opposite pairs and so they contribute nothing to the sum. They never influence the system s motion. Eventually, net force on a system = vector sum of external forces only. We need to consider external forces only in order to describe the motion of the system. 5
Examples Net force on a baseball = interaction with the Earth (gravity) + interaction with a bat + interaction ti with the air + interactions among protons, neutrons, and electrons in it External forces: what we need to consider Internal Forces: their vector sum is zero I am hit by myself (internal forces) and other person (external forces). I am pushed due to external forces only. Internal forces do not make any contribution. 6
Pushing a Stalled Car Two people are pushing a stalled car. The mass of the car is 000kg. One person applied a force of 300 N, the other 400N. Friction opposes this motion with a force of 600N. What is the acceleration of the car: F c,man1 F c,man y F cg =f x ΣF = + 600N 300N 400N ΣF = 100N a = ΣF m 100N m = = 0.0505 000kg s 7
A FBD for Every Situation A skydiver is descending di with a constant velocity. eocty A force is applied to the right to drag a sled across loosely-packed l snow with a rightward acceleration. A car is coasting to the right and slowing down A football is moving upwards towards its peak after having been booted by the punter. 8
ILQ 1 When a car accelerates from rest, what force causes the acceleration of the car? A) The rotating engine on the drive shaft B) The force of the axel on the tires C) The friction force of the road on the tires 9
ILQ A person is standing on a bathroom scale. Which of these is not a force exerted on the scale? A) a contact force due to the feet of the person B) the weight of the person C) a contact force due to the floor D) the weight of the scale 10
Newton s Law of Universal Gravitation F 1 F 1 m 1 m r The magnitude of gravitational force is: (= F 1 = F 1 ) where G = 6.674 10-11 Nm /kg (universal gravitational constant) Note: m 1 and m need to be in kg, and r needs to be in m. The direction of gravitational ti force is: each object is pulled toward the other s center (attractive force) on line connecting the masses; always attractive very weak, but this holds the universe together! 11
Comparison with EM Force F q,1 F 1, r r 1 F 1, = force on q 1 due to q = kq 1 q = F,1 = force on q due to q 1 Direction: on line connecting the masses; can be attractive or repulsive k = universal constant = 8.99 x 10 9 N-m /c e e q 1 r 1 Fgravity ( electrons) Gm = =.4 10 E ( electrons) kq electric q = 1.6 10 C m = 9.11 10 Kg e 9 31 e 1 43
Weight Weight is the force of gravity on an object with mass Units of weight are Newtons or Pounds Same mass but Different weight! mm planet F = G r r On earth W=mg where g=9.8 m/s 13
Weight on Earth Your weight on Earth is the magnitude of Earth s gravitational force exerted on you (m). W GM R m GM = m R E E = where R is the distance between you and Earth s center The weight of an object of mass m near Earth s surface is: where (g is called the gravitational field strength) 14
Weight on Other Planets The weight of an object of mass m near a planet s surfaceis: GM m GM W at Planet = = m = R GM Planet where g Planet = R mg Planet Planet Planet Planet R Planet Planet For example, g Moon = 1.6 N/kg 1/6 g Earth. Let s say there is a man whose mass is 100 kg. At the surface of Earth, his mass and weight are 100 kg and 980 N (=m g Earth ), respectively. At the surface of Moon, his mass and weight are 100 kg and 16 N (=m g Moon ), respectively. 15
Weight on Earth and on Moon How far above the surface of the Earth does an object have to be to have the same weight as it would have on the surface of the moon? Neglect effects from the Earth s gravity on the Moon s surface and vice versa r = M E M M F E = Gm = Gm = r r M r E M M M 4 5.97 10 Kg r = ( 1.74 10 3 km) = 1.57 10 4 km 7.35 10 Kg 4 3 3 Heightoversurface r-r = 1.57 10 km 6.371 10 km = 9.3 10 km E M F M 16
Things are different on the Moon Earth Moon Surface gravity 1 0.17 compared to Earth Your mass 40 Kg 40 Kg Energy to stop a 1 Kg 65 Joules 65 Joules ball moving at 90 km/hour How much can you lift 10 kg 60 kg How high can you jump 0 cm 10 cm How far can you kick a ball 0 m 10 m 17
Force of Gravity For objects on the surface of the earth: F = GMm/R = m(gm/r ) = mg g = GM/R = 9.8 N/kg = 9.8 m/s What about at the top of Mount Everest? (h=8850m or 9,035 feet GMEm The approximation works well since: F= W = r WEverest 1 heverest = r = 1 W + = surface r h r + ( ) ( ) Everest h 3 1 Everest = 1.76 10 = 1 0.0078 = 0.997 r h Everest 3 8.850 10 = = 1.389 10 6 6.371 10 18 r 3
r r 1 Your weight decreases as your altitude goes up. 19
Weight The weight (W) of an object is equal to the magnitude of the gravitational force acting on a body of mass m W = mg Dropping an object causes it to accelerate at free-fall acceleration g F g = mg W = F g 0
ILQ: Gravitation Does a man weigh more A) at the top of Mt. Everest or B) at the base of the mountain? 1
Which Forces Enter in a FBD? Several force must be taken into account: Gravity Normal Force Friction Push or Pull Tension W Gravity: if the sled has a mass m the force due to gravity is W = mg
Which Forces Enter in a FBD? Normal force: always perpendicular the surface with which h a body is in contact. Friction: the frictional force is parallel to the surface and it always opposes the direction of motion. Push or pull N f N W P W 3
Normal (= Perpendicular) Force The normal force is a contact force perpendicular to the contact surfaces that prevents two objects from passing through one another. Normal force is a vector. Direction: always perpendicular to the contact surface (rather than the horizon) Magnitude: depends on the weight of the object (see different cases on next pages) Type: contact force (not long-range force) Normal force is usually denoted by N. 4
What Causes Normal Force? Atoms inside solid objects are inter-connected by molecular bonds which act like springs. When you place an object on top of a table, the table deforms slightly. This bend is usually not visible to the eye. 5
Normal Force: Case 1 If the table s surface (contact surface) is horizontal, Direction of the normal force is perpendicular to the contact surface. In this case, vertically upward. Magnitude of the normal force is the book s weight, according to Newton s First Law of Motion. N = W (= mg) according to ΣF y = 0 for an object in equilibrium 6
Normal Force: Case If the contact surface is horizontal and there is another vertical force acting on the book, Direction of the normal force is perpendicular to the contact surface. In this case, vertically upward. Magnitude of the normal force is the book s weight plus the magnitude of the additional force, according to Newton s First Law of Motion. N = W (= mg) + F according to ΣF y = 0 for an object in equilibrium 7
Normal Force: Case 3 If the contact surface is not horizontal (with an inclination angle θ), Direction of the normal force is perpendicular to the contact surface. In this case, it is not vertical. Magnitude of the normal force is the book s weight times cosθ, +y according to Newton s First Law of Motion. θ N = W cosθ (= mg cosθ) +x according to ΣF y = 0 for an object in equilibrium Wsinθ θ Wcosθ 8