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Unformatted text preview: Chapter 4
The Laws of Motion
Conceptual questions: 1,3,4,5,9,18 Quick quizzes: 1,2,4,8 Problems: 6,55,34,40,80 Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting on them Conditions when Classical Mechanics does not apply
very tiny objects (< atomic sizes) objects moving near the speed of light Contact and Field Forces Fundamental Forces Types Characteristics Strong nuclear force Electromagnetic force Weak nuclear force Gravity All field forces Listed in order of decreasing strength Only gravity and electromagnetic in mechanics Newton's First Law If no forces act on an object, it continues in its original state of motion; that is, an object at rest remains at rest and an object moving with some velocity continues with that same velocity. Inertia Is the tendency of an object to continue in its original motion Mass
A measure of the resistance of an object to changes in its motion due to a force
Scalar quantity Measure of inertia in translational motion Newton's Second Law The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F or F = ma a
m
F and a are both vectors Units of Force SI unit of force is a Newton (N) kg m 1N 1 2 s US Customary unit of force is a pound (lb) 1 N = 0.225 lb Problem 46
A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a constant pull of 7.5 x 105 N, how long does it take to increase the speed of the train from rest to 80 km/h? Solution: F = 7.5 105 N a=
m 1.5 107 kg = 5.0 102 m s 2 v=vo + at
vvi (80 km h  0km/h) 0.278 m s 1 min t= = a 5.0 102 m s 2 1 km h 60 s t=7.4 min Gravitational Force Mutual force of attraction between any two objects Expressed by Newton's Law of Universal Gravitation: m1 m2 Fg = G 2 r Gravitational constant, G=6.67 x 1011 Nm2/kg2 Weight The magnitude of the gravitational force acting on an object of mass m near the Earth's surface is called the weight w of the object w = m g g can also be found from the Law of [a special case of Newton's Second Law] Universal Gravitation More about weight Weight is not an inherent property of an object mass is an inherent property Weight depends upon location of an object You are talking by interplanetary telephone to a friend who lives on the Moon. She tells you she has just won 1 Newton of gold in a contest. Excitedly, you tell her that you entered Earth's version of the same contest and also won 1 Newton of gold? Who is richer? Quick Quiz 4.4 (a) Your friend, (b) you, (c) it's a draw. Newton's Third Law If two objects 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. F12 may be called the action force and F21 the reaction force Quick Quiz 4.1 True or false: (a) It is possible to have motion in the absence of a force. (b) If an object is not moving, no external force acts on it. Quick Quiz 4.2 True or false: (a) If a single force acts on an object, the object accelerates. (b) If an object experiences an acceleration, a force acts on it. (c) If an object experiences no acceleration, no external force acts on it. Some ActionReaction Pairs n and n' n is the normal force, the force the table exerts on the TV n is always perpendicular to the surface n' is the reaction the TV on the table n = n' More ActionReaction pairs Fg and Fg' Fg is the force the Earth exerts on the object Fg' is the force the object exerts on the earth Fg = Fg' Forces Acting on an Object Newton's Law uses the forces acting on an object n and Fg are acting on the object (in the figure it is the TV set) n' and Fg' are acting on other objects (table) Free Body Diagram Diagram must identify all the forces acting on the object of interest Choose an appropriate coordinate system If the free body diagram is incorrect, the solution will likely be incorrect Equilibrium An object either at rest or moving with a constant velocity is said to be in equilibrium The net force acting on the object is r zero F =0 F x =0 F y =0 Solving Equilibrium Problems Make a sketch of the situation described in the problem Draw a free body diagram for the isolated object under consideration and label all the forces acting on it Resolve the forces into x and y components, using a convenient coordinate system Apply equations, keeping track of signs Solve the resulting equations Problem 455
(a) What is the resultant force exerted by the two cables supporting the traffic light in Figure P4.55? (b) What is the weight of the light? Conceptual questions 1. A ball is held in a person's hand. Identify the external forces acting on the ball and the reaction on each. 4. A rubber ball is dropped onto the floor. What force causes the ball to bounce? Newton's Second Law Problems Similar to equilibrium except r r F = ma Use components F x = ma x F y = ma y ax or ay may be zero Conceptual questions 3. If a car moves with a constant acceleration, can you conclude that there are no forces acting on it? 18. A truck loaded with sand accelerates along a highway. If the driving force on the truck remains constant, what happens to the truck's acceleration if its trailer leaks sand at a constant rate through a hole in its bottom? Solving Newton's Second Law Problems Make a sketch of the situation described in the problem Draw a free body diagram for the isolated object under consideration and label all the forces acting on it Resolve the forces into x and ycomponents, using a convenient coordinate system Apply equations, keeping track of signs Solve the resulting equations If more than one object is present, draw free body diagram for each object Connected Objects Apply Newton's Laws separately to each object The acceleration of both objects will be the same The tension is the same in each diagram Solve the simultaneous equations Problem 434
Two objects with masses of 3.00 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.34. Determine (a) the tension in the string, (b) the acceleration of each object, and (c) the distance each object will move in the first second of motion if T T a Rising mass Falling mass a W1=29.4 N W2=49.0 N (T29.4) N = a (3.00 kg) (49.0T) N = a (5.00 kg) Inclined Planes Choose the coordinate system with x along the incline and y perpendicular to the incline Replace the force of gravity with its components x Forces of Friction When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion This is resistance is called the force of This is due to the interactions between the object and its environment friction More About Friction Friction is proportional to the normal force The force of static friction is generally greater than the force of kinetic friction The coefficient of friction () depends on the surfaces in contact The direction of the frictional force is opposite the direction of motion The coefficients of friction are nearly independent of the area of contact Static Friction, s Static friction acts to keep the object from moving If F increases, so does s If F decreases, so does s s n Quick Quiz 4.8 You press your physics textbook flat against a vertical wall with your hand. What is the direction of the friction force exerted by the wall on the book? (a) downward (b) upward (c) out from the wall (d) into the wall. Kinetic Friction The force of kinetic friction acts when the object is in motion k = n Problem 440 A woman at an airport is towing her 20.0kg suitcase at constant speed by pulling on a strap at an angle of above the horizontal (Fig. P4.40). She pulls on the strap with a 35.0N force, and the friction force on the suitcase is 20.0 N. Draw a freebody diagram of the suitcase. (a) What angle does the strap make with the horizontal? (b) What normal force does the ground exert on the suitcase? Solution Velocity is constant, Fnet=0
Fx = F cos  f = 0
f 20.0 N cos = = = 0.571 F 35.0 N
=55.2o Fy = n + F sin  mg = 0
n = mg  F sin = 196  35.0 sin ( 55.2) N =167 N Conceptual questions 5. If you push a heavy box that is at rest you must exert some force to start its motion. However, once the box is sliding, you can apply a smaller force to maintain that motion. 9. What force causes an automobile to move? A propeller driven airplane? A rawboat? Terminal Speed Another type of friction is air resistance Air resistance is proportional to the speed of the object When the upward force of air resistance equals the downward force of gravity, the net force on the object is zero The constant speed of the object is the terminal speed Problem 480
A fire helicopter carries a 620kg bucket of water at the end of a 20.0m long cable. When the helicopter is flying back from a fire at a constant speed of 40.0 m/s, the cable makes an angle of 40.0 with respect to the vertical. Determine the force exerted by air resistance on the bucket. y R T x W Constant velocity means that a x= 0 a y= 0 Thus: o Fx= 0 o Fy = 0 415. Find the tension in each cable supporting the 600N cat burglar in Fig. P4.15
. 449. Find the acceleration experienced by each of the two objects shown in Figure P4.49 if the coefficient of kinetic friction between the 7.00kg object and the plane is 0.250. ...
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This note was uploaded on 12/02/2008 for the course PHYS 1A taught by Professor Onuchic during the Spring '07 term at UCSD.
 Spring '07
 Onuchic
 Physics, Force

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