2 Dynamics: Newton’s Laws of Motion Chapter 4Dynamics: Newton’s Laws of Motion
3 4-1 ForceA force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity.The magnitude of a force can be measured using a spring scale.
4 4-2 Newton’s First Law of Motion Newton’s first law is often called the law of inertia.Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.
5 4-2 Newton’s First Law of Motion Inertial reference frames:An inertial reference frame is one in which Newton’s first law is valid.This excludes rotating and accelerating frames.An example is a cup resting on the dashboard of a car. It will stay at rest as long as the car’s velocity remained constant. If the car is accelerating, the cup may begin to move toward you, even though no force was exerted on it in that direction. This is an accelerating reference frame and Newton’s 1st law does not hold.
6 4-3 MassMass is the measure of inertia of an object. In the SI system, mass is measured in kilograms.Mass is not weight:Mass is a property of an object. Weight is the force exerted on that object by gravity.If you go to the moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass, however, will be the same.
7 4-4 Newton’s Second Law of Motion Newton’s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass.(on formula sheet)
8 4-4 Newton’s Second Law of Motion Force is a vector, so is true along each coordinate axis.The unit of force in the SI system is the newton (N).Note that the pound is a unit of force, not of mass, and can therefore be equated to newtons but not to kilograms.
9 4-4 Newton’s Second Law of Motion What average net force is required to bring a 1500 kg car to rest from a speed of100 km/h within a distance of 55 m?
10 4-5 Newton’s Third Law of Motion Any time a force is exerted on an object, that force is caused by another object.Newton’s third law:Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first.
11 4-5 Newton’s Third Law of Motion A key to the correct application of the third law is that the action and reaction forces are exerted on different objects. Make sure you don’t use them as if they were acting on the same object.
12 4-5 Newton’s Third Law of Motion Rocket propulsion can also be explained using Newton’s third law: hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket.Note that the rocket does not need anything, such as air, to “push” against. If it did rockets would not operate in space.
13 4-5 Newton’s Third Law of Motion What exerts the force on a car?What makes a car go forward?
14 4-5 Newton’s Third Law of Motion Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source.This need not be done indefinitely, but is a good idea until you get used to dealing with these forces.(4-2)
15 4-5 Newton’s Third Law of Motion We tend to associate forces with active objects such as humans, engines, or a moving object like a hammer. However, inanimate objects at rest can exert a force due to elasticity.A force influences the motion of an object only when it is applied on that object.A force exerted by an object does not influence that same object. It only influences the other object on which it is exerted.
16 How can this sled move if the forces are all balanced? Example 4-5, showing only horizontal forces. Seventy-year-old Michelangelo has selected a fine block of marble for his next sculpture. Shown here is his assistant pulling it on a sled away from the quarry. Forces on the assistant are shown as red (magenta) arrows. Forces on the sled are purple arrows. Forces acting on the ground are orange arrows. Action-reaction forces that are equal and opposite are labeled by the same subscripts but reversed (such as FGA and FAG) and are of different colors because they act on different objects.
17 To determine if the assistant moves or not, we must consider only the forces on the assistant.
18 A massive truck collides head-on with a small sports car. Which vehicle experiences the greater force of impact?Which experiences the greater acceleration?Which of Newton’s laws is useful to obtain the correct answer?
19 4-6 Weight – the Force of Gravity; and the Normal Force Weight is the force exerted on an object by gravity. Close to the surface of the Earth, where the gravitational force is nearly constant, the weight is:What do the bold letters mean?On Earth a mass of 1.0 kg weighs about 2.2 lb
20 4-6 Weight – the Force of Gravity; and the Normal Force An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there?The force exerted perpendicular to a surface iscalled the normal force. It is exactly as large as needed to balance the force from the object (if the required force gets too big, something breaks!)
21 4-6 Weight – the Force of Gravity; and the Normal Force Weight and Normal Force are NOTaction-reaction pairs.What is the reaction force to Weight and the Normal Force?
22 (a) A box of mass 10.0 kg is resting on the frictionless surface of a table. Determine the weight of the box and the normal force on it.(b) Now you push down on the box with a force of 40.0 N. What is the normal force on the box?(c) Then you pull up on the box with a force of 40.0 N. What is the normal force on the box?Example 4-6. (a) A 10-kg gift box is at rest on a table. (b) A person pushes down on the box with a force of 40.0N. (c) A person pulls upward on the box with a force of 40.0N. The forces are all assumed to act along a line; they are shown slightly displaced in order to be distinguishable. Only forces acting on the box are shown.
23 The normal force is elastic in origin The normal force is elastic in origin. The table sags slightly under the weight of the box.What happens if the table can not exert a force equal to the normal force?Does the normal force always have to be vertical?
24 What happens when you pull up on the box with a force of 100.0 N?
25 A 65 kg woman descends in an elevator that briefly accelerates at 0 A 65 kg woman descends in an elevator that briefly accelerates at 0.20g downward when leaving a floor.During this acceleration, what is her weight and what does the scale read?What does the scale read when the elevator descends at a constant speed of 2.0 m/s?
26 Vector Sum of Forces Equilibrant (a) Two forces, FA and FB, exerted by workers A and B, act on a crate. (b) The sum, or resultant, of FA and FB is FR.EquilibrantWhat is the resultant?
28 Which is the correct Free-Body Diagram for a hockey puck sliding across frictionless ice?
29 What is the acceleration of the box and the normal force of the box? Free Body Diagram(a) Pulling the box, Example 4-11; (b) is the free-body diagram for the box, and (c) is the free-body diagram considering all the forces to act at a point (translational motion only, which is what we have here).
30 4-7 Solving Problems with Newton’s Laws – Free-Body Diagrams When a cord or rope pulls on an object, it is said to be under tension, and the force it exerts is called a tension force.Find the acceleration of each box and the tension in the cord connecting the boxes.
31 Atwood’s Machine Calculate the acceleration of the elevator and the tension in the cable. Example (a) Atwood's machine in the form of an elevator-counterweight system. (b) and (c) Free-body diagrams for the two objects.
32 A mover is trying to lift a piano up to a second story apartment A mover is trying to lift a piano up to a second story apartment. He is using a rope looped over two pulleys as shown. What force must he exert on the rope to slowly lift the piano’s 2000 N weight?
33 The car is stuck in the mud The car is stuck in the mud. The driver ties a strong rope to the car bumper and the other end to a boulder as shown. The driver pushes at the midpoint of the rope with a force of 300 N. The car just begins to budge with the rope at an angle of 5 degrees. With what force is the rope pulling on the car?Example (a) Getting a car out of the mud, showing the forces on the boulder, on the car, and exerted by the person. (b) The free-body diagram: forces on a small segment of rope.
34 4-8 Applications Involving Friction, Inclines On a microscopic scale, most surfaces are rough. The exact details are not yet known, but the force can be modeled in a simple way.For kinetic – sliding – friction, we write:is the coefficient of kinetic friction, and is different for every pair of surfaces.
36 4-8 Applications Involving Friction, Inclines Static friction is the frictional force between two surfaces that are not moving along each other. Static friction keeps objects on inclines from sliding, and keeps objects from moving when a force is first applied.
37 4-8 Applications Involving Friction, Inclines The static frictional force increases as the applied force increases, until it reaches its maximum. Then the object starts to move, and the kinetic frictional force takes over.
38 4-8 Applications Involving Friction, Inclines Our 10.0 kg box rests on a horizontal floor. The coefficient of static friction is 0.40 and the coefficient of kinetic friction is Determine the force of friction acting on the box if a horizontal applied force is exerted on it of magnitude:a) b) 10 N c) 20 N d) 38 N e) 40 N
39 How does pushing horizontally keep the box from moving vertically?
40 Which requires less force, pushing or pulling? (assume the angles are equal)
41 Calculate the acceleration. 40.0 N 10.0 Kgμk = 0.30When an object is pulled by an applied force (FA) along a surface, the force of friction Ffr opposes the motion. The magnitude of Ffr is proportional to the magnitude of the normal force (FN).If Ff were greater than FPX, what would you conclude?
43 4-8 Applications Involving Friction, Inclines An object sliding down an incline has three forces acting on it: the normal force, gravity, and the frictional force.The normal force is always perpendicular to the surface.The friction force is parallel to it.The gravitational force points down.If the object is at rest, the forces are the same except that we use the static frictional force, and the sum of the forces is zero.
44 A skier has just begun descending the 30° slope A skier has just begun descending the 30° slope. Assuming the coefficient of friction is 0.10, calculate her acceleration and her speed after 4.0 s.Notice + and – on coordinate axes.Example A skier descending a slope; FG = mg is the force of gravity (weight) on the skier.
45 Suppose in the previous example that the snow is slushy and the skier moves downthe 30˚ slope at constant speed. What canyou say about the coefficient of kineticfriction?