Newton s First Law Any object remains at constant velocity unless acted upon by a net force. AND In order for an object to accelerate, there must be a net force acting on it. Constant velocity could mean at rest but doesn t necessarily! Force is a vector Net force means adding the vectors (vector components in each direction) Object A is at rest, Object B is moving at constant velocity, which is true: A. There are more forces acting on B than A B. There are more forces acting on A than B C. There are an equal number of forces acting on both D. There are no forces acting on either E. None of the above An object has two forces that do not change magnitude acting on it, which is true: A. The object must be at rest. B. The object must be accelerating. C. The object must be moving at a constant velocity. D. The object might be at rest, accelerating or moving at a constant speed. There is not enough information to tell. How does an object respond to a net force? It depends on the magnitude of the net force Also, it depends on the object itself: all objects resist acceleration (change in velocity), this tendency is called inertia Numerical measure of an object s inertia is its Mass, m (SI units: kg) Mass is not Weight!!! You can be weightless in outer space, but still have the same mass as on Earth Mass is simply a property of an object, always Total mass in the universe does not appear to change: Conservation of Mass law Newton s Second Law If an object has mass, then in order for it to undergo an acceleration there must be a net vector force on it equal to the product of the mass times the acceleration Notice the SI units of Force: kg m/s 2 =N lbs is also a measure of force, but not the SI units Try this: (example 4-4) The net force acting on a student weighing 130 lbs has a magnitude of 25.0 lbs. What is the magnitude of her acceleration? (1 lb = 4.448 N) 1
When an object experiences a non-zero net force, A. The magnitude of its acceleration is equal to its mass B. The vector components of its acceleration are in the same direction as the vector components of the force C. It may have zero acceleration D. It will always have non-zero velocity E. All of the above Physics is a mix of concepts! For example, kinematics and Newton s second law. A 5 kg object starts from rest. A force, F, is acted on the object until the object has moved 4.5 meters, at which point its velocity is 6.0 m/s. What is F? A. 2 N B. 5 N C. 10 N D. 20 N E. None of the above A small boat pushes on a big boat (more massive), the boats move apart but the small boat moves more, which received the greater pushing force? A. The small boat did B. The big boat did C. Both boats received the same pushing force D. Neither received any pushing force Newton s Third Law When two objects interact, the force exerted by object B on object A is equal and opposite to the force exerted by object A on B. Can there be forces without motion? 2
During a football game, a defensive linebacker collides head on with the quarterback (quarterback is less massive than linebacker). During the collision, A. The linebacker exerts a greater amount of force on the quarterback than the quarterback on the linebacker. B. The quarterback exerts a greater amount of force on the linebacker than the linebacker on the quarterback. C. Neither exerts a force on the other, though there may be some injuries. D. The linebacker exerts a force on the quarterback but the quarterback does not exert a force on the linebacker. E. The linebacker exerts the same amount of force on the quarterback as the quarterback exerts on the linebacker. You push a snow sled with a child on it on flat snow-covered ground. As you increase your pushing speed, A. Neither you nor the sled exert a force on the other because you are both in motion. B. The amount of force you exert on the sled is the same as the amount of force the sled exerts on you. C. The amount of force you exert on the sled is greater than the amount of force the sled exerts on you. D. The amount of force you exert on the sled is less than the amount of force the sled exerts on you. E. You are the one burning calories, so you exert a force on the sled but the sled doesn t exert a force on you. Types of simple forces Pushing Pulling (tension) Normal force perpendicular to surface Example: your hand exerts a normal force on your pen to keep it from falling Weight (gravitational force), the one common force that doesn t require contact Applying Newton s Laws, mainly the second law Net force on an object will give the object s acceleration Equilibrium (zero acceleration): If an object is at rest or moving with constant velocity, its acceleration is zero, the net force is zero, and the sum of the force components are all zero. Static Equilibrium: special case of equilibrium: zero velocity. Just like in 2-D motion kinematics, Separate forces into directions! Drawing Free Body Diagrams (F.B.D.) 1. Every object of interest in a problem gets its own FBD 2. Draw an arrow for every force acting on ( felt by ) that object 3. All arrows must be adjusted to point away from the object 4. Specify positive x and y direction in diagram 5. Use the FBD to analyze the x and y components of each force (you will need trigonometry!) 6. Apply Newton s Second Law to EACH direction SEPARATELY Examples to follow Example 4-6 A dog pulls the dogsled with a force of 150N at 25 above the horizontal. The mass of the sled-passenger-rope particle is 80kg and there is negligible friction between the sled runners and the ice. Find (a) the acceleration of the sled and (b) the magnitude of the normal force exerted by the surface on the sled. 3
Example 4-8 A picture weighing 8.0N is supported by two wires with tensions T 1 and T 2. Find each tension. Example 4-10 Suppose that your mass is m, and you are standing on a scale fastened to the floor of an elevator. The scale measures force in Newtons. What does the scale read when (a) the elevator is rising with upward acceleration of magnitude a. (to help you practice not plugging in numbers yet), (b) the elevator is accelerating downward with magnitude a'. (c) What does the scale read when your mass is 80 kg and the elevator accelerates downward at 8.0m/s 2 Another contact force: Friction When an object is sliding along a surface, there is a certain amount of drag force that resists the motion. The direction of the frictional force always opposes the object s motion. In a free body diagram, the frictional force vector should be drawn opposite the motion direction Friction example problem with a ramp A 5.0 kg block is sliding down an inclined plane that is at an angle of 45 degrees with the horizontal. While the block is moving, the plane provides a frictional force of 10 N. What is the block s acceleration in the direction of motion? Force exerted by a spring When a spring is stretched or compressed from its unstressed length, it exerts a force on an object in contact with it k is the force constant or spring constant, a measure of the spring s stiffness Practice Problem 4-3 A 4.0 kg bunch of bananas is suspended from a spring balance whose force constant is 300 N/m. By how much is the spring stretched? 4
Solving two body problems with Newton s Second Law You get multiple equations from the x and y directions, these equations can be solved simultaneously to find unknowns Draw a separate free body diagram for each object Apply Newton s second law to each object for both directions (x and y) Solve the resultant equations for the unknown quantities Example 4-13 In outer space, an astronaut pushes on a box of mass m 1, with force F A1. The box is in direct contact with a second box of mass m 2. a) What is the acceleration of the two boxes? b) What is the magnitude of the force each box exerts on the other? Example 4-9 As your jet plane speeds down the runway on takeoff, you decide to determine its acceleration, so you take out your yo-yo and note that when you suspend it, the string makes an angle of 22.0 with the vertical. (a) What is the acceleration of the plane? (b) If the mass of the yo-yo is 40.0g, what is the tension in the string? 5