Summary for last week: Newton s 2 nd Law + 1 st Law

Transcription

1 ! F resultant = Summary for last week: Newton s 2 nd Law + 1 st Law F! " i = F! 1 + F! F! N = m! all forces acting on object due to other objects a Object if we measure acceleration in an inertial coordinate system

2 Newton s Third Law If object A exerts a force F AonB on object B, there is an equal and opposite force F BonA = - F AonB that B exerts on A. Both forces have exactly same magnitude, regardless of motion (acceleration) of either object. The two forces act on different bodies and in opposite direction. They are called a Action-Reaction Pair. => F Action = - F Reaction

3 Examples I Gravitational downwards Force - mg on object of mass m <=> equally strong upwards Force + mg on Earth Person pulling with force F on object <=> object pulls with force -F on person Person pushing object forward <=> object pushes back on person with equal force Weight of object - mg pushing down on support <=> support pushing object up with normal force + mg. Rocket pushing out gas - gas pushing rocket forward.

4 Examples II: Tension Rope, Chain etc.: Imagine cut at some point upper half exerts force on lower half lower half exerts force on upper half Equal : Action-Reaction Pair F U = -F L => Tension T = F U = F L at that point Force acting at end point = Tension at that point T 1 mg T 2

5 Important Points: For Newton s Second Law, use only forces acting on object to calculate ΣF = m a, not reaction forces on other objects. No object can exert a net force on itself (Münchhausen trick): Force of one part on another exactly balanced by Reaction Force => total sum = zero. Nothing can experience a force without exerting a force HOWEVER: Effect of (reaction) force on one object may be a lot smaller than the effect of the (equal-sized) action force on the other object (cannon recoil ) Action+Reaction pair = INTERACTION (most fundamental; all forces are due to interactions)

6 How can we tell that a force is acting (and how strong it is)? Operational definition based on Newton s Second Law. By looking at its effects: the object (mass point) is accelerating a solid is stretched or bent (spring [balance], rope, ) From our knowledge of Force Laws: an object of mass m will experience a force F y = - mg pointing downwards on the surface of Earth A rope which is pulled with force of strength F at one end will exert force of same strength at its other end (in the direction of the rope) if it doesn t accelerate and its weight is negligible (Newton s 3rd Law). General gravitational force law (later in semester), electromagnetism (even later in semester)

7 Web of Forces and Masses Use Newton s 2 nd and 3 rd law to create relationships between known forces and masses and unknown ones: Masses: Standard in Paris Force Laws: Gravitation Known Forces: Springs Compare accelerations (3 rd Law, 2 nd Law) Balance forces (Superposition) New Forces Measure a, m (2 nd Law) Balance with known force (spring, pulley + weight, ) Observe reaction (3 rd Law) Develop Force Law, apply to new situations Unknown mass

8 Scalars and vectors Scalars are observables which can be expressed with a simple number (and appropriate units). Examples: Time, mass, temperature,... a Vectors are observables which have both a magnitude (a number with units) and a direction. Examples: Displacement, velocity, force, acceleration It is very important to distinguish these! two entities: use different notation (A for scalar, A or A for vector), and clearly indicate size and direction for a vector result.

9 Example: Displacement Size: actual distance from Point A to Point B (don t forget units) Direction: Describe which way to go. Note: Vectors which have different sizes, different units, or different directions are different. BUT: starting point does not matter:

10 Specifying a vector 1.) By giving its length (size, magnitude, absolute value - with units) and its direction. Examples: 1100 m exactly northeast from here or 0.17 m at an angle of 45 o above the x-axis, in the x-y plane. 2.) You can represent vectors by drawing arrows. The length of the arrow represents the size of the vector (e.g., 2 cm represent 2 N) and the direction of the arrow is in the direction of the vector.

11 Vectors can be added to (or subtracted from) each other. 1.) Geometrically: See examples. Use either tail to head method or parallelogram method 2.) Mathematically (a bit too advanced for our purpose)

12 Example: Equilibrium - car at rest Equilibrium: All forces acting on an object add up to zero (vectorially). The object will either be (stay) at rest or will move with constant velocity. Example: Car sitting still on an inclined plane (or moving down with constant velocity) F Friction F Normal x y F Weight α

13 Example: Car accelerating down ramp Net force: All forces acting on an object add up to a net force along the ramp (vectorially). The object will accelerate down the ramp. F Friction F Normal x y F Weight α

14 Equilibrium - Sailboat Wind Force Drag Normal Force on Keel