5: Newton's Laws of Motion

Transcription

1 5: Newton's Laws of Motion The First Law of Motion (The Law of Inertia) An object at rest will remain at rest and an object in motion will remain in motion (at constant velocity) unless acted upon by an external force. An object has a constant velocity unless there is a net force acting on it. Forces are the causes of changes in motion. forces on an object arise from interactions with other objects. forces are vectors the net force on an object is the vector sum of the individual forces acting on that object The inertia of an object is its resistance to changes in its motion. Mass is a measure of inertia. If the net force on an object then it's velocity is constant (and visa versa) Inertial Frame of Reference: a frame of reference in which Newton s Law of Inertia holds constant velocity! counter examples: not an accelerating aircraft or a rotating merry go round p250c5:1

2 The Second Law of Motion: how motion changes The rate of change of velocity with time is proportional to the net applied force and is in the same direction as the net force a= F m or F =m a Force causes acceleration! Mass is the measure of inertia Units: 1 Newton = 1N = 1 kg m/s 2 1N ~ 1/4 pound p250c5:2

3 Problem Solving Strategies Draw a free body diagram all forces on each object are shown Choose the object to be isolated. Draw it and any geometric aspects are important. Keep it simple! Draw all forces on that object as vector arrows, approximately to scale and in the correct direction. Label all forces clearly! Choose a coordinate system and indicate it on the diagram. Shown the positive direction of displacement, velocity, acceleration, etc. Resolve vectors into components as necessary. Apply Newton's Second Law to each coordinate direction repeat for each object in the problem. p250c5:3

4 Example: Moe, Larry and Curly push on a 752 kg boat that floats next to a dock. They each exert an 80.5 N force parallel to the deck. a) What is the acceleration of the boat if they all push in the same direction? b) What is the magnitude and direction of the boat's acceleration if Larry and Curly push in the opposite direction to Moe's push? Example: Foamcrete is used to decelerate aircraft that run past the end of a runway. If a 1.75E5 kg Boeing 747 with an initial speed of 26.8 m/s is slowed to a stop in 122 m, what is the retarding force on the aircraft? p250c5:4

5 Example: A pitcher throws a 0.15 kg baseball, accelerating it from rest to a speed of about 90 mph. Estimate the average force the pitcher exerts on the ball. p250c5:5

6 Newton s Third Law For every action there is an equal and opposite reaction For every action (force) there is a reactive force and the action and reaction forces are equal in magnitude and opposite in direction, and act upon different bodies. Often action/reaction occurs through contact forces. eg. two boats pushing off from each other or, carts kicking off from each other (demo) If body A exerts a force F AB on body B, then B exerts a force F BA on A so that F AB = - F BA p250c5:6

7 Example: A box of mass m 1 = 10.0 kg rests on a smooth frictionless box of mass m 2 = 5.00 kg. If a force of 20.0 N is applied to box 1 to accelerate both boxes, determine the acceleration of the boxes and the magnitude of the contact force between the boxes. Repeat the problem for the case where the order of the boxes is reversed. p250c5:7

8 Forces as Vectors Net force (add as vectors) on an object produces acceleration. Take components Add components F x = ma x etc. Example: Jack and Jill lift upward on a 1.3 kg pail of water. Jill exerts 11.0 N at an angle of 28 with respect to the vertical. Jack exerts a 7.00 N force. At what angle should Jack exert his force so that the pail will accelerate straight upward? p250c5:8

9 Example: A 4.60 kg sled is pulled across a smooth ice surface. The force is 6.20 N in magnitude and is directed at an angle of 35.0 above the horizontal. If the sled is initially at rest, how fast is it moving after 1.15s. p250c5:9

10 Weight: the force exerted by earth (via gravity) on an object In free fall, gravity is the only force acting on the object F = ma = mg = w Weight = (mass)(acceleration of gravity) usually, weight is often given as the magnitude of the force weight will depend upon local acceleration of gravity Example: As a fire alarm goes off, a 97.0 kg fireman slides down a 3.00 m pole in 1.20 s. What was the average upward force exerted by the pole on the firelman? p250c5:10

11 Apparent Weight: such as effect of elevator ride accelerating up or down. example: A 5.00 kg salmon is weighed using a spring scale in an elevator. What is the scale reading if the elevator is a) at rest? b) accelerating upward at 2.50 m/s 2? c) accelerating downward at 3.20 m/s 2? p250c5:11

12 Normal Force: the contact force exerted by the surface of a rigid object Normal Force N Normal Force N Normal Force N tension weight w weight w Normal means perpendicular Normal force prevents object from sinking into surface weight w Example: A 6 kg ice block sits on a table and is acted on by two forces, a 13.0 N force acting down and to the left at an angle of 30 below the horizontal, and an 11.0 N force acting down and to the right at an angle of 60 below the horizontal. What is the normal force of the table on the block? What is the acceleration of the block? p250c5:12

13 Example: A child of mass m slides down a toboggan on a slick hill which makes an angle q with respect to the horizontal. What is the acceleration of the child? What is the normal force exerted by the toboggan on the child? p250c5:13