Physics 380 Physics and Society Lecture 2: Newton s Laws, Mass, Force and Motion 1
Topics for This Lecture Mass Force Motion: acceleration, speed and displacement Newton s three Laws Equations of motion One-, two- and three dimensional motion The monkey and the gun Complexity versus approximation Friction 2
Mass Mass is a measure of the quantity of matter an object contains. By definition, a mole of 12 C atoms (6.023x10 23 atoms) has a mass of 12 grams Inertial mass versus gravitational mass - they are the same to high precision 3
Force Force: an external influence that causes an acceleration - a push or a pull Forces are vectors and add as vectors F = F 1 +F 2 F 1 Mass F 2 a F 1 Mass F 2 a 4
Force in Nature There are only 4 basic forces: Gravitational force Electromagnetic force Strong force Weak force 5
Motion Force produces an acceleration (a) Acceleration changes the velocity (v) Velocity over time produces a displacement in position (x, y, z) x v 1 v 2 t 1 t 2 v 1 v 2 t Two examples of acceleration 6
Motion in One Dimension Use Δ to represent change in Acceleration changes the velocity: Δv Velocity changes position: Δx a = Δv/Δt v = Δx/Δt A car moves at a constant speed in a constant direction: a = Δv/Δt = 0 A car moves 10 m in 5 s: Average velocity: v = Δx/Δt = 10 m/5 s = 2 m/s 7
Newton s s Laws 1. An object at rest remains at rest unless acted on by a force. An object moving at a uniform velocity continues at that velocity unless acted on by a force. 2. F = ma 3. Every action produces an equal and opposite reaction 8
Motion Example a Slope = 0 v Slope = a v 0 Constant acceleration Velocity Position t x t Slope = v 9 Slope = v 0 t
Equations of Motion a = constant v = v 0 + at v 0 = constant x = x 0 + v 0 t + 1 / 2 at 2 x 0 = constant If a = 0, then velocity is constant: v = v 0 If a = 0, and v 0 = 0, then the position is constant: x = x 0 10
Problem Solving Problems in physics can be approached systematically 1. Draw a picture 2. What is being asked for? 3. What is given? 4. What else do you know? 5. Determine the method 6. Write out the steps and solve 11
Equations of Motion Example If you fall from an airplane flying at an altitude of 6 miles, how long will it take to reach the ground if there is no air resistance? What is given? x 0 = 6 miles x 1609 m/mile= 9654 m v 0 = 0 What else do you know? v = v 0 + at x = x 0 + v 0 t + 1 / 2 at 2 a = -9.8 m/s 2 acceleration due to gravity (down) 12
Equations of Motion Example (2) Method: Find time (t) when x = 0 Solve x = x 0 + v 0 t + 1 / 2 at 2 0 = 9654 m + 0 + 1 / 2 (-9.8 m/s 2 )t 2 t = (2 x 9654/9.8) t = (1970) t = 44.4 s Less than one minute! How fast will you be moving? v = v 0 + at v = 0 + (-9.8 m/s 2 )(44.4s) v = -435 m/s = -973 miles/h 13
Equations of Motion Example (3) But, what really happens is that you rapidly reach a terminal velocity of ~100 miles/h. How long does it take to reach the ground then? What else do you know? a = 0 constant velocity v 0-100 miles/h = -45 m/s Method: Find time (t) when x = 0 x = x 0 + v 0 t + 1 / 2 at 2 0 = 9654 m + (-45 m/s)t + 0 t = 214 s t = 3.6 minutes 14
Dropping Weights Time for you to perform an experiment: get up and find two objects that have different masses but that you can drop safely wherever you are, e.g., an eraser and a golf ball. Do not use something really large and light like a piece of paper you need to keep air resistance low. Stand on a chair with your arms outstretched and drop the objects at the same time from the same height. Which one hits the floor first? 15
Dropping Weights Hopefully you found that the two objects hit the floor at the same time. The reason is in the equation x = x 0 + v 0 t + 1 / 2 at 2 There is no dependence in this equation on the mass of the object. There is something fascinating about science; one gets such wholesale conjecture from such a trifling investment of fact. Mark Twain 16
Three Dimensional Motion Motion in each of the directions (x, y, z) is totally independent of one another. Instead of releasing two balls and letting them fall to the ground, drop one and throw the other one exactly sideways. When do the two balls hit the ground? 17
Three Dimensional Motion (2) The two balls hit the ground at the same time! The motion down and the motion sideways are independent of each other. It does not matter how fast you throw the ball sideways, the time to hit the ground is the same as the ball that is dropped. 18
Motion of Real Objects If you throw a ball through the air, it follows a parabolic curve. 19
Motion of Real Objects (2) If you throw a more complex object through the air, its center of mass also follows a parabolic curve. A thrown shoe will tumble at the same time it follows a parabola. Try it yourself. 20
Range Range is the distance that a thrown object reaches. The range of a thrown object depends on the angle at which it is thrown. Objects thrown at 45 have the largest range. 60 45 30 21
Monkey and the Gun Watch the video clip on the monkey and the gun. A monkey hanging from a tree sees the flash of a hunters gun and drops from the tree. The bullet from the hunter s gun aiming at the monkey, falls at the same speed as the monkey. 22
Complexity So far we have considered simple motion, but lots of details effect actual real life motion. Consider a baseball to determine exactly how far it will go, you need to know: Initial speed in three dimensions Air resistance Gravity and any local variations in it Spin of the ball Light pressure on the ball Temperature of the ball Roundness of the ball 23
Friction Friction is caused by roughness of surfaces at the microscopic level rubbing against each other. Friction at rest (static friction) is greater tan friction in motion (kinetic friction). The frictional force always acts in the direction to oppose an external force. Friction depends on the mass and shape of an object. 24 Friction External Force
Topics for This Lecture Mass Force Motion: acceleration, speed and displacement Newton s three Laws Equations of motion One-, two- and three-dimensional motion The monkey and the gun Complexity versus approximation Friction 25