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1) Forces of 3.0 N east and 7.0 N north act on an object. What is the net force on the object? 7.6 N 67º N of E 2) Forces of 8.0 N 30º north of east and 3.5 N 15º west of north act on an object. What is the net force on the object? 9.5 N 51º N of E Remember to draw vector diagrams with arrows, eh. “If I have seen further it is by standing on the shoulders of giants.” The “Giants” that Newton’s quote refers to are Galileo and Copernicus. Both contributed ideas that proved central to our modern-day understanding of DYNAMICS. Nicolaus Copernicus (1473 - 1543) Galileo Galilei (1564 - 1642) Dynamics is the study of forces, the cause of motion. Remember that a force can be a or a KINEMATICS + DYNAMICS = MECHANICS Greeks (like Aristotle) had noticed 2500 years ago that in order to keep something moving you had to keep pushing on it. If you stopped pushing, it stopped moving! This seems to be true from our everyday experience. Aristotle (384 -322 B.C.) Aristotle believed that any object’s “natural state” is to be AT REST. Do you agree with his view? Can you think of something that the Aristotle didn’t account for? Galileo’s Experiments Galileo came up with two “thought experiments” (they could only be imagined, not done in real life). Galileo Galilei He imagined a world where there was no friction. No, he didn’t think that this was the way the world actually IS, but he believed friction complicated his study of dynamics, and by ignoring it, he could simplify his theories about the cause of motion. Let’s take a look at what he was thinking . . . . Experiment Number 1 Ignoring everything else, an object rolling down a slope will speed up. The only reason its velocity will increase is because it is going down a slope while gravity is pulling down on it. Ignoring everything else, an object rolling up a slope will slow down. The only reason its velocity will decrease is because it is going up a slope while gravity is pulling down on it. If the ball is moving on a level surface it has no reason to speed up or slow down! It will move at a constant velocity forever. Experiment Number 2 A ball rolls down a slope on one side, then rolls just as high up a similar slope on the other side. The ball now has to roll up a slope that is not as steep, but rolls to the same height. Notice the distance it must go along the slope is greater. Since it has no slope to go up, it should keep moving forever along the level surface at a constant velocity. Galileo said that this is the “natural state” of the object. In these two “experiments,” Galileo was saying that without friction, an object moving at a constant velocity forever is just as natural as an object staying at rest forever. Here’s another way to look at Galileo’s ideas in a more modern way… What do you have to do to keep the box moving at a constant velocity of 2.0 m/s in each of these situations? 1) 3) 2) 4) So in the real world, the constant pushing we do to keep something moving at a constant speed is just to overcome friction! In short their contributions were: Nicolaus Copernicus Our planetary system is heliocentric, meaning that the planets, including earth, rotate about the sun. The sun does NOT rotate around earth. It takes a force to stop a moving object, that is an object does not have a tendency to just come to rest. Gravity accelerates all objects at the same rate, regardless of their mass. Galileo Galilei Newton’s genius was in unifying these ideas into three concise statements explaining why objects move the way they do under the action of a force. The scope of Newton’s work was so broad and impressive, he gets a little bit of extra credit. Any object will remain at a constant velocity unless acted upon by an unbalanced force. Newton’s first law is called the LAW OF INERTIA. The tendency of matter to continue in its current state of motion (whether it is moving or at rest) is called inertia. When moving difficult to stop When stationary difficult to push An unbalanced force is the vector sum of all the forces acting on an object. It is also called the net force. The symbol for net force is: Fnet Imagine that you are a passenger in a car . . . . . Ex. 1: Question:When the car approaches a red light and brakes, your body lurches forward. Why does this happen? Ex. 2: Question:When the car makes a sharp right-hand turn which way does your body lurch? Ex 3. Question: It is easier to push and stop a child on a swing compared to an adult? Ex 4. Question: Why are lids helpful for pop and coffee when you go drive thru? Ex 5. Question: Why do headrests in cars help to elleviate the severity of whiplash? Both you (the dot) and the car (the box) are originally moving with the same velocity (red vector), together. The force that made the body of the car turn has not acted on you. Your body’s tendency is to keep moving in its original direction. With respect to the car, it seems you are pushed left. If you are wearing a seat belt, you will still feel the sensation, but you won’t slide to the left very much. Your velocity will, after a short time interval, be in the same direction as the car’s velocity, because the seat and seat belt exert unbalanced forces on you. Check out some car crashes of your choice! Check out some stat’s that will make you want to buckle up! To Summarize Newton’s 1st law! when forces are balanced the net force is zero, the resultant acceleration is zero, there is no change in velocity- inertia! an object in motion will remain in motion unless acted upon by an outside (unbalanced) force an object at rest will remain at rest unless acted upon by an outside (unbalanced) force inertia is the property of an object to remain in motion (or remain at rest) Bart and the Case of Inertia… 1. Bart is using a force of 60 N west to ride his skateboard, the force of friction on the skateboard is 60 N east. Bart and the skateboard have a mass of 45 kg. a. draw a free body diagram b. describe the motion of Bart and the skateboard FN Fapp = 60 N Ff = 60 N Fg