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Week3 GSCI101-­‐104 Fall 2012 Wednesday evening HELP sessions Sometime after 7:00PM Available on request (email should suffice) (message to my cell) Solve homework or answer questions Physics building (same hallway as robotics lab) 2378 This week we will focus on force. Force is a push or a pull. It is usually starightforward to recognize forces. Is an object being pulled? Is it being pushed? Of course, as always, this fact that identifies a force has to be integrated into our scientific understanding carefully so that there is a real understanding. In addition to the statement above, Newton realized that forces have a direct and often simple impact on an ojects motion. Forces make objects move. Newton quantified this in three laws. 1. First law: If an object experiences no net force, then its velocity is constant.
2. Second law: The acceleration of a body is along the direction and directly
proportional to the total F acting on the body. F = ma.
3. Third law: Action means reaction
Some say that the first law is a special case of the second law. However, the way I like to think about this law is that it defines “natural motion” [not an official vocabulary word in physics]. If you isolate an object how does it behave? In our world objects come to rest due to friction. They fall due to gravity. Newton first wants to establish that things “don’t move by themselves”. If isolated and object experience no force and it follows the first law. Of course Newton also needed to recognize that being at rest from one person’s perspective can mean constant velocity for another and these two viewpoints are consistent with “not moving” i.e. no total force acting. The second law defines how an object’s motion is affected by forces. STEP1: The first step is to identify the forces. Then determine their magnitudes and directions. STEP2: Add the forces together as vectors to find the total force. The total force will have a single magnitude and a definite direction. Identifying and adding all the forces can be very challenging. STEP 3: Find the acceleration (divide by the massè This involves taking the magnitude of the force and dividing it by the mass of the object to find the magnitude of the acceleration.) Assign the direction of the acceleration as the direction of the force. STEP 4: Find the change in the object velocity. ∆𝑣 = 𝑎∆𝑡. Here you need to recognize that the acceleration acts for at time period and that it changes the velocity by changing the speed, direction or both. So we need to do the above calculation by finding the amount and the direction of the change and the add this to the starting velocity as a vector. If you think about the motions you observe in everyday life ( a yoyo) you should recognize that these simple relationships that connect velocity changes with acceleration and acceleration with force can result in very complex motion. In this class we will restrict ourselves to forces and motion that are more straightforward than the general case. IMPORTANT: Newton’s Law also tells us about forces if we know the motion. AN OBJECT WITH CONSTANT VELOCITY IS EXPERIENCING NO TOTAL FORCE. To get a good understanding of the impact of force on motion, consider throwing and catching a baseball. You push the ball during the throw. It would be useful if you could imagine this process in space so that there are no forces acting between the throw and catch. It accelerates. You release the ball it now (no gravity) travels in a straight line at constant speed. To catch the ball you exert a force opposite the motion and lower the speed. We will return to this example when we consider energy. Mass. You need to know what mass is to apply Newton’s second Law. • measured in kg • distinguish between inertial mass (Newton’s) & gravitational Einstein’s o Inherently different concepts that are found to be the same. o inertial mass is a resistance to motion. If you want to throw an object the more inertial mass the harder it is to throw it. o gravitational mass tells you how heavy something is. Students might think that if something is hard to throw then it should be heavy. These are not unrelated concepts. In space however massive objects are still hard to move but experience minimal gravitational forces. Astronauts can pick things up except for the inertial mass impact. weight (gravity) è well known force (g=9.8 m/s-­‐s Inertial mass measures the resistance to motion. Gravitation mass measures how attracted to bodies are under the influence of gravity. Interesting thing is that they are related. The heavier the object the harder it is to move. Of course you say but if that is your point of view then your missing the argument. The statements above are two independent facts. There is no reason for these two quantities to be related. They are we have intuitively learned this connection and so we assume it is a required connection but it is not. Einstein puzzled over this and found a way within the theory of gravity to link these two facts. 
Fg = −mgzˆ which means: magnitude mg, direction down equilibrium static è balance small object ∑ forces=0 € extended ∑ Torques=0 (gsci101 need not worry about torque or rotation) rotational force is a torque We need to identify when things are in balance. In general for extended objects such as ladders leaning on walls and people on a balance beam there are two conditions: 1 total force=0; 2 total torque=0 (rotational force). Torque is just a easier way to deal with the forces that one experiences on objects that have length, width and height. If you hold a bowling ball with your arm extended down you side it is a very different experience than when you hold the ball with your arm extended outward. The problem becomesè the ball pulls on you hand, you hand pulls your arm, your arm is attached to the shoulder so muscles can hold the arm …. The forces of the ball must be balanced by various forces in the body. If the body experiencing the force doesn’t stretch (much) or flow (water) then you can simplify the result of forces acting by introducing torques. These are therefore special forces that make some problems simpler. However, the basic rules are Newton’s laws and they do cover the full impact of the way forces affect motion. GSCI101 will only worry about balancing forces (no problems with torques) BALANCING FORCES WILL BE AN IMPORTANT CONCEPT Forces to know [Unit of force is the Newton] gravity mg down Support force or Automatic force of a surface [away from the surface] Normal Friction Force that resisits motion [surface may exert along its sur.] Net Vocabulary word for the total force Spring force Force that a compressed or stretched spring exerts Air resistance Type of frictional Tension Stretching force that ropes exert Tension is a complicated phenomenon. Sometimes it is easier to examine ropes used to support or pull something [under dynamic equilibrium or balance] At each point the rope is pulled equally in both directions. The amount or magnitude of this pull is the tension. Tension is the amount of force applied to the end. For balance each end must have a force equal to the tension applied. Rope forces act along the direction of the rope. A pulley or person (on a rope swing). Feels forces equal to the number of contacts to the rope. (On the swing imagine that your hands are supporting you and then you see that each hand will feel a rope force up.) spring buoyant floating external Free Body diagrams • isolate the object • consider only forces directly acting on the object object connected by ropes • only the rope acts on each object horse pulling a cart • cart feels the force of the horse • horse feels the force of the cart • draw all forces as vectors paying attention to direction and magnitude • graphically add vectors • recognize balance o total force is zero o need a additional force to balance the other forces