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Transcript
Sections 4.4 What Forces Do and 4.5 Newton’s Second Law NOTES AP Physics I If something has a net constant force applied to it, experiment shows that it moves at a constant acceleration. For a force F, say, the velocity -vs- time curve might look something like: velocity slope4 = 4a apply force 4F slope3 = 3a slope2 = 2a slope1 = a apply force 3F apply force 2F apply force F time Mass constant acceleration 4a 3a 2a a F 2F 3F 4F Force Mass constant From this we see that acceleration is directly _____________ to force: Next we perform a series of experiments where we keep the force constant but vary the mass. velocity apply mass m slope = a a slope = 2 apply mass 2m a slope = 4 apply mass 4m time Force Constant acceleration a 3a/4 a /2 a /4 m 2m 3m 4m mass Force Constant Acceleration is _________________ proportional to the mass: Small digression for directly and inversely proportional relationships: Things that are directly proportional have the general form: (as one variable increases, the other variable increases). The relationships for two coordinates on a curve that is directly proportional (x1, y1) and (x2, y2) are: Things that are inversely proportional have the general form: (as one variable increases, the other variable decreases). The relationships for two coordinates on a curve that is directly proportional (x1, y1) and (x2, y2) are: Example Problems: A man pulling an empty wagon causes it to accelerate at 2.5 m/s2. What will the acceleration be if he pulls with the same force when the wagon contains a child whose mass is six times that of the wagon? A truck has a maximum acceleration of 10.0 m/s2. What will the maximum acceleration be if the truck is towing a car whose mass is half that of the truck? Section 4.5 Newton’s Second Law From last section we found that acceleration, a, is directly proportional to the ______________ and inversely proportional to the ___________. We can put these two relationships together into one equation relating acceleration, force, and mass: This relationship is called ________________________________. An object of mass m is subjected to forces F1 , F2 , F3 ... will undergo an acceleration a given by: where the net force Fnet F1 F2 F3 ... is the vector sum of all forces acing on the object. The acceleration vector points in the same direction as the _______________ vector. Newton’s Second Law equation is more often written in the rearranged form: Using the rearranged form of Newton’s Second Law we can easily derive the units of force for the SI system: 1 kg m/s2 is called a _______________, ______. The English system’s unit of force is called the _____________, ____. The conversion between Newtons and pounds is: 1 pound = 4.45 N. Example Problems: Scallops eject water from their shells to provide a thrust force. The graph below shows a smoothed graph of actual data for the initial motion of a 25 g scallop speeding up to escape a predator. v (m/s) 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 t (s) a.) What is the magnitude of the net force needed to achieve this motion? b.) How does this force compare to the 0.25 N weight of the scallop? Very small forces can have tremendous effects on the motion of very small objects. This is particularly apparent at the scale of the atom. An electron, mass 9.1 x 10-31 kg, experiences a force of 1.6 x 10-17 N in a typical electric field at the earth’s surface. From rest, how much time would it take for the electron to reach a speed of 3.0 x 106 m/s, 1% of the speed of light. Assignment Newton’s First and Second Laws AP Physics I (numbers correspond with problem numbers of text on pages 155 to 156) 13.) The figure below shows an acceleration-vs-force graph for three objects pulled by rubber bands. the mass of object 2 is 0.20 kg. What are the masses of objects 1 and 3? Explain your reasoning. a (m/s2) 6 1 2 5 4 3 3 2 1 0 0 1 4 5 2 3 6 Force (number of rubber bands) 14.) A constant force applied to object A causes it to accelerate at 9 m/s 2. The same force applied to object B causes an acceleration of 24 m/s2. Applied to object C, it causes an acceleration of 14 m/s2. a.) Which object has the largest mass? b.) Which object has the smallest mass? c.) What is the ration of mass A to mass B (mA/mB)? 15.) A utility vehicle has a maximum acceleration of 6.0 m/s2 when it carries only the driver and has a total mass of 5000 kg. What is its maximum acceleration after picking up six passengers and their luggage, adding an additional 800 kg of mass? 16.) A constant force is applied to an object, causing the object to accelerate at 10 m/s2. What will the acceleration be if a.) the force is halved? b.) the object’s mass is halved? c.) the force and the object’s mass are both halved? d.) the force is halved and the object’s mass is doubled? 17.) A constant force is applied to an object, causing the object to accelerate at 10.0 m/s2. What will the acceleration be if a.) the force is doubled? b.) the object’s mass is doubled? c.) the force and the object’s mass are both doubled? d.) the force is halved and the object’s mass is halved? 21.) The figure below shows an object’s acceleration-versus-force graph. What is the object’s mass? a (m/s2) 6 5 4 3 2 1 0 0.0 0.5 1.0 1.5 F (N) 22.) In t-ball, young players use a bat to hit a stationary ball off a stand. The 140 g ball has about the same mass as a baseball, but it is larger and softer. In one hit, the ball leaves the bat at 12 m/s after being in contact with the bat for 2.0 ms. Assume constant acceleration during the hit. a.) What is the acceleration of the ball? b.) What is the net force on the ball during the hit? 23.) Two children fight over a 500 g toy car. The 30 kg boy pulls to the right with a 12 N force and the 25 kg boy pulls to the left with a 15 N force. Ignore all other forces on the toy car (such as its weight). a.) At this instant, can you say what the velocity of the car is? If so, what are the magnitude and direction of the velocity? b.) at this instant, can you say what the acceleration of the car is? If so, what are the magnitude and direction of the acceleration? 24.) A 5000 kg truck is traveling along a straight road at 10 m/s. Two seconds later its speed is 9 m/s. What is the magnitude of the net force acting on the truck during this time? 25.) The motion of a very massive object can be minimally affected by what would seem to be a substantial force. Consider an oil supertanker with mass 3.0 x 108 kg. Suppose you strapped two jet engines (with thrust as given below) onto the sides of the tanker. Ignoring the drag of the water (which, in reality, is not a very good approximation), how long will it take the tanker, starting from rest, to reach a typical cruising speed of 6.0 m/s?