5 1 Visualize Assess Note that the climber does not touch the sides of the crevasse so there are no forces from the crevasse walls 5 2 Visualize 5 3 Visualize 5 4 Model Assume friction is negligible compared to other forces Visualize 5 5 Visualize Assess The bow and archer are no longer touching the arrow so do not apply any forces after the arrow is released a One rubber band produces a force F two rubber bands produce a force 2F and so on Because F 5 6 Model An object s acceleration is linearly proportional to the net force a Solve and two rubber bands force 2F produce an acceleration of 1 2 m s2 four rubber bands will produce an acceleration of b Now we have two rubber bands force 2F pulling two glued objects mass 2m Using 2 4 m s F ma 2 2 F 2 m a a F m 0 6 m s 2 5 7 Solve Let the object have mass m and each rubber band exert a force F For two rubber bands to accelerate the object with acceleration a we must have a We will need N rubber bands to give 2 F m acceleration 3a to a mass m Find N 1 2 Three rubber bands are required a 3 3 NF m 1 2 2 F m 2 NF m N 3 5 8 Visualize Please refer to Figure EX5 8 Solve Mass is defined to be m 1 slope of the acceleration versus force graph A larger slope implies a smaller mass We know by comparing their slopes Thus m 2 0 20 kg and we can find the other masses relative to 2m Similarly m 1 m 2 1 slope 1 1 slope 2 slope 2 slope 1 1 5 2 0 40 m 1 0 40 m 2 0 40 0 20 kg 0 08 kg m 3 m 2 1 slope 3 1 slope 2 slope 2 slope 3 1 2 5 2 50 m 3 2 50 m 2 2 50 0 20 kg 0 50 kg 2 5 5 2 Assess From the initial analysis of the slopes we had expected our numerical answers m m 2 3 and m m 2 1 This is consistent with 5 9 Visualize Please refer to Figure EX5 9 Solve Mass is defined to be Thus The ratio of masses is m 1 slope of the acceleration versus force graph m 1 m 2 slope of line 1 slope of line 2 1 1 1 1 5 a 1 3 N 3 a 1 5 N 3 5 5 3 9 25 m 1 m 2 9 25 Assess More rubber bands produce a smaller acceleration on object 2 so it should be more massive 5 10 Solve Use proportional reasoning Given that distance traveled is proportional to the square of the time d 2 t so should be constant We have d 2 t 2 0 furlongs x 2 2 Thus the distance traveled by the object in 4 0 s is x 8 0 furlongs Assess A longer time should result in a longer distance traveled 4 0 s 2 0 s 5 11 Solve Use proportional reasoning Let T period of the pendulum L length of pendulum We are told T L so should be constant We have T L Solving the period of the 3 0 m long pendulum is Assess Increasing the length increases the period as expected 3 7 s 3 0 s 2 0 m x x 3 0 m 5 12 Force is not necessary for motion Constant velocity motion occurs in the absence of forces that is when the net force on an object is zero Thus it is incorrect to say that force causes motion Instead force causes acceleration That is force causes a change in the motion of an object and acceleration is the kinematic quantity that measures a change of motion Newton s second law quantifies this idea by stating that the net force netF on an object of mass m causes the object to undergo an acceleration cid 71 The acceleration vector and the net force vector must point in the same direction cid 71 a cid 71 netF m 5 13 Visualize Solve a Newton s second law is F ma When F 2 N we have 2 N 0 5 kg a hence a 2 4 m s F 1 N we have 1 N 0 5 kg a b When After repeating this procedure at various points the above graph is obtained hence a 2 2 m s 5 14 Solve Newton s second law tells us that 2 a N 0 200 kg 5 m s 1 F F ma Compute F for each case 2 F N 0 200 kg 10 m s 2 b Assess To double the acceleration we must double the force as expected 5 15 Visualize Please refer to Figure EX5 15 Solve Newton s second law is find the mass Choosing the force F ma F 1 N We can read a force and an acceleration from the graph and hence Newton s second law yields gives us 0 25 kg 2 4 m s m a 5 16 Solve a This problem calls for an estimate so we are looking for an approximate answer Table 5 3 gives us no information on laptops but does give the weight of a one pound object Place a pound weight in one hand and the laptop on the other The sensation on your hand is the weight of the object The sensation from the laptop is about five times the sensation from the pound weight So we conclude the weight of the laptop is about five times the weight of the one pound object or about 25 N b According to Table 5 3 the propulsion force on a car is 5000 N A bicycle including the rider is about 100 kg This is about one tenth of the mass of a car which is about 1000 kg for a compact model The acceleration of a bicycle is somewhat less than that of a car let s guess about one fifth We can write Newton s second law as follows F bicycle mass of car acceleration of car 1 10 1 5 5000 N 50 100 N So we would roughly estimate the propulsion force of a bicycle to be 100 N 5 17 Solve a This problem calls for an estimate so we are looking for an approximate answer Table 5 3 gives us no information on pencils but does give us the weight of the U S quarter Put the quarter on one hand and a pencil on the other hand The sensation on your hand is the weight of the object The sensation from the quarter is about the same as the sensation from the pencil So they both have about the same weight We can estimate the weight of the pencil to be 0 05 N b According to Table 5 3 the propulsion force on a car is …
View Full Document
Unlocking...