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Chapter 2 - Question Keys1. Shown below is a speed-time graph for a cart moving in front of the motionsensor. For convenience it has been divided into four sections (A,B,C,D).During each of the four separate periods shown on the graph (A, B, C, D),was an unbalanced force acting on the cart? YES or NO. If not, how can youtell from the graph? If yes, did the unbalanced force act in the same directionas the cart’s motion, or against it? Briefly explain how you can tell this fromthe graph.A The speed of the cart is increasing. For this to happen the forces must beunbalanced, with the strongest force in the same direction as the motion.B The speed of the cart is decreasing. For this to happen the forces must beunbalanced, with the strongest force in the opposite direction to the motion.C The speed of the cart is constant. For this to happen the forces acting on it must bebalanced.D The speed of the cart is decreasing again. For this to happen the forces must beunbalanced, with the strongest force in the opposite direction to the motion.

2. In the left column below there are three situations where a cart is acting on bymore than one force. The direction and strength of each force is shown. Inthe second column state whether the forces acting on that cart are balanced orunbalanced. If balanced, leave the third column blank. If unbalanced, in thethird column draw the net force on the cart (the single equivalent force) andmake sure you include its direction and strength in N.Object with forces acting on it(a)Are forcesbalanced orunbalanced?If unbalanced, draw the netforce7 NUnbalanced(b)Balanced(c)UnbalancedPET Chapter 2 Question Keys8 N2

3. Five identical crates are initially atrest, side-by-side. One is acted onby a single force of 45 N, as shown.45 NWhich of the other crates, shown below, would move side-by-side with thecrate described above? (Choose as many as you think appropriate.)a)b)25 N10 N10 Nc)50 N25 N40 N20 Nd)75 N30 N15 N60 NBriefly explain your choice(s).Since they are identical, in order for the other crates to move side-by-side with thefirst one they will need to have a net force acting on them that has the same strengthand direction as the single force acting on the first crate; namely 45 N to the right.Both of crates b) and c) have this.Crate b) has a total of 90 N to the right and 45 N to the left. Subtracting 45 N from90 N gives a net force of 45 N to the right.Crate c) has 75 N to the right and 30 N to the left. Subtracting 30 N from 75 N gives anet force of 45 N to the right.(The net force on crate a) is only 25 N to the right. The net force on crate d) is 45 N tothe left.)PET Chapter 2 Question Keys3

4. Block A, shown below, is moving to the right. At the moment shown, threedifferent forces are acting on the block. The strengths and directions of thethree forces are shown in the force diagram.a) Will block A speed up, slow down, or move at constant speed? Brieflyexplain how you know.Block A will slow down as it moves. This is because the forces acting on it areunbalanced, with the net force acting opposite the motion of the block.b) Suppose there was another block (B) that was identical in size and mass toblock A. At the same moment shown above, block B is alongside block Aand is moving at the same speed as block A. What single force should beapplied to block B, so it continues to move side-by-side with block A?Draw this force (strength and direction) on the block below, and brieflyexplain how you know.3NSince the blocks are identical, Block B will need the same net force acting on it inorder to move side-by-side with Block A. The net force acting on Block A is 3 N tothe left (12 N to the left minus a total of 9 N to the right) so that is the singleforce that should act on Block B.PET Chapter 2 Question Keys4

5. A hockey player uses his stick to maintain acontinuous constant strength push on the puck ashe moves it across the smooth ice. Assuming that theeffects of friction are negligible, which of the followingchoices best describes the motion of the puck whilethis constant strength push is acting on it?a)b)c)d)The speed of the puck will continuously decrease.The puck will move at a constant speed.The speed of the puck will continuously increase.Something else – you describe it.Briefly explain the reasoning behind your choice (remember to include adescription of the motion if you chose option d).We learned in class that when a constant strength force acts on an object, it speeds up.As long as the force continues to act the puck’s speed will continuously increase.6. A soccer ball is rolling across the ground. A child briefly taps the ball with herfoot at right angles to its direction of motion. A force diagram for the intervalof time that the child’s foot is in contact with the ball is show below to the left(top view).During TapAfter TapIn the picture to the right, draw a motion arrow showing how the ball will bemoving after the tap. Pay attention to both the length and direction of themotion arrow. Briefly explain why you drew it this way.The sideways tap will not change the speed of the ball, only its direction, so the lengthof the motion arrow will be the same but it will point in a different direction. Since theball was already moving to the left it will continue to do so (since no force acted to makethat change), but it will also move upward at the same time, due to the effect of thetap. The combination of these means that the ball will be moving diagonally up and to theleft after the tap.PET Chapter 2 Question Keys5

7. Imagine you had two different fan units. Fan #1 hadmore batteries than fan #2. Fan #1 can push the cartwith a force of 20 N. Fan #2 can push with a force of5 N. Suppose you start an experiment by mountingFan #1on a cart and release the cart from rest on avery smooth track. You can ignore the effects offriction throughout this problem. Below is a speedtime graph for the motion of fan #1 pushing the cart.Fans 1&2Fan #2a) Suppose you replaced fan #1 with fan #2 (the weaker one) and mounted itby itself on the same cart. When the cart is released from rest, you observethat it speeds up. Sketch what the speed-time graph for Fan #2 might looklike on the graph above. Label it Fan #2. Below, briefly explain why youdrew the graph the way that you did.Fan #2 is a lot weaker than Fan #1 so the cart will speed up at a much slower ratewith Fan #2 than it did with Fan #1. (In fact, since friction can be ignored, andsince the force is only one fourth a strong, the cart will speed up at one fourth therate, so it will only reach a speed of about 20 cm/s after 2.5 seconds, as opposed toabout 80 cm/s with Fan #1.)PET Chapter 2 Question Keys6

b) Now suppose you mount both fans on thesame cart, but with the two fans trying topush the cart in opposite directions. Whenyou release this cart from rest you observethat it speeds up. Sketch what the speedtime graph for the combined fans mightlook like on the same graph on theprevious page. Label it Fans #1 & #2.Below, briefly explain why you drew thegraph the way that you did.With both fans mounted on the cart in the way indicated there will be an unbalancedcombination of forces acting on it. The strength of the net force will be 15 N (20 Nin one direction, minus 5 N in the other direction). This net force will make the cartspeed up at a rate that is slightly lower than that for the 20 N force alone. (Theextra mass of the added fan will also be a factor in reducing the rate of speedingup.)c) Below, draw a force diagram for the cart with the two fan units on it whilethe cart is speeding up. (Remember to include all relevant forces, labelthem appropriately, and also include a speed arrow if appropriate.)20 NForce exerted oncart by Fan #1PET Chapter 2 Question Keys5 NForce exerted oncart by Fan #27

8. A group of students arrange two leveltracks side-by-side so they can have arace between two carts with fansmounted on them. They start with thetwo fan units having the same strength(same number of batteries). Cart #2has extra blocks on it so its mass isgreater than the mass of cart #1.The students next want to adjust the strength of fan unit #1 (by changing thenumber and size of batteries) so the two carts will tie in a race (that is, whenturned on and released they will each speed up at the same rate).Should the strength of fan unit #1 be made greater than, equal to, or less thanthe strength of fan unit #2?The strength of fan #1 should be made less than the strength of fan #2Justify your answer.Since cart #1 has less mass than cart #2 it will require less force strength to make itspeed up at the same rate. (We learned in class that the more mass an object has theslower its rate of speeding up will be for a given force strength.)PET Chapter 2 Question Keys8

9. A group of students arrangetwo level tracks side-by-sideso they can have a racebetween two carts. Theymount identical fan units(each with two real batteries)on two identical carts. Whenthe two carts, with fans turnedon, are releasedsimultaneously from the end of the tracks they speed up at the same rate,traveling side-by-side, and so the race ends in a tie (Experiment 1).The students then add extra mass to one of the carts and repeat theexperiment (using the same fan units), and record speed-time data for bothcarts (Experiment 2).a) The next week, when they look at the speed-time data they graphed(shown below), there are two lines (labeled A and B), and they are notsure which is which. Can you help by identifying which line representsthe motion of the cart with the added mass? Justify your choice.60Speed .05.56.0Time (s)Line B represents the motion of the cart with added mass. Since the fan units wereidentical they would have provided the same strength force on each cart. However,the cart with the added mass would have sped-up at a slower rate than the onewithout the extra mass. The line that represents a lower rate of speeding up is B.PET Chapter 2 Question Keys9

b) However, one of the students remembers that they also attempted tobreak the tie in Experiment 1 by adding a additional battery to one of thefan units without adding extra mass to either cart (Experiment 3). Couldthe speed-time data shown in the graph on the previous page be fromExperiment 3? Yes or No. Justify your answer.Yes, the data could be from Experiment 3. In this experiment two differentstrength forces were applied to identical carts. This would mean that the cart withthe stronger fan force acting on it would speed up at a higher rate than the othercart – this would correspond to line A, with line B being the cart with the weaker fanforce acting on it.10. A cart has a fan unit and a friction padattached. A student adjusts the friction padso it rubs lightly against the table. When thefan is turned on, the cart speeds up slowly tothe right.Explain why the cart speeds up to the right.Draw the Force Diagram:Force exerted oncart by fan unitFrictional force exertedon cart by trackWrite the explanation:For an object to speed up an unbalanced force (or unbalanced combination of forces)must act on it. For the cart to speed up slowly to the right the forces acting on it mustbe unbalanced, with the strongest force pushing to the right. This must mean that theforce exerted on the cart by the fan must be stronger than the frictional forceopposing the motion. (However, it cannot be very much stronger, since the slow rate ofincreasing speed indicates that the net force is not very large.)PET Chapter 2 Question Keys10

11. A group of students arrangetwo level tracks side-by-sideso they can have a racebetween two carts. Theymount identical fan units(each with two real batteries)on two identical carts. Whenthe two carts, with fans turnedon, are releasedsimultaneously from the end of the tracks they speed up at the same rate,traveling side-by-side, and so the race ends in a tie.The students then add some extra mass to one of the carts (Cart A) and addan extra battery to the other cart (Cart B). They then repeat the race and seethat Cart B now speeds up more quickly than Cart A and so pulls ahead of itand wins the race. Your task is to write an explanation for why Cart B nowspeeds up more quickly than Cart AExplanation: Why does Cart B speed up more quickly than Cart A?Draw the Force Diagrams:(One for each cart)Force of fanunit on cartCart A: Added mass and2 batteries in fan unitForce of fanunit on cartCart B: No added mass and3 batteries in fan unitWrite the explanation:Cart B has two factors that make it speed up more rapidly than Cart A. First it has lessmass and so, even with an equal force, it would speed up more quickly. Second it has astronger force (due to the extra battery) so this would make it speed up more quicklyalso, even if the masses were the same. Both factors work in favor of Cart B so itspeeds up a lot more quickly than Cart A.PET Chapter 2 Question Keys11

12. A small child is pushing the box of toys across the room at a constant speed.Create an explanation for why the box moves at a constant speed as the childpushes it.Draw the Force Diagram:Force exerted onbox by childFrictional forceexerted on box byfloorWrite the explanation:For an object in motion to move at a constant speed the forces acting on it must bebalanced. If the box in question does move at a constant speed this must mean that thestrength of the force acting in the direction of motion must be exactly equal to that ofthe force opposing its motion. Therefore the box moves at a constant speed becausethe strength of the child’s push is equal to that of the frictional force exerted on it bythe floor.PET Chapter 2 Question Keys12

with a force of 20 N. Fan #2 can push with a force of 5 N. Suppose you start an experiment by mounting Fan #1on a cart and release the cart from rest on a very smooth track. You can ignore the effects of friction throughout this problem. Below is a speed time graph for the motion of fan #1 pushing the cart. Fan #2 Fans 1&2