ACTIVITY 6: Falling Objects

Transcription

1 UNIT FM Developing Ideas ACTIVITY 6: Falling Objects Purpose and Key Question You developed your ideas about how the motion of an object is related to the forces acting on it using objects that move horizontally. However, it can be shown that exactly the same ideas can be applied to objects that move vertically (up and down). You know that if you hold an object up and then release it, it will fall to the floor. In a previous unit you saw that this behavior can be explained using the idea that there is a gravitational interaction between the object and Earth. In this activity you will explore how different objects fall and, in particular, how their mass affects how they fall. You will also consider how the results can be explained using your ideas about forces. For example, suppose you dropped a soccer ball and a bowling ball from the same height at the same time. Which one would reach the ground first and, why? The key question for this lesson is: How does the mass of an object affect how it falls? Initial Ideas If you were to drop a bowling ball and a soccer ball from the same height, at the same time, which one do you think would reach the floor first? Explain your reasoning NextGenPET FM-55

2 Unit FM To help illustrate your thinking about the force(s) acting on each ball, sketch a force diagram for both balls at the same moment in time as they are falling. (Remember, they are released at the same time from the same height.) Be sure to include arrows representing the gravitational force acting on each ball, as well as any speed arrows you think appropriate. Do you think that the strength of the gravitational force acting on each ball would remain constant as it falls or do you think these force strengths would change as the balls get nearer to the ground? Explain why you think so.! Draw your group s force diagrams and graphs on a whiteboard. Participate in a class discussion about everyone s ideas and make a note of any ideas or reasoning different from your own. FM-56

3 Activity 6: Falling Objects Collecting and Interpreting Evidence You will need: Computer with internet connection Two objects with very different masses (e.g. a 1 kg and a 100 g mass) Several objects with different masses (but similar size and shape) Hard board such as a whiteboard (to drop balls onto) Exploration #1: How do falling objects move? STEP 1. In a previous activity you saw that when a ball is dropped from a height of about 2 meters its speed increases as it falls. Suppose a small ball were dropped from the top of a tall building. Do you think its speed would continue to increase all the time it is falling? Why do you think so? (You may assume the effects of the air are negligible.) To check your thinking, watch UCF-A3-Movie 1. It shows a simulation of a young man at the top of a building, holding a baseball in his hand. When you play the movie, he will release the ball and a speed-time graph for the falling ball will be plotted. When you are ready, run the simulation. While the ball was falling, was a force acting on it the whole time? How do you know? FM-57

4 Unit FM Did the strength of the force acting on the ball change significantly as it fell, or did its strength remain approximately constant? How do you know? (Hint: Consider whether the rate which the speed increases stays the same or not.) 1 STEP 2. Now, imagine you were to hold two spheres of a similar size, but different mass, at the same height above the ground and released them at the same time. Which sphere do you think would hit the ground first (if either)? Explain your thinking in terms of the strength of the gravitational force acting on each of the two spheres. STEP 3: Lay the hard board (i.e. one of the whiteboards) on the floor. From those available to you, select two similarly sized spheres of different mass and hold them (one in each hand) at the same height (about head high) above the board. Release them at the same time. 1 Actually, the strength of the gravitational force exerted on an object depends on its distance from the center of the Earth. Thus, even when an object falls to the ground from a great height, such as an aircraft, its distance from the Earth s center changes by only a very small relative amount and so the gravitational force has about the same strength throughout its fall. FM-58

5 Activity 6: Falling Objects ALL of your group members should watch and LISTEN carefully as the spheres hit the board. Listen to see if they hit the board at the same time (single plunk), or at different times (plunk... plunk). Be aware that some of the spheres have a tendency to bounce once they hit the board so you may want to have one group member be in charge of watching to see if one of the spheres bounced. You need to be able to distinguish between a soft plunk... soft plunk (each sphere hitting the board at a different time) and a loud plunk... soft plunk, plunk due to both spheres hitting the board at the same time and then one of the spheres bouncing. You may need to repeat the experiment a few times to check. Make sure that everyone in your group agrees on what you saw and heard. Does the more or the less massive sphere CLEARLY hit the board first or do they both appear to hit at the same time? STEP 4. Now repeat the experiment using different pairs of spheres of varying masses. Describe your observations about which object hits the board first (if either). Based on your observations, when you drop two spheres of different mass, do they increase speed at the same rate as they fall or at different rates depending on their mass? What evidence supports your conclusion? FM-59

6 Unit FM Exploration #2: How does mass affect the strength of the gravitational force? STEP 1. Having now seen how objects with different masses fall, we will consider how the strengths of the gravitational forces acting on them compare. In what follows you should apply the ideas you have already developed about force and motion to guide you. While you developed them in the context of objects moving horizontally (forward and backward) scientists have found that they are equally valid for vertical (up and down) motion. Hold out one of you hands, palm upward, place a small object on your palm and leave it there so it does not move. Now consider the following questions about this situation. The object on the palm of your hand is not moving so what can you say about the forces acting on it, are they balanced or unbalanced? The two forces acting on the object are the gravitational force of the Earth pulling downward on it and a supporting force applied by your hand pushing upward on it. How does the strength of the upward supporting force being applied by your hand compare to the strength of the downward gravitational force? Is one stronger than the other or are they both the same strength? How do you know? STEP 2. Keeping one hand holding the small object up, stretch out your other hand and have someone place an object with significantly more mass on it. Again, do not let the object move while you are holding it up. FM-60

7 Activity 6: Falling Objects How does the strength of the upward supporting force of your hand on this second object compare to the strength of the downward gravitational force acting on it? How do you know? Now focus on the effort you are having to exert to hold each object steady and what you can infer from this about the strength of the supporting force being applied to each object by you hand. How do the strengths of the upward supporting forces being applied by each of your hands to the objects on them compare? Is the supporting force being applied by each hand the same strength or is one supporting force stronger than the other, and if so which one? What can you infer from your answers to the previous questions about the strength of the gravitational force acting on the two objects with different masses? Does the gravitational force have the same strength regardless of the object s mass or is it stronger for one of the objects and, if so, which one? Carefully explain your reasoning.! Discuss your answer and reasoning with another group and try to resolve any differences. FM-61

8 Unit FM STEP 3. You have now seen that similarly shaped spheres increase speed at the same rate as they fall regardless of their masses, yet the strength of the gravitational force acting on them depends on their mass. Considering the following questions about some races between fan-carts may help you in understanding these results. Imagine you had a race between two low-friction fan-carts on side-by-side tracks, like those shown here. These carts have different masses (6 kg and 2 kg), but the same strength force (20 N) acting on each of them. Would these two carts increase speed at the same rate, so making the race end in a tie? If so, why? If not, why not and what could you do to make the race end in a tie? Carefully explain your reasoning. Suppose you had a race between two different mass fan-carts that did end in a tie. Would this be evidence that the strength of the fans was the same, or that it was different, and if so which one was stronger? Explain your thinking. Earlier in this activity you saw that objects of different mass all fall at the same rate of increasing speed. Does this evidence support the idea that the strength of the gravitational force acting on them has the same strength, regardless of their mass, or does it support the idea that the strength of the gravitational force acting on an object depends on its mass? FM-62

9 Activity 6: Falling Objects Recall that in the previous unit you saw that the rate at which an object s speed increases is given by the relationship: Rate of change in speed = Strength of net force Mass of object Explain, in terms of this relationship, why it is that all objects fall at the same rate of increasing speed 2. Summarizing Questions S1: Does the strength of the gravitational force of the Earth pulling an object toward the ground depend on the object s mass? What evidence supports your answer? S2: Your observations in this activity suggest that if the 6 kg and 2 kg carts were dropped from the same height at the same time, they would reach 2 Close to the surface of the Earth, and in the absence of any other effects, the rate at which all objects increase speed as they fall has been measured to be approximately 9.8 (m/s)/s. This means their speed increases by 9.8 m/s for every second that they are falling. This value is sometimes called the acceleration due to gravity and is determined by the mass of the Earth. Close to the surface of the Moon the acceleration due to gravity is only 1.6 (m/s)/s because the Moon s mass is much less than that of the Earth. Because all objects fall with the same rate of increasing speed people often say that gravity pulls the same on everything, but we have seen that this is not true. It would be more appropriate to say that the pull of gravity on an object depends on its mass, but the effect it causes (rate of change of speed) is the same for all objects. FM-63

10 Unit FM the ground together. In other words the race to the ground would end in a tie. a) How could you explain such a result in terms of the relative strengths of the gravitational forces pulling the carts downward and their masses? b) Draw force diagrams for both carts as they are falling side-by-side. Be sure to include both force and speed arrows of appropriate lengths? S3: It is common for people to explain that objects of different mass fall together because the gravitational force acting on them is the same strength. If the gravitational forces acting on a bowling ball and a soccer ball were truly the same strength as they fell, which one would actually reach the ground first? Explain your reasoning. FM-64

11 Activity 6: Falling Objects S4: In a previous activity Han and Samantha had the following conversation about the motion of a fan cart. Who do you agree with now? Explain your reasoning. I think that, as long as the fan keeps pushing on it, no matter how long the track is, the cart will keep speeding up. I agree that the cart will speed up to start with, but I just don t believe it could keep speeding up forever. I think that at some point its speed will become constant. Han Samantha FM-65

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