1.1 Observe and Represent a) In order to hold the medicine ball I have to push up on it a lot more than I do with the tennis ball.

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1 PUM Physics II - Dynamics Lesson 1 Solutions Page 1 of Observe and Represent a) In order to hold the medicine ball I have to push up on it a lot more than I do with the tennis ball. b) We could use words or arrows like in motion diagrams. c) and d) e) The medicine ball would be moving upwards. This means that there must be another object interacting with the ball. f) is interacting with the medicine ball, pulling it down in the opposite direction of my hand is pushing up. 1.2 Test Your Reasoning a) Air could down on the ball. b) We hang an object inside a container on a spring and pump the air out of the container. c) If the air pushes down on the object then when it is removed from the container, the object should move upwards. e) Air must push up on the object since the object went down instead of upwards. My hypothesis has been disproven. 1.3 Represent and Reason a) is the object that exerts this downward pull. b) c) The length of the arrows are the same on my diagram. If was longer than F on ball then the object would move up. If it were the other way around then the object would move down.

2 PUM Physics II - Dynamics Lesson 1 Solutions Page 2 of 7 d) The force arrows are much longer in this case: 1.4 Represent and Reason a) The force arrows are balanced in each of the diagrams. b) = - + = 0 c) No. This would change where the negative sign was in the first statement. However the total force exerted on the ball would remain the same even if the axis was switched: - = + = 0 d) The total force exerted on the tennis ball and medicine ball is zero in both cases. However the length of the arrows in the medicine ball case are larger. e) The tennis ball is also in equilibrium since we are holding it still. F hand on tennis ball = -F on tennis ball F hand on tennis ball + F on tennis ball = Observe and Explain Results will vary for first two columns depending on equipment. Air on object effect negligible Experiment Draw a List Draw a Discuss what objects Write a picture of objects force exert forces balancing mathematical the interacting diagram the force that expression for apparatus. with the for the exerts on the object. the forces What is/are the exerted on the object of object. direction of the object. Specify interest. balancing your axis. force/forces? (a) Hang an object from a spring scale. Record reading of the scale here 10g Spring F SSonO The Spring Scale pulls up balancing the downward pull of You could also say air pushes up slightly. F SSonO = -

3 PUM Physics II - Dynamics Lesson 1 Solutions Page 3 of 7 Experiment Draw a picture of the apparatus. List objects interacting with the object of interest. Draw a force diagram for the object. Discuss what objects exert forces balancing the force that exerts on the object. What is/are the direction of the balancing force/forces? Write a mathematical expression for the forces exerted on the object. Specify your axis. (b) Lower the object onto a platform scale so it touches the scale. Record new reading of the spring scale 7g Record the reading platform scale 3g Spring Platform F SSonO F PSonO The spring scale is pulling up and the platform scale is pushing up to balance F SSonO + F PSonO = - (c) Remove the spring scale and leave the object on the platform scale. Record new reading platform scale 10g Platform F PSonO The platform scale is pushing up to balance F PSonO = - (d) You place the object on a horizontal meter stick whose ends rest on two blocks. Record what happens The meter stick bends in the middle at first, but stops. Meter stick, F MSonO The middle part of the meter stick is pushing up on the block to balance the downward pull of F MSonO = - (e) You place the object on a thick, foam cushion. Record what happens The object sinks into the foam cushion at first but eventually stops. Foam cushion, F FConO The foam cushion under the object pushes up to balance F FConO = - (f) You place the object on a tabletop. Record what happens The object sits on the table. Table, F TonO The table pushes up on the object to balance the downward pull of F TonO = -

4 PUM Physics II - Dynamics Lesson 1 Solutions Page 4 of 7 (g) You place the block on the platform scale and then tilt the scale at a small angle. Record what happens The reading is less than if it is sitting upright. Platform The platform scale still has to push up on the object to balance. F PSonO = - However, the scale reads differently, meaning that something slightly different is going on with F PSonO. There could be different parts adding up to balance and only one of those parts is what is being read by the scale. a) It s the same way that I can use a meter stick to push another object. The meter stick is pushing on the other object since I am not interacting with the object directly. Another way to think about it is that the stuff inside the table is not letting the object through. So if is pulling down on the object then the stuff in the table must be pushing up to keep it from going through the table. b) Jim would say this because (almost) any book you put on the table is supported by the table. To argue the opposite, if you were to put too massive of a book on the table, the table may break and the book would fall therefore it is possible that the table cannot always exert the same magnitude force as the earth. 1.6 Reason F PSonO a) A supporting object will push or pull up opposite the direction that is pulling down on the object, provided that the object is sitting level on the supporting surface. b) The force of a supporting object is not always equal in magnitude or direction. If we put an excessively heavy object on top of a table, the table will eventually break and the object will no longer be in equilibrium, meaning that there is a limit to how much the table can push up. In terms of direction, if we tilt the platform scale then the scale reads less and eventually slides off of the scale. This indicates that the surface of the platform kind of exerts two forces, one perpendicular to the surface, the other horizontal to the surface. The former keeps the object from going through the platform scale, while the latter keeps the object from sliding off initially. c) If you dragged the box on the carpet, the force of the rope on the box would be larger because you would need to pull harder to move it. You could put another horizontal arrow to show that the carpet is pulling back on the object as well.

5 PUM Physics II - Dynamics Lesson 1 Solutions Page 5 of Reason Without switching our axis and calling horizontal vertical (because then we could just look at an object sitting on a table!) the only time this could really happen is if was not there and we were to pull an object across a rough surface. Sketch: Force Diagram: F rope on object F surface on object 1.8 Represent and Reason a) Forces in the vertical direction balance. However the force in the horizontal direction is not balanced. b) The unbalanced force is to the right. This seems reasonable since the direction of the unbalanced force is the direction in which the person is also pushing the box and the direction that the box is moving. 1.9 Represent and Reason Represent and Reason a) i. ii. iii. iv. F ice on puck F ice on puck F plane on box F hand on SC F water on boat F on puck F earth on box F on SC F on boat v. vi. F on sled F me on sled F grass on mower F on mower F land on mower i. Unbalanced force is to the left. ii. Unbalanced force is in the direction that the box is sliding down. iii. Un balanced force is up. iv. Forces are balanced. F me on mower

6 PUM Physics II - Dynamics Lesson 1 Solutions Page 6 of 7 v. Forces are balanced. vi. Unbalanced force is to the right. b) The force diagram on the left could represent a suitcase that you lift only slightly so that the suitcase still rests on the ground. The force diagram on the left could be a sled being pulled across the snow, speeding up. F you on SC F ground on SC F me on sled F on SC F on sled 1.11 Reason (d), floor, and you; pulls down (not gravity, since gravity is not an object), the floor pushes up, and you push down on the chair Represent and Reason a) Since the ball is steady the forces must be balanced. In b) the force of the hand on the ball is bigger than on the ball. In e) the arrows are not connected to the dot object properly. F H on B F E on B 1.13 Estimate Uncertainty It is impossible to know who is correct because the spring scale does not read precisely to the tenth of a Newton. It is only possible to read to half of the smallest increment, in this case 0.5 Newton. Rob and Tina could say that it either weight 2 N or 2.5 N, but no more precisely Estimate Uncertainty Bathroom Scale Force of person on the scale, measured in pounds, smallest unit is a tenth of a pound, but it is difficult to read in between these markings. a) Experimental uncertainty is ±0.1 pound b) 125 ± 0.1 lbs Measuring cup Volume, measured in cups, smallest unit is half a cup. a) Experimental uncertainty is ±0.25 cups b) 2 ± 0.25 cups

7 PUM Physics II - Dynamics Lesson 1 Solutions Page 7 of 7 Thermometer temperature, measured in F, smallest unit is a single degree. a) Experimental uncertainty is ± 0.5 F b) 70 ± 0.5 F 1.15 Estimate Uncertainty Average time: (1.11 s s s)/3 = 1.12 s Random uncertainty: ±0.02 t = 1.12 ±0.02 s 1.16 Significant Figures Jake is likely to get more per month since he says he gets $15 give or take a dollar. However Robin is more precise with 4 significant figures, so she gets exactly $15.00.