Tutorial includes complete laboratory (including methods and materials, experimental data, full explanations, and diagrams) with the following questions answered:
Experiment 1: Newton’s First Law
4. Record your observations for each type of motion from Step 4 in the space below. Comment on where the water tended to move. If it spilled, note which side it spilled from.
Questions
1. Explain how your observations of the water demonstrate Newton’s law of inertia.
2. Draw free body diagrams for the box of water from the situation in Procedure 4d. Draw arrows for all forces exerted on the box—this will include the force of gravity, the normal force (exerted by your hands), and the stopping force (also exerted by your hands). What is the direction of the acceleration of the box?
3. Describe two situations where you feel forces in a car in a particular direction. Explain these forces in terms of the car’s acceleration and your body’s inertia.
Experiment 2: Unbalanced Forces-Newton’s Second Law
Table 1: Motion Data
Trial Number Time (s) Trial Number Time (s) 1 6 2 7 3 8 4 9 5 10 Average Time:
Calculations
1. Find the average acceleration of the washers using the average time above and the measured distance (half the total string length) using the kinematics equations:
Questions
1. Which example(s) represent balanced forces acting on the objects? Which example(s) demonstrate unbalanced forces?
2. Draw a FBD for both sets of washers when you had 5 suspended on each side. Calculate and label the magnitude of all forces, taking the mass of each washer to be 3.5 g. Label the tension force from the string T (what direction does this always point?).
3. Write out Newton’s second law fore each mass depicted in your FBD. Calculate the acceleration of each mass and the tension (T) of the string.
4. Draw similar diagrams for the cases where the mass is uneven, again labeling all forces. Use m1 = 5 washers and m2 = 10 washers.
5. Write out a second law equation for each mass in this uneven case. Why must the accelerations be equal?
6. Combine the above equations to solve for the overall acceleration of both masses and the string tension (T).
7. Use this equation to find the acceleration for the washers in Procedure 2 (6 and 5 washers). Why can you use the arbitrary mass units of 6 washers and 5 washers instead of grams or kilograms and still calculate an acceleration in m/s2?
8. Are your results in accordance with your prior calculation? Find the percent error between your calculated (theoretical) and measured (actual) values.
Experiment 3: Action/Reaction Pairs
Questions
1. Describe the motion of the balloon and the container once the pressure became too great.
2. If you conducted this experiment in outer space, how would the test tube and balloon move?
3. Calculate the accelerations for a 10 g balloon and a 5 g test tube if the force of the chemical reaction is 0.05 N. What would the velocity of each object be if the reaction exerted this force for 2 seconds?
4. Explain what causes the recoil of a powerful rifle or cannon when a projectile is fired at high speeds. Calculate the force required to accelerate a 30 g bullet to a speed of 400 m/s in 0.0025 s.
Experiment 4: Accelerating Balloon
Questions
1. Explain what caused the balloon to move in terms of Newton’s Third Law.
2. What is the force pair in this experiment? Draw a Free Body Diagram (FBD) to represent the (unbalanced) forces on the balloon/straw combination.
3. Add some mass to the straw by taping some metal washers to the bottom and repeat the experiment. How does this change the motion of the assembly? How does this change the FBD?
Tutorial includes complete laboratory (including methods and materials, experimental data, full explanations, and diagrams) with the following questions answered:
Questions 1. If you were to throw a ball horizontally and at the same time drop an exact copy of the ball you threw, which ball would hit the ground first and why is this so?
2. What forces are acting on the marble before and after it leaves the ramp?
3. Describe the acceleration of a marble for the period after it leaves the ramp and before it hits the ground.
4. Did your prediction in Procedure 2 come close to the actual spot? Find the percent error of your predicted distance (expected) compared to the actual average distance (observed).
5. Explain some possible sources of error that could have produced the deviation above.
Experiment 2: Squeeze Rocket projectiles
Questions
Draw a FBD (free body diagram) (you can review free body diagrams in the Week 3 lecture) for a rocket flying at an arbitrary angle. Indicate the force vector due to gravity and force vector due to air resistance. Why does the direction of the net force change over the course of the rocket’s trajectory?Explain how the launch angle affects both the trajectory and final range of the rocket. What angle (or range of angles) appears to produce the greatest range?Knowing the kinematics equations, what angle should yield the greatest projectile range, disregarding air resistance and other factors? Show all calculations.How does air resistance affect the accuracy and precision of your rocket data in this lab?Calculate the percent error between your measured values and the predicted values. Given the nature of the squeeze rocket and your results, comment on any other sources of error that significantly affect your distance measurements.How would a kicker on a football team use his knowledge of physics to better his game? List some other sports or instances where this information would be useful.
1.Paste your graphs from Item 1 of the procedure here.
2.What is the average velocity that you found in Item 1?
3.What is the average acceleration that you found in Item 1?
4.Paste your graphs from Item 2 of the procedure here.
5.What is the major difference between the velocity data in Items 1 and 2?
6.Paste your graphs from Item 3 of the procedure here.
7.What were the average accelerations that you found from the straight line fits to the velocities?
8. What feature of your velocity graphs signifies that the motion of the cart is away from the sensor?
9.What feature of your velocity graphs signifies that the cart is speeding up?
10.Paste your graphs from Item 4 of the procedure here.
11.Is there a significant change in the velocity-time graph at the instant of closest approach?
12.Make a straight-line fit of the velocity-time graph. How does the average acceleration (slope) compare to the acceleration found in the previous item?
13.Paste your graphs from Item 5 of the procedure here.
14.Fill in the table below. Use a plus sign if the quantity is positive and a minus sign if it is negative.
How did the force required to move the door vary as you moved toward the hinges? How did the speed of the door change?Assuming you applied the same force at each position of the door; describe how the applied torque varied as you moved closer to the hinge.Assuming that the door is relatively thin, the moment of inertia will be the same as that of a rod rotating about an axis at its end.* If the mass of the door is 10 kg and its width is 1.5 m, find the angular acceleration of the door after applying a 50 N pushing force (about 10 lbs) at a) 1 m from the hinge, compared to b) 20 cm from the hinge.Explain why door handles are positioned where they are, and not closer to the hinges.
Experiment 2: Rotating Ruler
Questions
How much effort was required (approximately) to rotate the ruler when you reduced the end mass by a factor of two?Which clay setup produced the largest moment of inertia? The smallest? Explain why in terms of the relationship between torque and angular acceleration. Make sure to incorporate the distance from the axis of rotation in your answer.Estimate how much more clay you had to add in step 5 for the moment of inertia for each setup to appear the same.Use the information in Table 1 to show that it requires four times as much mass at half the distance from the center in order to produce the same moment of inertia. Assume the ruler mass is negligible.
Experiment 3: Static Lever
Table 1: Balancing force applied to lever at varying distance
Questions
How did the required force vary as R1increased?Determine the applied torque at each distance (make sure to use the correct distance!) to complete the above table. Comment on your results.How would you expect your data to change with an R2 value half of what you used above?Write an expression equating the torque applied by the spring scale and the mass. Rearrange this to create an expression for the applied force F in terms of R1, R2, the total mass m, and g.Make a plot of the force F vs. R2/R1 using the graph paper. Draw a line of best fit through your data, and measure the slope. m = _______________What does this slope value represent? Find the percent difference from the known value. (Hint: compare your expression from Question 4 with the general slope-intercept form y = mx +b.)
Lab 12: MomentumExperiment 12.1: Conservation of MomentumIn this experiment you will demonstrate transfers of momentum similar to those of the Newton’s Cradle toy pictured in Figure 12.1. Thevelocity of a marble after impact depends on the original velocity and the mass of the objects at hand.Procedure1. Fold a sheet of paper in half to create chute for your marbles to travel down.2. Line up four marbles in the center of the ruler, making sure they are all touching. Set up a barrier so that you can catch your marbleseasily when they leave the ruler.3. Hold the chute so that the end lies in the ruler’s groove, and let a marble go inside. You want the marble to exit the chute onto theruler groove and collide with the line of marbles you set up.4. Try angling the chute less or placing the marble closer to the ruler to decrease the speed of the collision, noting any difference in thevelocity of the marbles after collision.5. Increase the speed of the collision and see what happens.6. Finally, try dropping two marbles at once so that they hit the line as a pair.Questions1. When one marble hit the end of the line of marbles, how many shot off the other end? Explain why this happens, as opposed to morethan one shooting off.2. How did the speed of the marble that comes off the end of the line change as you increased the speed of themarble that travels down the chute? Use what you know about the conservation of momentum to describewhat is happening.3. What happened when you sent two marbles down the chute?4. Write down the total momentum for two marbles of mass m both moving at velocity v. What is the kinetic energy?5. When you drop two balls at once, why doesn’t only one marble come off the end twice as fast? Write down the kinetic energy of onemarble with mass m and velocity 2v and compare this to your answer in Question 4 to check. (Note that we are assuming the collisionsare perfectly elastic, when in reality this is an approximation.)Experiment 12.2: Egg DropWhen a fragile object is subject to a sudden acceleration, the strain on the material can cause it to break. By increasing the time anddistance over which an object accelerates or decelerates you can prevent damage that might occur otherwise, even if the total changein momentum is the same. In this lab you will attempt to decelerate a falling egg so that it does not break.Questions1. Did you come up with a design that prevents the egg from breaking?2. Why did adding layers of paper work better than one thick layer with the same number of sheets? (Hint: over how much time is theforce applied in each case?)3. What did you do to improve your apparatus?4. Explain how a circus net prevents trapeze artists from injuring themselves even after falling from a large height.5. Why it is important to bend your knees when you hit the ground after jumping from several feet in the air?
1. What happened to your applied force Fapp as you decreased the amount of water in the cup?
2. Assume the mass of the cup and water to be equal to the mass of water alone. Calculate the normal force FN for 300 g and 150 g. Use these values to complete the table above.
3. Why doesn’t the normal force FN depend on the cup material?
4. Right as the cup begins to slide the applied force is equal to the force of friction—draw a free body diagram for each type of cup (a total of three diagrams). Calculate and label the force due to gravity mg, the normal force FN, and the friction force Ff. What makes this a state of equilibrium?
5. What is the ratio of the applied force to the normal forceF1/FN1? Compare this to your values for F2/FN2. What can you conclude about the ratio between the normal force and the applied force of friction?
6. The ratio Ff/FN is called the coefficient of friction between the two materials in question. We can also write Ff = μFN with the Greek letter μ representing the coefficient of friction. Does it take more force to slide an object across a surface if there is a high value of μ or a low one?
Experiment 2: Velocity and Air Resistance
Questions
What are we assuming by using the average velocity from Procedure 1 to estimate the height of the fall in Procedure 2?Is the object actually traveling at the average speed over the duration of its fall? Where does the acceleration occur?Draw a free body diagram for a) the coffee filter right as it begins to fall (brief acceleration) and b) once the filter has reached terminal velocity (constant velocity).How do your measured and calculated values for the height in Procedure 2 compare? If they are significantly different, explain what you think caused the difference.Draw the FBD for the 2-filter combination falling at constant velocity. What is the magnitude of the force of air resistance in this case compared to with only one filter?How would the FBD differ for a round rubber ball dropped from the same height? How would the acceleration differ over the course of the fall?
1. What happened to the washers when you dropped the cup? How fast are they falling relative to the cup?
2. What force is keeping the water from accelerating downward while you hold the cup in place?
3. What forces are no longer present on the water while the cup is falling?
4. You have probably seen videos of astronauts moving in a “weightless” environment. Does this mean that gravity doesn’t exist in space? Explain.
Experiment 4.2: Distance of Free Fall tavg= _____________
Questions
1. What gives a falling object its acceleration?
2. What was the difference between the noise patterns produced by equally-spaced nuts compared to the second spacing given to you?
3. For the second nut spacing, show that the total distance from the end of string for each nut increases according to the linear kinematics equations.
4. Which of the weights had the highest velocity when hitting the cookie sheet? Calculate this velocity (in m/s) using the kinematics equations.
5. Using the time it took a single hex nut to reach the pan, calculate the height from which it was dropped. Is this accurate compared to your known height?
6. Say you have a very long string and want the hex nuts to hit the ground 1 second apart. Using the kinematics equations, determine the spacing for 5 nuts to hit with equal timing. How much string would you need?
7. Draw approximate plots for the single hex nut’s position, velocity, and acceleration vs. time. Label your axes and include approximate numerical values.
Experiment 4.3: Graphing linear motion
Questions (use Figure 7 to answer the questions below)
1. During which period(s) is the object traveling in a positive direction?
2. During which period(s) is the object traveling in a negative direction?
3. During which period(s) the object at rest?
4. During which period(s) is it traveling at constant velocity?
5. During which period(s) does it experience positive acceleration?
6. During which period(s) does it experience negative acceleration?
7. What are the magnitudes of the above accelerations? Draw a plot of the acceleration vs. time for this object using Figure 7.
Sketch and label what the arrangement of objects and liquids is in the beaker.Rank the liquids and solids in order of least to most dense.Which of the solid materials used in this experiment would make the best boat?Would it be easier to design a boat in a world with oceans of maple syrup? What property of maple syrup might prevent boats from traveling in it very effectively compared with in water?
Experiment 2: Principles of Moving Fluid
Questions
Why did the candle blow out in Procedure 1?Draw the air flow around the beaker and illustrate what happened to cause the candle to go out.What did you observe when blowing over the strip of paper in Procedure 2? Describe why this happens in terms of a) the pressure on each side of the strip, and b) the force exerted on the air by the strip surface.Would this experiment still work if the curved strip was made of a light but rigid (unbendable) material? Draw the direction of airflow over the top of a rigid, curved strip. Indicate the forces exerted on both the moving air and the strip material.
Experiment 3: Bernoulli’s Principle
Questions
What happened when you blew into the horizontal straw?Explain why this happens in terms of air velocity and pressure above and inside the vertical straw.Were you able to blow either index card off the table very easily in Procedure 3? Explain.
4. Describe what happens to the cards as the air moves underneath using Bernoulli’s principle.
Tutorial includes complete laboratory (including methods and materials, experimental data, full explanations, and diagrams) with the following questions answered:
Lab Exercise
Experiment 1: Balancing the Centripetal Force
Table 1: Period data for revolving washer with variable radius
Questions 1. If you suddenly cut the string connected to your rotating mass, what would be the direction of its velocity? Draw a diagram showing the direction of motion of an object just cut from a circular revolution.
2. How did the period of revolution change to account for a larger and smaller radius? How did the angular frequency change?
3. Draw a circle to represent the path taken by your rotating mass. Place a dot on the circle to represent your rotating washer. Add a straight line from the dot to the center of the circle, representing the radius of rotation (the string). Now label the direction of the tangential velocity, centripetal force, and the centrifugal “force.”
4. Use your data to find the average period for each radius. Use this and the rest of your data to calculate a) the average velocity of your spinning mass, b) its angular velocity in rad/sec, and c) the centripetal acceleration for each radius.
5. How is the centripetal force on the revolving washer related to the force of gravity on the hanging washers? Write an expression that equates the centripetal force Fc of the rotating mass to the force of gravity on the hanging mass. Write your expression in terms of m1 (revolving mass), m2 (hanging mass), T, R, and g.
6. What do you notice about your centripetal acceleration values in Question 4? Explain this result knowing the relationship between centripetal acceleration and centripetal force, given the experimental constant 4m1 = m2.
7. Solve your expression above for the period T in terms of R and g.
8. Plug in your radius values into this equation to find the expected frequency of rotation. Record these values in the table above. Were your experimental values close? How could you improve the experiment to reduce error?
9. Use the rotational kinematics equations to calculate the angular acceleration necessary to increase the angular velocity of your spinning mass from 10 rad/s to 20 rad/s in a time of 8 seconds.
Tutorial includes complete laboratory (including methods and materials, experimental data, full explanations, and diagrams) with the following questions answered: Experiment 1: Identifying the Center of Mass Questions
1. Explain why the figure below does not represent a realistic object and center of mass.
2. For most circumstances, the terms “center of mass” and “center of gravity” refer to the same point in space. Can you think of any situations where using the term “center of gravity” might not make sense?
3. Find the position of the center of mass in Figure 3 with the following information: m1 = m2 = 3 kg, m3 = 5 kg, x1 = 2 m, x2 = -2 m, x3= -3 m. Copy the figure below and draw in the center of mass as point CM.
4. Why is it important for the lemurs below (Figure 5) to have such long tails? What kind of environments are animals like these suited for?
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Tutorial includes complete laboratory (including methods and materials, experimental data, full explanations, and diagrams) with the following questions answered:
Experiment 1: Newton’s First Law
4. Record your observations for each type of motion from Step 4 in the space below. Comment on where the water tended to move. If it spilled, note which side it spilled from.
Questions
1. Explain how your observations of the water demonstrate Newton’s law of inertia.
2. Draw free body diagrams for the box of water from the situation in Procedure 4d. Draw arrows for all forces exerted on the box—this will include the force of gravity, the normal force (exerted by your hands), and the stopping force (also exerted by your hands). What is the direction of the acceleration of the box?
3. Describe two situations where you feel forces in a car in a particular direction. Explain these forces in terms of the car’s acceleration and your body’s inertia.
Experiment 2: Unbalanced Forces-Newton’s Second Law
Table 1: Motion Data
Trial Number Time (s) Trial Number Time (s)
1 6
2 7
3 8
4 9
5 10
Average Time:
Calculations
1. Find the average acceleration of the washers using the average time above and the measured distance (half the total string length) using the kinematics equations:
Questions
1. Which example(s) represent balanced forces acting on the objects? Which example(s) demonstrate unbalanced forces?
2. Draw a FBD for both sets of washers when you had 5 suspended on each side. Calculate and label the magnitude of all forces, taking the mass of each washer to be 3.5 g. Label the tension force from the string T (what direction does this always point?).
3. Write out Newton’s second law fore each mass depicted in your FBD. Calculate the acceleration of each mass and the tension (T) of the string.
4. Draw similar diagrams for the cases where the mass is uneven, again labeling all forces. Use m1 = 5 washers and m2 = 10 washers.
5. Write out a second law equation for each mass in this uneven case. Why must the accelerations be equal?
6. Combine the above equations to solve for the overall acceleration of both masses and the string tension (T).
7. Use this equation to find the acceleration for the washers in Procedure 2 (6 and 5 washers). Why can you use the arbitrary mass units of 6 washers and 5 washers instead of grams or kilograms and still calculate an acceleration in m/s2?
8. Are your results in accordance with your prior calculation? Find the percent error between your calculated (theoretical) and measured (actual) values.
Experiment 3: Action/Reaction Pairs
Questions
1. Describe the motion of the balloon and the container once the pressure became too great.
2. If you conducted this experiment in outer space, how would the test tube and balloon move?
3. Calculate the accelerations for a 10 g balloon and a 5 g test tube if the force of the chemical reaction is 0.05 N. What would the velocity of each object be if the reaction exerted this force for 2 seconds?
4. Explain what causes the recoil of a powerful rifle or cannon when a projectile is fired at high speeds. Calculate the force required to accelerate a 30 g bullet to a speed of 400 m/s in 0.0025 s.
Experiment 4: Accelerating Balloon
Questions
1. Explain what caused the balloon to move in terms of Newton’s Third Law.
2. What is the force pair in this experiment? Draw a Free Body Diagram (FBD) to represent the (unbalanced) forces on the balloon/straw combination.
3. Add some mass to the straw by taping some metal washers to the bottom and repeat the experiment. How does this change the motion of the assembly? How does this change the FBD?