Physics Lab Final
Suppose you lay a book on your desk and push horizontally on it with 5 N of force which causes it to slide across the desk at constant velocity. What is the magnitude of the friction force acting on the book?
5 N
A block attached to a spring undergoes simple harmonic motion. When the block passes through the equilibrium position, which of the following statements about it are true? True: The block's acceleration is zero The elastic potential energy of the spring is zero The block's kinetic energy is a maximum Not true: The block's speed is zero The total mechanical energy of the block-spring system is zero
A block attached to a spring undergoes simple harmonic motion. When the block passes through the equilibrium position, which of the following statements about it are true? True: The block's acceleration is zero The elastic potential energy of the spring is zero The block's kinetic energy is a maximum Not true: The block's speed is zero The total mechanical energy of the block-spring system is zero
Look again at Hooke's Law (Eqn. 1). What does the slope of the graph of F vs. x represent?
According to Hooke's Law, the slope of the graph of F vs x represents the spring constant, which is k. This is derived from Hooke's Law equation that states F = -kx.
As the hanging mass m2 is falling towards the ground, many people would guess that the tension in the string decreases, but this is incorrect! In fact, the tension remains constant over time. Prove that the tension remains constant over time as the mass is falling using Newton's 2nd Law. To do this, draw a free body diagram of the hanging mass and note there are two forces acting on it: the tension and the force of gravity. Then use this to write out Newton's 2nd Law for the hanging mass and explain how this shows that the tension is constant given that the acceleration is constant.
According to Newton's second law, the hanging mass equation is ma = T - mg, where tension is = ma + mg. Because the mass is unchanging, and g is a constant, as long as acceleration stays constant, none of the values are changing on descent of the hanging mass to the ground.
Was the value of μS you obtained reasonable? To support your answer, refer to the reported values here for a similar pair of materials noting that the block is wood.
According to our calculations using the derived equation above, μS can be calculated using tan(theta). The value obtained was 0.33. This is reasonable, but slightly lower than the theoretical value. According to the reported values, the static range should be around 0.4-0.6. However, our value was 0.33. It fell within the range for dynamic friction, which is 0.2-0.4.
Figure 2 is a graph of the empirical cumulative distribution function (CDF) vs the linear acceleration for two different data sets (HITS and NFL). The CDF is the fraction of observations that are below the specified value on the x axis. For example, about 90 percent of the sub- concussive impacts in the HITS data (solid black line) occurred at accelerations below 50 g. According to the NFL data set, what was the highest acceleration experienced that did not cause a concussion? What was the minimum acceleration that did cause a concussion?
According to the NFL data set, the highest acceleration experienced that did not cause a concussion was 100g. The minimum acceleration that did cause a concussion was just below 50g.
Our results support the idea that an object's natural vibration frequency depends on properties intrinsic to the system itself (like k and m) but is independent of the external force the creates the vibration in the first place. Based on this fact, how does the natural frequency of vibration of a 1 m^3 block of lead compare to that for 1 m^3 block of aluminum? Assume the atoms are a lattice connected by springs (shown at right), and that the stiffness of the bonds between neighboring atoms is the same for aluminum as for lead. Hint: look at the relative masses of these two elements on the periodic table.
As seen in equation two, mass and frequency are inversely proportional. Since the block of lead and the block of aluminum have the same volume (1 m^3), the frequency will depend on which of the two elements has the lower molar mass. The element with the lower molar mass will yield the higher frequency, because mass and frequency are inversely proportional. The literature molar mass of lead is 207.2 g/mol, while the literature molar mass of aluminum is about 27g/mol². So, aluminum has a lower molar mass and therefore a greater natural frequency of vibration.
What is the time value when the ball in your video is at its maximum height?
At the maximum height of 0.53 meters, the time value is 3.130 seconds.
Imagine a large truck collides with a much less massive shopping cart. Which of the two has a greater force acting on it?
Both the large truck and the shopping cart have equal forces acting on it. This is proved by Newton's Third Law of Motion, which explains that the forces applied on each other are equal. Essentially, the truck exerts the same amount of force on the cart as the cart exerts on the truck.
Compare the trends in the data in your three plots. In which of the plots, position, velocity, or acceleration,does the value increase linearly with time? In which, if any, is the trend nonlinear? Did any of the plots show a constant value over time?
Both velocity and acceleration were linear plots, but only velocity increased linearly over time. The position plot was not linear over time, but rather the graph curved. While acceleration was linear, it did not increase. It was a constant value over time.
Use the expressions for Win air and Win water from the figure above to show that the buoyant force is equal to the difference between the weight in air and the weight in water. Show your work.
Due to the fact that the object does not move up or down in water, the net force in the y-direction is 0, and the following equation can be used: -mg + FB + T = 0 FB = mg - T (Win air) FB = Win air - Win water
Both barbells have the same total mass, so what is it about Barbell 2 that makes it difficult to move quickly?
Even though both barbells have the same mass, barbell 2 is more difficult to move quickly than barbell 1 because barbell 2 has a higher moment of inertia than barbell 1. Barbell 1 has a lower moment of inertia due to the fact that the masses are located at the center of the rod. The distance value is less in barbell one than barbell two, and the moment of inertia is directly proportional to "r", which is the distance from the center of the mass. This leads to barbell 1 needing a lower moment of inertia to move, thus making it easier to move quickly than barbell 2.
Did the cart travel the same distance from one interval to the next? Use your data to support your statement.
For intervals 2, 3, and 4, the cart all traveled 0.064 meters from one interval to the next. Intervals 1, 5, and 6 were close to that value, but not quite the same, as they traveled 0.073 meters, 0.065 meters , and 0.061 meters respectively.
Angle in radians is often an unfamiliar unit, so let's gain more familiarity by looking at our graph of radians vs. time. About how many radians did your cube move through from start to finish of your tracking? Check for internal consistency: How many radians are there in a circle? Is the number you are reporting reasonable?
From start to finish, the cube moved about 3.35 radians on the smooth surface. The cube moved 4.49 radians on the frictional surface. There are 2π (about 6.28) radians in a circle, so the numbers that we are reporting are reasonable. This is because the data was collected during part of the circular motion, but not during an entire period.
If you were a tightrope walker, which barbell would you rather be carrying?
If I were a tightrope walker, I would rather carry barbell two. As explained in question 1, barbell two has a higher moment of inertia, so it is more difficult to move barbell 2 compared to barbell one. Therefore, this would be ideal in a situation requiring balance.
How would your calculation and for this experiment change if the pulse and echo traveled through human tissue instead of air? To answer this, assume the distance stays the same and look up how the speed of sound in tissue such as bone or muscle compares to that in air.
If pulse and echo traveled through human tissue instead of air, the speed at which the sound waves in the experiment traveled would be altered. The speed of sound in muscle² is about 1588 m/s, while the speed of sound in air is 343 m/s. Clearly, sound travels much faster through muscle than it does through air. If pulse and echo had to travel through muscle and bone, then the pulse would travel faster, and therefore the time that the pulse would take to travel would be shorter. Therefore, the frequency would be higher.
What change, if any do you expect in the frequency of vibration if we increase the mass on the spring? Hint: see Equation 2.
If the mass on the spring is increased, the frequency of vibration should decrease. This can be observed in the equation below. In this equation, m is mass, and f is frequency.These two values are inversely proportional, meaning that as one increases, the other decreases. Therefore, it can be concluded that if mass is increased, frequency of vibration should decrease. This was supported by the results. As shown in the results table, the frequency decreased each time an additional 50g was added to the hanger. For example, when the mass was 100g, the frequency was 1.02 Hz. When the mass was increased to 150g, the frequency ranged from 0.901-0.910 Hz.
If you were to double the mass, but halve the radius of one of the barbells, how would the moment of inertia compare to the original value?
If the mass was doubled and the radius of one of the barbells was halved, the moment of inertia would be half of the original value. This is because: Moment of Inertia (original): 2mr2 Moment of Inertia (after doubling mass and halving radius): 2(2m)(½ r)2 =mr2 This value is half of the original.
How can the trend of the data on the chart allow you to conclude whether you observed motion with constant speed?
If the slope is equal to the instantaneous speed, it can be concluded that the cart moved at a constant speed. This is because the slope represents the average speed of motion, and when an object moves with constant speed its average speed and instantaneous speed are equal.
It's very likely that the actual acceleration of the cart was less than the theoretical value you calculate. Do you think including friction in our theoretical analysis would bring our predicted value more in line with the actual value we measured or would including friction make our theoretical value even farther from what we measured? A brief qualitative answer is all that's needed here.
In our theoretical analysis, friction would bring our predicted value more in line with the actual value. This is because this is a force working in the opposite direction, so it would lower our net acceleration.
In the experiment diagrammed above, how far does the pulse travel between the time it leaves the fingers and returns to the microphone? Answer in terms of the distance L.
In the diagram, the pulse travels a distance of 2(L). This is because the pulse has to travel all the way to the wall from the microphone and then all the way back, as it bounces off the closed tube. The distance (L) in the diagram is about 0.35 meters, so the pulse would travel 2(L)=2(0.35)= 0.7 meters.
Recall that for translational motion it takes more force to accelerate a larger mass, which is explained by Newton's 2nd Law: 𝐹 = 𝑚𝑎. This law also holds in rotation form: 𝜏 = 𝐼𝛼. In the rotational version of the law, force is replaced by torque 𝜏, and acceleration is replaced by angular acceleration 𝛼; what takes the place of mass?
In the rotational form of this law, the mass in Newton's second law is replaced by 𝐼, which is the moment of inertia.
How close is your value to the accepted value for the speed of sound in air? Refer to the percent difference.
In this experiment, the accepted value for the speed of sound of air¹ is 343 m/s. The experimental value for the speed of sound of air was 376.2 m/s. Therefore, there was a percent error of 9.7%. This was calculated using the percent error equation, which is (accepted value-experimental value) / (accepted value), and this is multiplied by 100%.
When trying to stop a car on icy pavement in as short a distance as possible, is it better to slam on the brakes and skid to a stop or apply the brakes more gently and roll to a stop? (Hint: What type of friction is acting between your tires and the roadway if your tires are sliding along the road? What if your tires are rolling along the road?) Briefly explain.
In this scenario, it would be better to apply the brakes more gently and roll to a stop. This is because if you were to slam on the brakes, the wheels lock and the tires are sliding along the road, and the friction in this situation would be kinetic friction. On the other hand, if the brake is applied gently, the friction in question is static friction as the tires are still rolling. Static friction is greater than kinetic friction because it generally takes greater force to start an object's motion than to keep it in motion.
The total buoyant force acting on both objects is simply the sum of the buoyant force on each individual object: FB, total = FB, wood + FB, slug. Explain why this is true using the fact that the buoyant force is due to the volume of the fluid displaced.
It is true that the total buoyant force acting on both objects is the sum of the buoyant force on each individual object due to Archimedes principle, which states that the buoyant force is equal to the weight of the displaced fluid. In this experiment, two objects were submerged in water, and the volume of each occupied an individual displaced volume. Thus, the total force of buoyancy on each object is impacted by the force generated by the other in the system.
When the cube falls off the edge of the turntable, which path will it take according to Newton's 1st Law? Use the figure at right showing the top-down view of the turntable to select a path A through E. Consider the horizontal plane only (not vertical motion).
It will follow path B. According to Newton's 1st law, an object in motion continues its constant motion in a straight line unless acted upon by an unbalanced force. When the net force exceeds the static friction, the cube falls off the edge of the turntable and continues in a straight line tangential to the point of circular motion at which it fell off (path B).
Which of Newton's Laws is explored in Part III of this lab?
Newton's Third Law of Motion is explored in Part III of this lab. This law states that when two objects interact, they apply forces to each other of equal magnitude and opposite direction. In this part of the experiment, one cart was pushed into the other to explore what forces the two carts applied on one other.
Which of Newton's Laws describes the hover puck's motion in region A?
Newton's first law of motion describes the hover puck's motion in region A, as it describes an object at rest will stay at rest until acted on by a force. In region A, the puck had not been pushed yet.
Which of Newton's Laws describes the hover puck's motion in region C?
Newton's first law of motion describes the hover puck's motion in region C, as it describes that an object in motion will remain in constant motion unless acted on by a force. In region C, the puck was moving freely in constant motion.
How can Newton's 3rd law be used to explain why the weight of the block is equal to the normal force acting on the block?
Newton's third law states that forces act in equal magnitude but opposite directions. If no force is applied to the block as it sits on the flat surface, it is exerting a downward force (its weight) equal to the block's mg (mass x acceleration due to gravity). Given Newton's third law, the flat surface must exert an equal force back on the block. Thus, the FN (normal force exerted on the block by the flat surface) is equal to the weight of the block in the opposite direction.
How can one find the pulling speed using the dots? Briefly describe using the definition of speed.
One can find the pulling speed using the dots by calculating the distance from the first dot to the last dot, and then dividing that value by the time it took to pull the tape through. The time was determined with the understanding that the dots were sparked every 0.1sec (10 Hz). This is because speed is defined by the distance traveled over time, traditionally in meters/second.
How does the pressure vary with depth? Support your claims with your results.
Overall, pressure and depth have a direct relationship; as depth increases, pressure increases, and vice versa. This was observed in most of the results of the experiment—from 5cm deep to 10cm deep, the pressure increased from 0.054288kPa to 0.055298kPa. From 20cm deep to 25cm deep, the pressure increased from 0.05437kPa to 0.05865kPa. However, from 15 cm to 20 cm, the pressure decreased from 0.05872kPa to 0.05437, which is an outlier value. This direct relationship was observed in almost each interval of the experiment.
The fit line is a way of incorporating all data into a single best estimate of the acceleration. Let's compare this to the instantaneous acceleration calculated at each moment. Look in the acceleration column your Capstone data table, these are the instantaneous acceleration values. How are the instantaneous acceleration values similar or different to the single acceleration value obtainedfrom the best-fit line?
Overall, the instantaneous acceleration values were similar to the single acceleration value obtained from the best-fit line. The instantaneous acceleration values ranged from 0.144m/s2 to 0.198m/s2, with most of the values being in the 0.160-0.170 m/s2 range. The single acceleration value was 0.173 m/s2. Although there was some range in values, the two are similar, which is expected since the best-fit line tries to minimize the distance between the line itself and all the data points.
How does one obtain the acceleration value from the linear fit of a graph of velocity vs time?(Refer to your textbook if necessary.)
The acceleration can be found from a graph of velocity vs time as the slope of the line of linear fit. This is because acceleration is the rate of change between velocity and time.
How does the duration (i.e., the time scale) of the impact differ between the two cases (with vs without the helmet)?
The average duration of the impact with the helmet was 0.042 seconds. The average duration of the impact without the helmet was 0.0727 seconds. Overall, the average duration of impact was greater in the trials conducted without a helmet.
Compare the average impulse from the trials with the helmet to those without the helmet. Was there a significant difference (more than about 20 %) in the average impulse between the two conditions? Was there a significant difference in the average maximum force between the two? It has been shown that higher accelerations of the head cause concussions, does your data support the common assertion that helmets help prevent concussions? Support your answer.
The average impulse from the trials with the helmet was 0.06705 Ns. The average impulse from the trials without the helmet was 0.1956 Ns. The percent difference between these values is 97.9%, which is a significant difference. The percent difference between the average maximum forces was about 113%, which is also a significant difference. Our data does support the idea that helmets prevent concussions— since acceleration and force are directly proportional (due to Newton's second law), greater force means greater acceleration. In this experiment, the trials with the greatest maximum force, impulse, and duration of impact were the ones without a helmet.
If an object moves at a constant speed, then its instantaneous speed at any given moment is the same as its average speed. Thinking about the speed of the cart during the entire 6-second trip, was the average speed equal to any interval's instantaneous speed? Explain your reasoning.
The average speed was 0.065 meters per second, and this matches with interval 5's instantaneous speed. It does not align with all of them, likely due to human error, as well as the limited accuracy of the instrument. For instance, interval one was 0.073, which was greater than all of the intervals, likely due to error in moving around the cart and tape before starting to ensure that the cart remained within the provided experimental space.
If they have the same radius and same mass, how will the moments of inertia of a solid disk and a bicycle wheel compare?
The bicycle wheel will have a greater moment of inertia.
Did the cart's instantaneous speed change from one interval to the next? Support your answer using your data.
The cart's instantaneous speed was the same for intervals 2, 3, and 4, as the cart traveled 0.064 meters/second from one interval to the next. Intervals 1, 5, and 6 were close to that value, but not quite the same, as they traveled 0.073 meters/second, 0.065 meters/second, and 0.061 meters/second respectively.
Do you think the metal is gold? To answer this, use a reliable online resource to look up the density of gold and other common metals. If you don't think your metal is gold, what is it likely to be? Use your data to support your answer.
The density of gold is about 19.32 g/cm3 at room temperature₁. The density obtained in this experiment was 9.05 g/cm3, so the metal was clearly not gold. However, it is possible that the metal was made out of erbium₂, which has a literature density of 9.07g/cm3.
Is the value of the density of the wood you found greater than or less than that of water? When fully submerged, how does the buoyant force acting on the wood compare to the gravitational force acting on the wood? Does this explain why it floats to the surface when not weighted down?
The density of water is about 1g/cm3, while the value of the density of the wood was 0.12 g/cm3 . When fully submerged, the buoyant force acting on the wood is greater than the gravitational force acting on the wood. This is because wood is less dense than water, and so it floats in water. Because of this, wood displaces a magnitude of water greater than the actual weight of the wood, and therefore the wood floats because the buoyant force is greater than the gravitational force.
What simplified expression did you obtain for the coefficient of friction? Does the expression depend on the mass of the cube? Using the expression you obtained, use Excel to calculate 𝜇ₛ for both the rough and smooth surfaces. Include the results of this calculation with your values for tangential velocity and radius in a table for your report.
The equation for the force of friction is derived from the equation for net force on the object. FNet = FC = mv2/r = FFRS, because when the object is not sliding on the turntable, the force of static friction is equal to the centripetal force. FFRS, the force of static friction is = µSFN, where µS is coefficient of static friction and FN is normal force. Thus, µS = (mv2/r) / mg. This expression does not depend on the mass of the cube, so µS = v2/rg.
What force or forces are acting on the cube as it rotates in a circle at constant speed? Draw a free body diagram for the cube as seen from the side. On your diagram, indicate the direction of the force(s) acting on the cube.
The forces acting on the rotating cube are normal force (FN), force of gravity (mg), centripetal force (FR), and the force of static friction (FFRS). Fn up, Fg down, FR in, Ffr in CORRECTION: centripetal and friction act along the same direction
Which general kinematic equation is most like the fit equation for the x position vs time? Which kinematic equation is most like the fit equation for the y position vs time?
The general kinematic equation most like the fit equation for the x position vs time would be x = x0 + v0t + ½at2. The same equation would be best fit for the y position vs time, except the y coordinates replace the x coordinates and the velocities in the y direction replace the velocities in the y direction: y = y0 + v0t + ½at2.
Calculate the linear acceleration of the cart from Part I using the trial with the highest force value you recorded. To do this, assume the cart has a mass of 0.2 kg and use Newton's 2nd Law to find the acceleration. Then Using this value of linear acceleration in g's refer to Figure 1 to determine the rotational acceleration that would have to occur for a 1% chance of concussion in your experiment.
The greatest force recorded was Fmax = 9.8711 N (Without Helmet, Trial #3). Using Newton's second law F = ma, where mass is 0.2kg, acceleration = 50m/s2 or 50g. From Figure 1, the rotational acceleration that would occur for a 1% chance of concussion in this experiment would be 4250 rad/s2.
Look up the hydrostatic pressure equation. According to the equation, what physical quantities are represented by the slope and y-intercept of the plot? What should the value of the slope and y-intercept be?
The hydrostatic pressure equation is ρ = Po + (p*g*h), where: Po = atmospheric pressure Ρ = pressure at point inside the fluid ρ = density of water g = gravitational constant h = depth According to the equation, the slope would be represented by the value p*g, which is the value given by multiplying density by the gravitational constant. The y-intercept would be represented by the value Po, which represents the atmospheric pressure.
How can the hypothesis for this lab be tested experimentally? In a few sentences, describe at least one way to test the hypothesis experimentally by using the rough and smooth surfaces available on the turntable.
The hypothesis for this lab could be tested experimentally by placing an object on 2 different surfaces: one rough (sandpaper) and one smooth (plastic). Then, the voltage at which the cube flew off of the surface was obtained, and the difference in these values between the two types of surfaces would be compared. The movement of the object would then be tracked using a computer program, and the radius was obtained. Finally, the tangential velocity at the point when the cube flies off the turntable would be acquired from the graph. The angle (in radians) of the centripetal motion would also be attained.
What is the maximum acceleration of the system if you were to hang an infinitely large mass from the string? Hint: plug 1000 kg in for m2 and 1 kg in for m1. (It may seem surprising that large hanging masses don't translate into large accelerations but remember gravity is providing the downward force!)
The maximum acceleration of the system if you were to hang an infinitely large mass will be -9.8 m/s2, which is the acceleration by gravity. This can be shown in calculation using Fy = (m1 + m2)a = m2g, which when substituted with values becomes (1+1000)(a) = 1000(-9.8). Here, the acceleration calculates to -9.79 m/s2 which is very close to -9.8 m/s2, our known value for g or gravity's force. This is because gravity is the downward force on the system.
When an object moves in a circular path at constant speed, which of the following best describes the net force acting on the object?
The net force acting on the object acts toward the center of the circle. It is possible for circular motion to be caused by a single force but it can also be caused by the net effect of several forces.
How many times per second should you hear a beat? Does the beat frequency you hear seem to agree with this calculated value?
The number of beats per second heard should correspond to the frequency of the beat. The beat frequency calculated, 7 Hz, suggests that 7 beats per second should be heard, and this agrees with the calculated value (500.0 - 493.0 = 7.0 Hz).
One person tosses a ball to another. Define the positive y-direction as vertically upward and the positive x-direction as left to right. Which choice best describes how a plot of the ball's x-component of velocity vs. time will appear? lgnore drag.
The plot will be a horizontal line indicating that the speed in the x-direction is constant over time.
What quantity is represented by the area under the curve in a graph of force vs. time?
The quantity represented by the area under the curve in a graph of force vs. time is impulse, which is also known as the change in an object's momentum.
What does the value of the slope represent in our graphs of velocity vs. time?
The slope in our graphs of velocity vs. time represents the acceleration, which was -3.54 m/s2 for graph 1, -4.66 m/s2 for graph 2, and -2.62 m/s2 for graph 3.
What is the x-acceleration according to your graph and fit of the x-velocity data? What would we expect it to be in this scenario according to the assumption that we have no forces in the x-direction?
The x acceleration according to our graph and fit of x-velocity versus time data is -5.54 m/s2. However, we would expect this value to be zero. There should have been no x acceleration, as the ball is being thrown up, and therefore only impacted by the y acceleration of gravity. There is no acceleration applied in the x direction.
Another group has hypothesized that adding 100 g extra mass to the center of the barbell where the hand is placed would have no effect on the ability of the person to rotate the barbell back and forth. Do you agree or disagree? Why?
We agree with this group. If 100 g of extra mass is added to the center of the barbell, the moment of inertia of the extra added mass would equal zero. Since the extra mass is added to the center of the barbell, the radius is zero, so it does not contribute to the moment of inertia.
One source of error in this experiment is that we ignored the effect of drag. In fact, the magnitude of the drag force is proportional to the speed of the ball. In light of this fact, is it safe to assume the magnitude of the drag force on the ball is the same at all points on its trajectory? Support your answer with your reasoning.
We cannot assume the magnitude of drag force of the ball is the same at all points. This is because the speed is not consistent at all times-for instance, while traveling upwards, the velocity decreases and while free falling velocity increases. As drag is proportional to the speed of the ball, it will vary just as the speed does as a result of acceleration.
Why do we need to use a quick sound like a finger snap for this experiment? For example, bats make a very short duration clicking sound for their ultrasonic sensing. Why does this work better than perhaps a slower sound like a squeak? To answer, refer to the duration of the pulse peak and echo peak shown in your graph.
We need to use a quick sound like a finger snap for this experiment because in order for this experiment to be successful, the sound needs to be able to be distinguished from the rest of the graph. Since the sound was quick, it yielded a sharp peak on the voltage graph, which was easily identified. However, if a slower sound like a squeak was used, it would yield a more rounded peak, and it would be more difficult to obtain the pulse peak. The duration of the pulse peak from our experiment was 5.8*10-4 seconds, and the duration of the echo peak from the experiment was 1.1*10-3. So, the duration of the pulse peak is faster than the duration of the echo peak.
How did the angular acceleration change with the new moment of inertia? Was your prediction correct?
When calculating the angular acceleration, we used the equation torque = Iα. The torque was found using information from the radius of the pulley, mass of the hanger, and the gravity (T = mhanger* g * rpulley). This was a constant value of 6.6*10-4 N*m. Once this was established, we evaluated how the angular acceleration changed as per different moments of inertia. The first moment of inertia was for the spheres being in the outer radius: 2.8*10-4, and the second moment of inertia was for the spheres being in the inner radius: 9.4*10-5. Using the aforementioned equation, the moment of inertia is inversely proportional to the angular acceleration. Therefore, we predicted the angular acceleration for the outer sphere (bigger moment of inertia) was predicted to be smaller than the angular acceleration for the inner sphere (smaller moment of inertia). This was supported by the numbers we found via calculations: the angular acceleration for the outer sphere was 2.36 rad/s2, while the angular acceleration for the inner sphere was 7.02 rad/s2.
When moving at constant speed how does the magnitude and direction of the friction force compare to that of the force you apply to the block?
When moving at a constant speed, the magnitude of the friction force is the same as the applied force, but the direction is the opposite.
When the person experiences a rotational acceleration of 7000 rad/s2, what value of linear acceleration in g's would result in a 5 % chance of concussion? What linear acceleration causes a 5% chance of concussion when the rotational value is lowered slightly to 6000 rad/s2?
When the person experiences a rotational acceleration of 7000 rad/s2, the value of linear acceleration that results in a 5% chance of concussion is 40g. A linear acceleration of 60g would cause a 5% chance of concussion when the rotational value is lowered slightly to 6000 rad/s2.
Why is the angle to get the block to start sliding larger than the angle to get the block to stop sliding? Referring to the graph in the figure below may help you.
When trying to get the block to start sliding, static friction is in play, since the object is at rest and we are trying to get it in motion. When trying to get the block to stop sliding, kinetic friction is in play because the object is moving and we are trying to get it to stop. Static friction is greater than kinetic friction, which results in the angle to get the block to start sliding being larger than the angle to get the block to stop sliding
Toggle between your runs. Do you notice a decrease of the amplitude among the three runs? When left to oscillate, the amplitude will slowly decrease over time. Explain why this might occur.
When you toggle from one run to the next, a decrease of the amplitude among the three runs can be observed; this is most likely due to air resistance. Amplitude of motion¹ is defined as the "reflection of the quantity of energy possessed by the vibrating object". The mass started with a high amplitude, as it had a lot of energy. However, as time progressed, energy was lost due to air resistance and subsequently, the amplitude decreased. This loss in energy is known as damping. In addition, friction contributed to this decrease in amplitude—this is because the friction force opposed the motion of the oscillation, therefore decreasing amplitude. If the system was left to oscillate for a long enough period of time, the amplitude would eventually be zero because the energy would keep decreasing.
When you toggle from one run to the next you will notice the position trace may shift to the left or right. Why does this occur?
When you toggle from one run to the next, the position trace did shift slightly to the left and right. This is because here, oscillatory motion is taking place. Since the external force on the spring is not exact, some horizontal motion will be observed. As the mass moves, the spring moves from a state of equilibrium to a state of maximum displacement, leading to the position trace shifting left and right. -PHASE SHIFT
Is the frequency about the same for your three runs? Present them in a table for your report.
Yes, the frequency is exactly the same for each of the three runs with an additional weight of 100g on the hanger. Run Frequency Run 1 1.02 Run 2 1.02 Run 3 1.02
Is the slope value (the number m in y = mx+b) from the equation within about 10% of the value of average speed calculated in Step d? Would you expect these two values to be similar? Why or why not?
Yes, the slope value is within 10% of the average speed. These values are expected to be similar as slope is a ratio between the change in y and the change in x. Here, the average speed is also a ratio between the speed and the time, which lines up with the slope calculation.
Is the time value when the ball in your video has zero y-velocity the same as the time value for when it is at maximum height? Would you expect them to be the same? Explain why or why not.
Yes, the time value for when the ball has zero y velocity is the same time value as maximum height, 3.130 seconds. This makes sense because at y maximum, there is no velocity due to the ball no longer going upwards, and also because Vy initial = = -Vy final
Compare your two tapes, the one done manually vs. that done by the cart. How can you determine by looking at the spacing of the dots whether the cart was moving at a constant speed? Support your answer in one or two sentences with your observations.
You can determine by looking at the spacing of the dots if the speed is constant by evaluating if the distance between all the dots are consistent. The cart was moving at a constant speed, as the dots were evenly spaced. However, the tape that was pulled through had varying distances between the dots, and therefore we concluded it was not pulled at a constant speed.
For the y-velocity vs time graph, how do you find the y-acceleration from the fit? What is the acceleration expected to be for such an object in free fall?
You can find the y-acceleration by looking at the slope from the y-velocity versus time graph. This is because acceleration is the rate of change of velocity over time. The expected acceleration for a ball in free fall is -9.8 m/s2 (acceleration caused by gravity) because the ball was moving in the negative y direction.
How could you prove to a skeptic that the beats are an interference effect that requires both sound sources? Test out your method to convince yourself that the beats require both sound sources and it is not a trick caused by one source alone.
You could prove to a skeptic that the beats are an interference effect that requires both sound sources because generally, destructive interference cannot be observed unless the amplitude of the superimposed wave is zero. In order for this condition to be met, a second source of sound has to be present in order to create another wave that overlaps with the first wave. This will cause both destructive and constructive interference.
When we hear beats produced by combining two sounds, we are hearing an example of
constructive and destructive interference
The well-known constant g is equal to 9.8 m/s2. This means that when you are standing on the surface of the Earth and holding a ball stationary in your hand, the ball has a constant acceleration of 9.8 m/s2.
false
The impulse is a useful metric for determining the likelihood of a concussion occurring in a particular collision. The impulse on an object in a collision can be written two ways: as the change in _________________ and of the object, or as the product of the ___________________ of the collision.
momentum force on the object and duration
The speed of an object can be found from the slope of a plot of plot of its
position vs time
Observe the figure below showing the force of friction on the y-axis, and the applied force on the x-axis. Indicate on the graph the following points Some amount of force is applied but the box remains stationary. Increasing the force slightly does not make the box move. (1) No force is applied. The box is stationary. (2) Enough force is being applied that the box is moving. (3) Some amount of force is applied but the box remains stationary. Increasing the force slightly causes the box to start moving. (4)
see doc
Show that one can find the density of the unknown object by dividing its weight by the buoyant force. To do this, use the following substitutions. Show your work.
see doc
Archimedes' Principle states that for any solid body immersed in a fluid, the buoyant force acting on it is equal to the __________ of the displaced fluid.
weight
