Physics Lab Exam
How could you prove to a skeptic that the beats are an interference effect that requires both sound sources and the phenomenon is not created using a pre-recorded sound? Test out your method to convince yourself.
- Beats: interference effect caused by two waves at close frequency combining together, not produced by pre-recorded sound. - Play one source individually to see if the beats are created, and then play both sources together to see if they are created.
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?
3rd: A exerts a force on B, B must exert an equal in magnitude opposite in direction force Block is exerting a force of gravity downward on the countertop, normal force exerted must be equal and opposite - equals weight
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
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?
7000 rad/s^2, linear acceleration: 40 g; 6000 rad/s^2, linear acceleration: 60 g
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
A. stationary, linear increase in static friction B. no force applied between static and kinetic friction C. box is moving as kinetic friction levels out D. force applied, but box stationary (initial point)
Where is the center of mass of your meter stick? Hint: the force of gravity acts at the center of mass of an object. Using this fact, balance the meterstick on the fulcrum to determine its center of mass. What is the value of the torque due to gravity acting on the meter stick when it is balanced on the fulcrum? Does this explain why it doesn't rotate?
Center of mass distance on meter stick = L/2, Torque due to gravity on meter stick = 0 N when balanced, If torque is 0, then net force acting on the meter stick is 0, The meter stick doesn't rotate because the force upwards on the center of mass is balanced by the downward forces on each end of the meter stick
Generally speaking, how does the amount of the Doppler frequency shift depend on the magnitude of the source frequency? In other words, at which source frequency 300 Hz or 1000 Hz will the Doppler shift be more noticeable to our ears? Try more observations with other frequencies if you like.
Doppler shift: apparent - original, at higher frequency apparent frequency will be much more different than observed, Doppler frequency shift is greater
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.
F = ma F = 38.777 N m = 0.2 kg a = 193.885 m/s2 1 g of acceleration = 10 m/s2 a = 19.389 g's According to figure 1, the rotational acceleration needed to cause a 1% chance of concussion with this calculated linear acceleration is around 6000 rad/s2
how using a mathematical relation why very large forces must be generated by the bicep to lift even a small weight. Be sure to accompany your proof with a short explanation.
F2r2 = F1r1 → this relationship shows that because the radius of the bicep muscle is smaller, it must still exert a great force in order to lift even small weights, to maintain static equilibrium.
How many times per second should you hear a beat? Does the beat frequency you hear seem to agree with this calculated value?
Fbeat = |F1-F2| = |259-250| = 9 beats/s
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?
Given the presence of the restoring force, the spring will move up and down when stretched by the addition of the weight. Since the spring is in motion, the position from run to run might shift.
Mechanical advantage comes at a cost. Prove mathematically that, as the wheelbarrow is lifted, the vertical distance the load moves is lower than the vertical distance the input force at the handle moves. Hint: you will need to use either the tangent formula or the arc length formula.
Holding F2r2 constant, if the vertical distance is smaller, than the force exerted by the muscle has to be larger, so as to maintain static equilibrium
What change, if any, do you expect in the frequency of vibration if we increase the mass in the spring?
If the mass of the spring is increased, the frequency would decrease since frequency is inversely proportional to the square root of mass
Write the energy conservation relationship Ei + W = Ef in terms of the initial and final speed of the cart v, the mass of the cart m, the distance traveled by the cart d, the coefficient of friction μ, and the gravity constant g.
KEi + W = KEf, (mvi2)/2 + umgd = (mvf2)/2
Let's again write out our energy conservation relation in terms of measurable quantities. Since we are releasing the cart from rest, there is no initial kinetic energy. Also, let's assign the spring as an external force doing work on the cart. Write the energy conservation relationship Ei + W = Ef in terms of the final speed of the cart v, the mass of the cart m, the distance traveled by the cart d, the coefficient of friction μ, the gravity constant g, and the work done by the spring Wspring.
KEi = 0 KEf = 1/2mv^2 Ff = uFN FN=mg Wtotal = Wspring - Ff Ei + W = Ef 0 + (Wspring - umg) = 1/2mv^2 Wspring - umg = 1/2mv^2
Putting on a pair of goggles shifts the center of mass of your head further toward your face. How would the muscle's force need to compensate to maintain equilibrium? Support your answer with a mathematical relation comparing the situations before and after putting on goggles.
Muscle force would need to increase. A mathematical relation would be, Before: Fmuscle r = Fweightr, After: Fmuscler = Weight(google width + r) → solve for force of muscle by dividing both sides by r
Make a prediction based on Bernoulli's equation: do you think the pressure will be higher in the wider area (at point 1) or in the constriction (at point 2) in Fig. 2? Support your answer.
P higher when A wider (pressure changes to accommodate change in velocity when moving from wider to smaller area)
Will Q be higher at point 1 or at point 2?
Q will be equal at point 1 and point 2 due to conservation of mass
Our results support the idea that if left to freely oscillate, a system will vibrate at a natural frequency that depends on the system itself, not on the initial push or stimulus that we impart. Based on this reasoning, how does the natural frequency of vibration of a block of lead compare to that for the same size 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.
Since lead has a higher atomic weight than aluminum, ~26 u vs. 207 u, the block of lead would have a lower frequency given that frequency is inversely proportional to the square root of mass. Furthermore, the lighter block with aluminum would have the higher frequency.
What do we mean by static equilibrium here? In other words, how can we state mathematically whether the model head is in static equilibrium (both rotational and translational)?
Static equilibrium means that the system is at rest or the forces acting on the system sum up to be 0, translational: Normal force (FN) = mg, rotational: Frsin(θ), where θ = 90 degrees → Fmuscle r = Fweight
As described in the introduction, the frequency is fixed by the source, which is constant. In that case, do we expect the frequency of the waves to change as they travel from Medium 1 to Medium 2? Further, when the waves enter the new medium how will their speed and wavelength be related? In other words, what will happen to the wavelength if the speed increases? What about if the speed decreases?
The frequency will remain fixed, meaning the speed and wavelength will change
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?
The highest acceleration experienced that did not cause a concussion, was around 100 g's, and the minimum acceleration that did cause a concussion was around 50 g's.
What happens to the constructive and destructive lines when the two sources are switched from in-phase to out-of-phase?
The lines that were constructive in-phase became destructive out-of-phase and the lines that were destructive in-phase became constructive out-of-phase
In static equilibrium the forces balance as well as the torques. Estimate the maximum muscle force we can apply before the meterstick lifts off the base.
The maximum muscle force we can apply before the meterstick lifts off the base is the force exerted by the gravity on the system. Since we used masses of 50g and 100g on two different hangers the maximum force will be Fmax= 0.150*9.8 = 1.47 N
When holding your arm out to your side, it tends to rotate about your shoulder joint. However, you can use the muscles in your arm to hold it stationary in which case it is in static equilibrium. Which of the following correctly describe the net force and net torque on your arm when in static equilibrium?
The net torque and net force on your arm are both zero.
Look again at Hooke's Law (Eqn. 1). What does the slope of the graph of F vs. x represent?
The spring constant, k.
If we want the slope to be the acceleration, which variable, velocity or time, goes on the x-axis? Why?
The time (s) variable goes on the x-axis. slope = y/x, acceleration = v/t, v must be y axis, t must be x axis
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.
There is a decrease in amplitude among the three runs, because of the friction due to air on the system
At the surface of the earth, all objects accelerate at 9.8 m/s^2
True
Calculate this expected theoretical period of the system and compare it to the value you measured by finding percent difference between the two values.
Ttheoretical = 2(m+Ms3)k = 2150+163310.45 = 27.78, Tobtained =2150 + 16310.45 =34.39, percent error = 34.39-27.7827.78*100=23.79%
Does the observed pattern resemble the pattern of interference from the two point sources from Part II? This is remarkable because the wave from a single source, the plane wave generator, is essentially interfering with itself!
Yes it does, because the two point sources from part 2 result in a pattern of waves that crash with each other. And although the observed pattern looks uniform, it is essentially the plane wave generated-wave interfering with itself.
Was your prediction approximately correct
Yes, our prediction was correct since our applied force (0.82N from the picture) was smaller than our Fweight (1.45N
Is the frequency about the same for your three runs?
Yes, the frequency remains the same for the three runs.
An object is moving in the x direction. What quantity is represented by the slope of a plot of the object's speed as a function of time?
acceleration
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.
apply brakes more gently, car is rolling → kinetic, kinetic < static
The work done by a constant force is simply W = Fd, but the work done by a varying force such as a spring is found from the integration of the force over the distance: W = ∫Fdx. This task is easy if we have a graph of F vs. x. How can we obtain the work done by the spring from a graph of F vs x?
area
From your graph, what is the trend for how the acceleration changes as the system gets more and more massive (while maintaining constant force)? Is this consistent with Newton's Second Law?
as system gets massive, while maintaining constant force, acceleration decreases, consistent with newton's second law
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
average impulse the same, average max force largely different, higher accelerations cause concussions, force is related to acceleration (F=ma), helmets prevent concussions
Use the concepts learned in this lab to explain why the back muscles are easily overtaxed when one is trying to rotate their torso to the upright position using the hips as the pivot. When answering, make use of the fact that the back muscles pull along the torso at an angle very nearly parallel to the torso. Also note that the center of mass of the torso is near the center of the torso.
class III lever would be the one that would most contribute to the diagram of the back muscles class III: weight is on both sides, simulates the muscle of the torso and the biceps as well when lifting up an object, adding force to one side w/ two mass, other lever exerts much more force (i.e. strain on back muscles) Lifting the box with your legs would be less taxing for your back muscles since one won't be exerting as much force on their upper body instead using their lower body as well.
When we hear beats produced by combining two sounds, we are hearing an example of...
constructive and destructive interference
Because sound is a wave, increasing the frequency of your voice __________ the wavelength of the sound you are generating.
decreases
How does the computer know the velocity when all it is measuring is time? Hint: what is the other part of the equation for average velocity?
determines velocity from position, which is consistent (0.05m), can relate to time for the interval, formula for velocity = Δdistance/Δtime so it just calculates for average velocity with its measured time.
How does the duration (i.e., the time scale) of the impact differs between the two cases (with vs without the helmet)?
duration of impact greatly increases with helmet run vs. without, increase of time decreases the maximum amount of force that impacts the "dummy but keeps the impulse relatively constant.
Looking at your velocity vs. time graph, how can you use the slope to tell whether friction is doing work on the cart? This can either be answered in terms of Newton's 2nd Law or in terms of energy conservation.
energy conservation: energy remains conserved, 2nd law: force is directly proportional to acceleration, acceleration negative, meaning force is decreasing (because friction force is negative)
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?
equal in magnitude, opposite in direction
What speeds did you find that you moved the phone? Were the values reasonable? (Around a meter per second is typical of the speed of human motion.)
fobs = fsource((Vsound∓Vobserver)/(Vsound∓Vsource)) 992 = 1000 ((343+0)/(343+x)) x = 2.77 m/s
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? ignore drag.
horizontal line indicating that the speed in the x-direction is constant over time.
The beat frequency we hear, sounds about the same as the 9 beats per second we are supposed to hear. What magnitude frequency shift did you estimate for moving the phone source? 1 Hz? 10 Hz? 100 Hz? As you move the phone away, do you expect to receive an upward or downward shift in frequency?
if 440 Hz is the original frequency - the phone is moving away, frequency slightly lower since the phone is moving relatively slow compared to the speed of sound, downward shift - phone away: 430 - phone toward: 450
Describe in words the shape of the velocity vs. time graph. (Does the slope stay constant? Is the y-intercept zero?)
linear with a positive, constant slope (acceleration value) for each trial; y-intercept is not zero
In a graph of F vs. x, where F is the force exerted by a spring, and x is the extension of a spring, what is represented by the slope m? (Note that F is plotted on the y axis and x is plotted on the x-axis)
m = -k
Atwood's machine is a simple apparatus for looking at how objects accelerate and is shown in Figure 1 below. To analyze how the blocks m1 and m2 will accelerate in Atwood's machine, note that the only unbalanced external force on the system is the force of gravity on the hanging mass: m2g, and this force accelerates both masses m1 + m2. We can assume m1 and m2 have the same magnitude acceleration since they are attached by a string. Plug these terms into Newton's 2nd law to derive the equation a = m2g / (m1+m2) for the acceleration of the blocks a in terms or their mass and g
m2g = (m1+m2) a
What are the SI units of Q?
m^3/s
Make a prediction: if we add 150 g to represent the weight of the head Fweight, how much muscle force is needed to maintain static equilibrium? Answer in Newtons and use g = 10 m/s2
mass = 0.15 kg, F = (0.15)(10 m/s^2) = 1.5 N
What quantity is represented by the area under the curve in a graph of force vs. Time?
measurement of impact that is produced in our experiment known as the impulse.
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 ___________ of the object, or as the product of the ________ on the object and ______of the collision.
momentum, force and duration
Imagine you are told that an unknown material has a specific gravity in water of 0.95. Will this object float in water? How does the density of this material compare to the density of water?
object will float in water, specific gravity less than 1, Its density is less than water.
How would your results be affected if the picket fence was dropped at an angle through the photogate?
recorded distance between the picket fence stripes smaller, experimental velocity values smaller
low standard deviation?
results are relatively reproducible
Class II levers like ankles and wheelbarrows are useful because they provide mechanical advantage, by amplifying the input force to provide a greater output force. In other words, we can lift a load without having to lift the full weight of the load. Starting from the condition of rotational equilibrium (net torque equals zero), prove mathematically that Class II levers provide mechanical advantage. Include a diagram that shows the relative position of the applied input force and the output force on the load. Also, to simplify we can assume the forces are perpendicular to the lever arm.
rmuscle*Fsin(90) = rweight*F(90), The muscle effort needed to lift the weight would be less because the radius is greater, and in terms of the wheelbarrow, most of the weight is at the bottom of the barrow and the radius is greater.
Looking at the graph you made of force vs. displacement, do you see a linear relationship? What does the slope of this graph represent?
spring constant (-k)
Prove using the equilibrium condition that the buoyant force is the difference between the weight of the object in air and the weight of the object in water.
the net force on the brass is Fnet = 0 = Ft + Fb - mg Ftair = mg. Ftwater = mg - Fb Fb = Ftair - Ftwater - buoyant force is the difference between the weight of the object in the air and the weight of the object in the water.
Is the wavelength longer or shorter in Medium 2 as compared to Medium 1? Is the wave traveling at faster or slower speed in Medium 2 as compared to Medium 1?
the wavelength should be shorter in Medium 2, move quicker (in shallow water)
If you push a cart and let it go, it will roll to a stop eventually because of friction. How does the sign of the work done by friction compare to that of the initial kinetic energy of the cart? Define the initial point just after you let go of the cart, and the final point where the cart stops
the work done by friction is negative and the initial kinetic energy is positive.
As mentioned, Bernoulli's principle is a statement of conservation of energy. Give at least one assumption that was made in order to apply Eq. 2 to this experiment.
there is no difference in the height between the two points in the pipe.
Why is the angle to get the block to start sliding larger than the angle to get the block to stop sliding?
to start sliding: need to overcome static friction, to stop sliding: need to overcome kinetic friction, static friction larger, will be harder to overcome, greater force required, kinetic force smaller, will be easier to overcome, smaller angle to stop sliding
Describe in words the shape of the distance vs. time graph for the free fall. How should this look (linear, quadratic, etc.)?
upward curve; quadratic function.
We'll measure the change in kinetic energy to find the work done by friction and the friction coefficient μ. Rearrange your equation from the previous question to solve for the friction coefficient μ in terms of measurable quantities.
v2f-v2i / 2 = ugd, u= v2f-v2i / 2gd
Looking at the data, you should notice that the time difference between successive data points is smaller and smaller the farther the picket fence falls. Why is this?
velocity is increasing as time passes. when acceleration is constant, the velocity is increasing at a constant rate.
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
standard deviation if all values the same?
would be zero
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 in the absence of forces in the x-direction?
x: -0.7919 m/s^2, in the absence of forces, expected x-acceleration = 0
Which general kinematic equation is most like the fit equation for the x position vs time data? Which kinematic equation is most like the fit equation for the y position vs time data?
x: d=vt, y: H = gt2/2
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?
y-acceleration = slope, acceleration, 9.8 m/s2
Is the time value when the ball 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 it's the same because at maximum height, velocity is 0
Does the shape of the transmitted waves resemble the point source wave we previously saw?
yes, they did
