PHYS 1111 Lab Final
Uniform Circular Motion: Additional Questions - No idea what the questions were, but here are the answers
1. The string, tension force 2. Gravitational, friction, normal force, weak and strong force, electromagnetic force 3. Friction, circular track rather than a straight balance, put it in a vacuum and measure gravity force
Motion With Constant Acceleration: (Meanings of A, B, and C) What are the physical meanings of A, B, and C? Explain.
A = 1/2a , B = Vo , C= Xo
Motion With Constant Acceleration: (Units of A, B, and C) What are the units of A, B, and C?
A = m/s^2 , B = m/s , C = m
Simple Harmonic Motion: How can the value A be deduced from a logger pro graph of this experiment?
A is the peak or max y-value.
Motion With Constant Acceleration: Since there is a tendency to lose sight of the physical principles at work while trying to make the computer do its job, it is beneficial for you to repeat Procedure 1 with somewhat different initial conditions. For example, you might try changing the angle of the incline, adding mass to the glider, or changing the initial velocity by starting the glider with a slight push. For our experiment, change the angle of the incline by removing one spacer. Measure the acceleration, deduce g, and compare your results to the accepted value. * only discuss what might logically happen if one of these changes happened, no calculations
Adding mass or increasing the angle would increase the acceleration. Starting the curve at zero would increase the calculated value of gravity and bring it closer to the theoretical value.
Static Equilibrium: Explain in your own words what is meant by the center of mass.
Center of mass means that on either side of the point on an object, the mass is equal.
Lab Intro Exercise: Air Track - (accelerated motion) What can you do to cause the glider to accelerate even after you let go (ignore friction)? Think of as many ways as you can to control the acceleration of the glider, but list at least two.
Changing the mass of the glider, angling the system downwards so that gravity conpounds with the acceleration from pushing the object
Static Equilibrium: If a ruler stick is balanced evenly perpendicular with the force of gravity, which directions do Fa , Fb , m1g , and msg point?
Fa and Fb = up (opposite of m1g and msg) , m1g and msg = down (opposite of Fa and Fb)
Static Equilibrium: How do you calculate Fa and Fb?
Find Fb: sum of torques = 0 = Fa(Ra) + Fb(Rb) - msg(Rs) - m1g(R1) ... (R = radius from point 0) Use Fb to find Fa: sum of forces = 0 = Fa + Fb - msg - m1g Compare with experimental values on logger pro
Ballistic Pendulum: Compare the speed v determined by the two independent methods. What is the percentage difference? Which method do you think is the more accurate? Why?
Find percent difference. The ballistic because both masses of the ball and bob are included in calculations and the change in heights have more consistent values.
Equilibrium Of A Point Mass: (analytical method) How do you measure the resultant magnitude?
Find the X and Y components. Find vector A = square root (Ax^2 + Ay^2) Find vector B = square root (Bx^2 + By^2) Calculate Ax + Bx = Rx (R = resultant vector) Calculate Ay + By = Ry Find R = square root (Rx^2 + Ry^2)
Motion With Constant Acceleration: Velocity at 80 cm (or 120 cm) mark = ______
Find velocity by finding the slope of the curve (rise over run)
Equilibrium Of A Point Mass: (analytical method) How do you measure the resultant direction?
Find ø = arctan(Ry/Rx)
Lab Intro Exercise: Air Track - (sources of friction) What are the sources of friction slowing the glider down? List as many as you can think of, but at least two.
Friction from the air, friction from the metal on glider and ruler strip
Standing Waves In A String: How do you find tension?
Ft = mg
Motion With Constant Acceleration: Equations?
General: X = Xo + Vo(t) + 1/2(a)(t)^2 V = Vo + a(t) V^2 = Vo^2 + 2a(X - Xo) a = g(sin(ø)) X-Components: Sum of Fx = m(a sub x) mgsinø = ma a = gsinø Y-Components: Sum of Fy = m(a sub y) N - mgcosø = 0 N = mgcosø
Ballistic Pendulum: What uncertainty, if any, is associated with the discrete number of teeth in the ratchet assembly of the ballistic pendulum?
Having a discrete number of teeth influences the final height. Having less teeth decreases the accuracy of the final height, and more teeth increases the accuracy.
Lab Intro Exercise: Motion Detector - (orientation) Experiment with the orientation of the motion detector. How does this affect what is recorded by the computer?
If it's pointed down, the graph is incorrect. Putting your hand in front of the goider adds weird peaks onto the graph.
Collisions: Unknown Mass - What could cause errors when experimentally determining an unknown mass via elastic collisions?
If the collision was not a perfect elastic collision because kinetic energy and momentum were lost.
Collisions: Inelastic - For the special case of an inelastic collision between objects of equal mass, one object being at rest, Vi = 2 Vf and Ki = 2 Kf, how can data show that this isn't true and why?
If the percent difference between Vi and 2Vf as well as Ki and 2Kf is significant then the data shows this special case is not true. This is because when objects of different masses collide, velocity is lost.
Static Equilibrium: What might be a reason why center of mass may be different at a predicted point versus an experimental point?
If the predicted point is measured by the exact center length of the object, but the mass on either side is uneven, then the center of mass would be different for the predicted point and experimental point.
Collisions: What is the difference between elastic and inelastic collisions?
In inelastic collisions (objects stick together), momentum is conserved but kinetic energy is not. In elastic collisions, both momentum and kinetic energy is conserved.
Standing Waves In A String: What does the slope of the tension (y) vs. C^2 (m / s)^2 graph mean?
It is the string mass, u or mu symbol.
Lab Intro Exercise: Air Track - (level air track) Is your air track level? How can you use the behavior of the air track to answer this question and, if the answer is "no," to make it level?
It must be facing toward the data collection device. If the readings make no sense, it isn't level.
Simple Harmonic Motion: How do you calculate the kinetic and potential energy of the glider in this experiment when x is at its first maximum?
KE = 1/2mv^2 PE = 1/2 kx^2
Collisions: Inelastic - How do you find Kf (J)?
Kf = ((m1 + m2)(Vf)^2) / 2
Collisions: Inelastic - How do you find Ki (J)?
Ki = 1/2(m1)(Vi)^2
Equilibrium Of A Point Mass: (graphical method) How do you find the resultant direction?
Measure the angle
Equilibrium Of A Point Mass: (graphical method) How do you find the resultant magnitude?
Measure the distance from the 2 points
Static Equilibrium: Is there a point on the meter stick where the sun of the torques would not be zero or where the system is not in static equilibrium?
No because all torques and forces are in equilibrium.
Motion With Constant Acceleration: (B and C reasonable? Explain.) Are the numbers obtained for B and C reasonable? Explain.
No, C is the initial position and B is the initial velocity, so they should both be theoretically zero
Uniform Circular Motion: Force vs. Radius - Would a force vs. radius graph give a straight line? How might you transform it to make it a straight line?
No, you would need to take the inverse of the coefficient. The coefficient = mass / radius, so its inverse is radius / mass. Plot the inverse coefficient against the radius to get a straight line.
Motion With Constant Acceleration: Equation for percent error?
Percent error = | (experimental value - theoretical value) / (theoretical value) | * 100%
Simple Harmonic Motion: How do you determine the period of motion from a logger pro graph? Should experimental values be similar to calculated values?
Period is determined by looking from peak to peak or trough to trough. Both experimental and calculated values should be similar.
Collisions: Elastic - Equations?
Pi = Pf Ki = Kf m1(V1i) + m2(V2i) = m1(V1f) + m2(V2f) 1/2(m1)(V1i)^2 + 1/2(m2)(V2i)^2 = 1/2(m1)(V1f)^2 + 1/2(m2)(V2f)^2 V1f = ((m1 - m2) / (m1 + m2))(Vi) V2f = ((2m1) / (m1 + m2))(Vi)
Collisions: Inelastic - Equations?
Pi = Pf Ki does NOT equal Kf Pi = (m1)(V1i) BEFORE COLLISION (if object 2 is at rest) Pf = (m1)(V1f) + (m2)(V2f) = (m1 + m2)(Vf) AFTER COLLISION (m1)(V1i) = (m1 + m2)(Vf) If masses are equal then Vi = 2Vi Ki = 1/2(m1)(V1i)^2 BEFORE COLLISION Kf = 1/2(m1 + m2)(Vf)^2 If masses are equal then Kf = 2Kf
Motion With Constant Acceleration: (Calculation of v at the x = 80 cm or 120 cm mark using the fit data) Recall that you were asked to deduce the velocity of the glider when it was at the 80 cm (or 120 cm) mark. On the basis of the computer's fit to your data, you are now in a position to calculate the velocity and compare it to the earlier deduced value. Do this calculation and comment on the agreement (or lack thereof) between the two velocities.
Plug data into Vf^2 = Vo^2 + 2a(Xf - Xo) The two velocties should be similar, differences are proportional to the percent error caused by friction/air resistance/graph not beginning at zero
Simple Harmonic Motion: Equations?
Position : x = Asin(wt + ø) Velocity : v = wAcos(wt + ø) Acceleration : a = -w^2(A)sin(wt + ø) Period : squiggly t = (2(pi))/w = 2(pi)(square root (m / k)) a = F / m = - (k / m)(x) F = -k(x)
Equilibrium Of A Point Mass: Equation for percent difference?
Relative Percent Change = (final value - initial value) / (initial value) * 100%
Lab Intro Exercise: Motion Detector - (accuracy) Whenever you use a new measuring device, you should always question its accuracy. This apparatus is supposed to measure the position of the glider. But how accurate are its measurements? The yellow ruler strip on the air track can be used to measure the distance between two successive placements of the glider. Design and run an experiment to compare distances measured with the motion detector to those measured with the ruler strip. [Note: Remember the relationship between position and distance.] How closely do the two measurements agree? What do your results say about the accuracy of the motion detector?
Ruler strip = 895 mm, motion detection = 0.836m Accurate to 0.1 but not 0.01
Motion With Constant Acceleration: (Sources of error) The final step in this first procedure is to think about sources of error. What are they? How might they be reduced? What could you do better?
Sources of error could be decreased by accounting for friction and air resistance in the calculations
Simple Harmonic Motion: Why do all peaks in the graphs get smaller as time increases?
The friction between the air track and glider cause energy to be lost over time
Collisions: Elastic - What happens to the left-handed glider after collision? Why?
The left hand glider stopped moving because it's momentum and kinetic energy was conserved by the right hand glider.
Motion With Constant Acceleration: (straight line) What does a straight line segment in a graph of position versus time mean?
The position (m) and time (s) move at a constant rate when there is a diagnol straight line. A vertical straight line means that position is increasing/decreasing while time is not, and a horizontal straight line means that time is increasing, but position is not.
Uniform Circular Motion: Force vs. Speed - From the Force vs Speed^2 graph, what does the slope of the line represent?
The slope is in N/(m^2/s^2) units, so it represents (m)(v)^2 in the Fr, net = ma sub r = ((m)(v)^2) / R equation
Collisions: Smaller Mass Hitting A Larger Mass That Is At Rest - Describe what you observe regarding speeds and directions of each glider before and after the collision.
The smaller glider has less mass and is hit by the larger glider and moves in the opposite direction and will accelerate at a faster rate.
Lab Intro Exercise: Motion Detector - (speed) Give the glider a gentle push and watch it travel at (nearly) constant speed. Start the motion detector to measure the glider position as a function of time. Use these data and the software's curve-fitting feature to determine the glider's speed.
The speed = the slope of the line given by the curve fit feature
Equilibrium Of A Point Mass: Can you conclude that a vector is equivalent to the sun of its components?
The sum of the forces (components) are equal to the vector because the components put the resultant forces in equilibrium.
Uniform Circular Motion: Force vs. Speed Does the force vs. speed^2 graph look like a linear relationship?
The x axis is speed^2 (m^2/s^2), so yes. The line of best fit is y = mx + b
Uniform Circular Motion: Force vs. Mass - What does the vertical intercept of a force vs mass graph represent?
The y-intercept is how much the carriage weighs with no additional masses added
Standing Waves In A String: How do you find upside down y thing? (m)
Upside down y (lambda) = c / f
Motion With Constant Acceleration: (Deduce g) Use Equation 4 ( a = g*sin(ø)) to deduce g, the acceleration due to gravity. To do so you will need to calculate the angle of the incline. Compare your result to the accepted value of g.
Use A = 1/2a to find a for a = gsinø If the curve does not start at zero, the experimental acceleration due to gravity will be lower than the theoretical acceleration due to gravity.
Ballistic Pendulum: How do you compute the kinetic energy of the projectile just before collision; call it E1. How do you compute the kinetic energy of the projectile-pendulum combination just after collision; call it E2. Why is there a difference between the computed results? Compare the fraction (E1 - E2) / E1 with ratio m' / (m + m'). What do you deduce to be the significance of the mass ratio?
Use E1 = 1/2mv^2 and E2 = 1/2(m + m')(v)^2. There is a difference between computed results because energy is lost during the collision. The higher the fraction ratios are, the more kinetic energy is lost.
Static Equilibrium: Describe two situations outside of lab where you have witnessed torque.
Using a screwdriver to screw in a screw and the wheel of a car turning because a force is applied on a rotating axis.
Static Equilibrium: What could cause percent error between experimental and calculated values in this experiment?
Values should be under 10% error. Sources of error are caused by the experimental value obtained from logger pro being inaccurate due to the swaying of the hanging masses. The sensors at the specified points could not be perfectly centered.
Motion With Constant Acceleration: (curved line) What does a curved line mean?
Velocity is not constant
Lab Intro Exercise: Motion Detector - (observations) Run several different motion experiments, and try to learn how all of the different software features described in Appendix A work. Use your imagination, don't be afraid to try bold things, and have fun. Briefly jot down your observations.
Velocoty quickly decreases then remains constant for less than a second and then reaches equilibrium with the air acting upon it
Collisions: Inelastic - How do you find Vi (m/s)? Vf (m/s)?
Vi is selected as the region just before collision and a linear fit is applied to it. The slope of the line is Vi. Vf is selected as the region just after the collision and a linear fit is applied to it. The slope of the line is Vf.
Motion With Constant Acceleration: (rebound pattern) What is the pattern when a glider strikes and rebounds from the end of the track?
When the glider rebounds, it switches direction, so the slope turns from positive to negative and then negative to position depending on the starting position, initial direction, and number of rebounds.
Simple Harmonic Motion: Does SHM take place? Why?
Yes, the glider experiences two equal but opposite restoring forces
Uniform Circular Motion: Force vs. Mass - How do you find the mass?
You set up a proportion! ((m)(v)^2) / R = ((m)(v)^2) / R The v^2 on both sides cancel out, and the coefficient (kg/m) can be plugged in on one side. You then multiply by the radius and are left with the calculated mass in kg.
Newton's Second Law (I missed this lab): Equations?
a = ((m2) / (m1 + m2 ))(g) a = 1/2(a' + a'') = (m2g) / ( m1 + m2)
Standing Waves In A String: How do you find c?
c = square root (Ft / u) u = kg/m, u = mu symbol
Ballistic Pendulum: Equations?
mv = (m + m')(V) 1/2(m + m')(V)^2 = (m + m')gy V = square root (2gy) x = vt h = 1/2(g)(t)^2
