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Physics 171/171H
Fall 2000
Professor Ellen D. Williams

 

A set of old exams from recent classes of Physics 171 is below.

You can scroll through all exams or click directly to each exam of interest:

 Exam # 1           Exam # 2           Exam # 3          Final Exam

If you would like a hard copy of the exams you can TRY printing directly from the web page.  However, formatting and printing of graphics is quite erratic.  For a nice quality output, you can download the exams as pdf files by clicking on the tabs below.  You will need to have Adobe Acrobat Reader installed on your computer to open the files.  If you don't have Acrobat Reader, you can download it for free from:

http://www.adobe.com/products/acrobat/readstep2.html
 
 

Click on the tab of choice to download

Exam 1 in pdf Format
Exam 2 in pdf Format
Exam 3 in pdf Format
Final Exam in pdf Format
Copyright (2000) University of Maryland, College Park. All rights reserved. Permission to redistribute the contents without alteration is granted to educational institutions for non-profit administrative or educational purposes if proper credit is given to the University of Maryland, College Park as the source.






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Physics 171 -Exam # 1
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 Do the attached problems on the paper provided. Extra paper is available at the front of the room if you need more. Be sure to write your name and the problem number on any extra sheets you use!!

You may use your own pens, pencils, erasers, calculator and one 8" x 11" sheet of paper pre-prepared with any information you think you might need.

The exam will be graded on the basis of CLARITY of PRESENTATION of your reasoning, as well as correctness of the final answer. You must also show the units on numerical answers to obtain full credit.

______________________________________
Name
 
 
 
 



1.    Draw carefully, and as quantitatively as possible, the acceleration vs. time (on the top graph below) and the position vs. time (on the bottom graph below) for a particle moving with the velocity curve shown.  Assume that at t = 0, the position is x = 0 m.  Lable the axes to show the magntitudes of the quantitities you are plotting.  Clearly label positions of maxima, minima, and zeros for both position and velocity.
 


 
 
 



2. A satellite is circling the earth at a height above the earth’s surface of 230 km, and thus a distance from the earth’s center of r = 6600 km. The satellite moves at constant speed and the period of the orbit is T = 88.9 minutes. The satellite is moving counter-clockwise in an xy plane defined to have its origin at the earth’s center, as shown in the Figure. An asteroid is traveling in the same plane, in a straight line at constant speed va = 6.75 km/s past the earth in the negative x direction as shown in the figure. At time t = 0, the satellite’s position is x = r, y = 0. a) What is the frequency of the satellite’s orbit? What are the velocity and acceleration of the satellite?

b) Write vector expressions for the velocities (as observed from the earth frame) of the satellite and the asteroid at t = 0, t = T/4 and t = T/2.
 

c) Write a vector expression for the velocity of the asteroid as observed by the satellite at time t = T/2. What is the magnitude of the relative speed of the asteroid and the satellite at this time?
 



3. During the eruption of a volcano a chunk of rock is ejected from the summit of the volcano. It lands 8.4 x 103 m east, and 1.8 x103 m below the summit. The block was ejected from the summit at a 35o angle from the horizontal.

a) Write the equations for the x coordinate of the rock as a function of time, and for the y coordinate of the rock as a function of time. Your equations should include the unknown initial speed vo as a parameter. Eliminate the time to find the trajectory of the rock, that is its x position as a function of its y position.

b) Find the initial speed vo of the rock.

The magnitude of the acceleration due to gravity is g = 9.8 m/s2
 



4. An observer on earth sees a photon and an energetic particle and a second observer, all traveling in the positive x direction, pass by at t = 0. The energetic particle’s speed is 0.667c, and the second observer’s speed is 0.750 c.

a) What values does the earth observer measure for the positions of the photon and the energetic particle at t = 10.0 ns after they pass by?

b) What coordinates (position and time) does the second observer measure for each of the events in part a? (The "events" are the photon and the energetic particle each at the position calculated in (a) at time t = 10 ns in the earth observer’s frame.)

c) What velocity does the second observer find for the photon and the energetic particle based on the result of part b? Explain why your answers are or are not consistent with your expectations based on the laws of relativity and your common sense.
 
 
 
 

Copyright (2000) University of Maryland, College Park. All rights reserved. Permission to redistribute the contents without alteration is granted to educational institutions for non-profit administrative or educational purposes if proper credit is given to the University of Maryland, College Park as the source.



Physics 171 -Exam # 2
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 Do the attached problems on the paper provided. Extra paper is available at the front of the room if you need more. Be sure to write your name and the problem number on any extra sheets you use!!

You may use your own pens, pencils, erasers, calculator and one 8" x 11" sheet of paper pre-prepared with any information you think you might need.

The exam will be graded on the basis of CLARITY of PRESENTATION of your reasoning, as well a correctness of the final answer. You must also show the units on numerical answers to obtain full credit.

______________________________________

Name
 
 
 
 



1. A block of mass m1 = 12.5 kg is sitting on a rough surface. The coefficients of friction between the block and the surface are ms = 0.75, andmk = 0.30. A cable is attached to the block and passes over an ideal massless pulley as shown in the drawing. A second mass m2 is suspended from the cable.

a) Draw and label on the diagram all of the forces acting on each of the masses.

b) If m2 = 10 kg, the two masses move with uniform acceleration. Find the tension in the cable in this case.

c) Find the total work done on mass m1 for 1.20 m of displacement during the constant acceleration of part (b).


 
 
 



2. A molecule approaching another molecule radially experiences (at small distances) a repulsive force  F(R) = 12e{ro12/r13}, where e and ro are constants.

a) Find the potential energy corresponding to this force. Specify your choice of the zero of potential energy.

b) For nitrogen (N2,, mass = 4.65x10-26 kg), the values of the parameters are e = 1.31x10-21J and ro = 0.415 nm. If a nitrogen molecule is placed at a distance R1 = 0.6 nm away from another nitrogen molecule, find the value of its potential energy.

c) If the molecule is released from rest (v1 = 0 m/s) at position R1, find its speed when it reaches a distance R2 = 5nm from the other molecule. (Assume the other molecule is stationary.)
 
 



3. Show that the force due to gravity near the surface of the earth is accurately approximated as a constant, F = mg, and derive the value g = 9.8 m/s2.

The binomial approximation is: 
 
 
 
 



4. A satellite of mass 2200 kg is in geosynchronous orbit above the earth. This means that it stays above the same place on the earth’s surface, so that its period of revolution is T = 24 hours.

a) Find the radius of the satellite’s orbit and its velocity.

b) If the satellite is to be "boosted" from its orbit so that it escapes entirely from the earth’s gravitational pull, how much energy would be needed?

c) If the energy needed for part b could be provided with direct conversion of mass to energy, how much mass would be needed?

Copyright (2000) University of Maryland, College Park. All rights reserved. Permission to redistribute the contents without alteration is granted to educational institutions for non-profit administrative or educational purposes if proper credit is given to the University of Maryland, College Park as the source.

Physics 171-Exam # 3
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 Do the attached problems on the paper provided. Extra paper is available at the front of the room if you need more. Be sure to write your name and the problem number on any extra sheets you use!!

You may use your own pens, pencils, erasers, calculator and one 8" x 11" sheet of paper pre-prepared with any information you think you might need.

The exam will be graded on the basis of CLARITY of PRESENTATION of your reasoning, as well as correctness of the final answer. You must also show the units on numerical answers to obtain full credit.

______________________________________

Name
 
 



1. Two masses, m1 and m2 are suspended from a cable that passes over a pulley. The pulley has mass M and radius R, and it is a homogeneous flat disk. Mass m2 is greater than mass m1 and the two masses are released from rest. The cable does not slip on the surface of the pulley.
a) Explain why or why not each of the following quantities is conserved: momentum, kinetic energy, total energy, angular momentum.

b) What is the moment of inertia of the pulley?

c) What is the speed of mass m2 after it has descended a distance h?

d) Is the torque on the pulley negative, zero or positive?

 
 

2. Two nuclei approach each other head on. The first has mass m1 = 20.00 mp, where mp is the mass of a proton. It is traveling at speed 0.89c. The second has mass m2 = 63.14 mp. The two masses collide inelastically, creating a new particle that is stationary (final velocity = 0).

a) What quantities are conserved in this process?

b) What was the initial speed of the nucleus of mass m2?

c) What is the mass of the new particle created in the collision?

 

3. A narrow rod has a mass of 4.42 kg and a length of 1.23 m. It is at rest on a frictionless surface. A point mass, m =2.40 kg traveling perpendicular to the stick with speed v = 0.334 m/s hits it 0.350 m off center.

a) What is the position of the center of mass when the point mass hits the rod? (treat the rod as having no width)

b) What is the angular momentum of the point mass with respect to the center of mass just as it hits the rod? (treat the rod as having no width)

b) If the point mass sticks to the rod in the collision, what is the velocity of the center of mass of the rod plus mass after the collision?

c) If the point mass sticks to the rod in the collision, what is the moment of inertia of the rod plus point mass with respect to an axis through the center of mass?

d) What is the angular velocity of the rod plus mass (as it rotates about the center of mass) after the collision


 
 
 
 
 


4. A satellite of mass 2500 kg orbits the earth in an elliptical orbit where its closest point is a distance rc = 15,000 km from the earth's center, and its farthest distance is rf = 60,000 km from the earth's center.

a) What is the total energy of the orbiting satellite?

b) What is speed of the satellite at its distance of closest approach?

c) What is the angular momentum of the satellite?
 
 

Copyright (2000) University of Maryland, College Park. All rights reserved. Permission to redistribute the contents without alteration is granted to educational institutions for non-profit administrative or educational purposes if proper credit is given to the University of Maryland, College Park as the source.


Physics 171 - Final Exam
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 Do the attached problems on the paper provided. Extra paper is available at the front of the room if you need more. Be sure to write your name and the problem number on any extra sheets you use!!

You may use your own pens, pencils, erasers, calculator and one 8" x 11" sheet of paper pre-prepared with any information you think you might need.

The exam will be graded on the basis of CLARITY of PRESENTATION of your reasoning, as well as correctness of the final answer. You must also show the units on numerical answers to obtain full credit.

_______________________________     _______________________________

Name Signature

Please sign at the right if you would like to have your grade posted in a non-alphabetical list using social security number identifiers.
 
 
 
 
 
 
 


1. A particle of mass 4.6 kg follows the trajectory:

  r(t) = (1m/s3 t3)x + (5m/s t)y

where r is the vector pointing to the particle, and x and y are the unit vectors in the x and y directions.  The trajectory is shown in the figure. The points in the figure show the positions measured at equal time intervals of 1s.

a) Find the expressions for the vector velocity, acceleration and force as a function of time, and draw the vectors indicating the directions of the velocity and force at points A and B on the diagram. Indicate the units on all numbers in your expression.

b) Find the angle between the direction of motion and the force at point A.

c) The force on the particle can also be expressed as a function of position as:

  F(r) = (27.6N/m1/3)x1/3x + 0y

Assuming the force is conservative, find an expression for the potential energy of the particle as a function of x.

d) Write down three different equations that could be used to calculate the work in moving the particle from point A to point B, and solve one of them to obtain a numerical value.
 
 
 
 
 
 
 
 
 



2. An observer on earth sees a photon and an energetic particle and a second observer, all traveling in the positive x direction, pass by at t = 0. The energetic particle’s speed is 0.750c, and the second observer’s speed is 0.500 c.

a) What values does the earth observer measure for the positions of the photon and the energetic particle at t = 10.0 ns after they pass by?

b) What coordinates (position and time) does the second observer measure for each of the events in part a? (The "events" are the photon and the energetic particle each at the position calculated in (a) at time t = 10 ns in the earth observer’s frame.)

c) Now let’s suppose that at t = 10.0 ns, the energetic particle broke apart into three pieces, one of which remained stationary (in the earth’s frame) at the point of decomposition. The second observer came by a small time later and measured (simultaneously) the position of the earth and the remaining piece of the energetic particle. What distance does the second observer measure between the remaining piece and the earth? Explain the relationship between your answer to this question and your answer to part b.
 
 
 


3. A narrow rod has a mass of 5.50 kg and a length of 2.00 m. It is at rest on a frictionless surface. A point mass, m =2.40 kg traveling perpendicular to the stick with speed v = 0.334 m/s hits it 0.350 m off center.

a) What is the position of the center of mass when the point mass hits the rod? (treat the rod as having no width)

b) What is the velocity of the center of mass of the rod plus mass.

c) What is the angular momentum of the point mass with respect to the center of mass just as it hits the rod? (treat the rod as having no width)

d) If the point mass sticks to the rod in the collision, what is the moment of inertia of the rod plus point mass with respect to an axis through the center of mass?

e) What is the position of the bottom end of the rod 1s after the collision? (Hint: tell me the position of the system center of mass, and the angle of rotation of the rod with respect to the system center of mass.)


 
 
 
 
 
 


4. A small block of mass m1 is sitting on top of a larger block of mass m2. The static coefficient of friction between the blocks is ms and the kinetic coefficient is mk. (As is always the case ms > mk.) The interaction between the large block and the floor is frictionless. A horizontal force Fo is applied to the large block.

a) When Fo is small, the two blocks slide together (with no slipping of m1 with respect to m2). What is the acceleration of the system in this case?

b) When Fo is large, the small block m1 slides along the large block m2. What is the acceleration of each of the two blocks in this case?

c) What is the value of the force Fo where the behavior of the system changes from no slipping (as described in a) to slipping (as described in b) of the small block m1 with respect to the large block m2?


5. An monoatomic ideal gas is confined in a two-dimensional container (only x and y motion allowed) and equilibrated at a temperature of 350K.

a) What is its internal energy? (Hint: how many translational degrees of freedom are there ?)

b) If the atomic mass of the atoms in the gas is 28.1 g/mole, what is the root mean square velocity of an atom?

c) The distribution of speeds of the atoms is found to obey the equation:
   N(v) = (2pAv)exp{-mv2/2kT)
Find an expression for A in terms of the macroscopic parameters of the ideal gas.
 
 


6. A diatomic ideal gas is held in a box of volume 9 m3, at a temperature of 500K and a pressure of 0.1 atm. The atoms in the molecules can rotate, but not vibrate at this temperature.

a) How much gas is in the box?

b) The gas is heated to 600K without changing volume. How much heat was transferred to the gas?

c) Then the gas is slowly allowed to expand at constant temperature (600K) until it reaches its original pressure. What is the final volume of the gas? How much work is done by the gas during this expansion

d) Draw a pressure-volume diagram for the two step expansion of the gas described in parts b and c. On the same diagram, draw the pressure-volume line for a one step heat transfer from 500K to 600K at constant pressure. Explain the difference in the work available from the two processes.
 
 


7. A particle of mass m is on a frictionless table. It is attached to a string that passes through a hole in the table. The particle rotates on the table around the hole with speed v and radius R.

a) What tension must be exerted on the string to maintain the particle in uniform circular motion?

b) If one pulls down on the string until the mass moves inward to 1/4 the original radius, what is the new speed of rotation? What is the new tension in the string? (Hint: what is conserved in this process?)

c) How much work had to be done to move the mass inward to the new radius?
 
 

Copyright (2000) University of Maryland, College Park. All rights reserved. Permission to redistribute the contents without alteration is granted to educational institutions for non-profit administrative or educational purposes if proper credit is given to the University of Maryland, College Park as the source.

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 Exam # 1     Exam # 2     Exam # 3     Final Exam