Physics midterm question: thrown upwards vs. downwards balls

Physics 5A Midterm 1, fall semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 3.6

[10 points.] You are standing on a balcony overlooking the beach. You throw and release a ball straight up into the air with an initial speed, and throw and release an identical ball straight down with the same initial speed. Neglect air resistance. Why would they have the same speed when they hit the ground (at different times)? Explain your reasoning using the properties of constant acceleration motion.

Solution and grading rubric:

• p = 10/10: Correct.
  Argues that the ball that was tossed straight up with an initial speed will come back down past its starting point with the same speed, and thus will fall downwards in the same manner from this point onwards as the ball thrown downwards with the same initial speed. Quantitatively this comes from v_fy² - v_iy² = 2·a_y·∆y because of the square of a positive or negative v_iy will result in the same v_fy, but a thorough qualitative argument is sufficient.
  
• r = 8/10:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  
• t = 6/10:
  Nearly correct, but argument has conceptual errors, or is incomplete. Some attempt at incorporating impulse and momentum in discussion. May use a graph, or equations, or argues qualtitatively that the ball that is thrown upwards will start moving downwards from a higher height with zero velocity, and thus will speed up over a greater downward distance to match the final speed of the downwards thrown ball.
  
• v = 4/10:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Argument based on same acceleration, and thus same final velocity, without appealing to how results from v_fy² - v_iy² = 2·a_y·∆y apply, or from the qualitative explanation given in response (p).
  
• x = 2/10:
  Implementation/application of ideas, but credit given for effort rather than merit. Interprets final velocities of balls when they hit the ground as being zero (which would be true after they have hit the ground).
  
• y = 1/10:
  Irrelevant discussion/effectively blank.
  
• z = 0/10:
  Blank.
  

Grading distribution:
p: 19 students
r: 1 student
t: 17 students
v: 6 students
x: 0 students
y: 0 students
z: 0 students

A sample of a "p" response (from student 0036) is shown below:

Physics midterm problem: diagonally thrown-downwards beanbag

Physics 5A Midterm 1, fall semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 3.42(c)

[20 points.] A beanbag is thrown with a velocity of 15 m/s at 45° below the horizontal from a window a height 30 m above the ground. At what horizontal distance from the point directly below the window will the beanbag hit the level ground? Neglect air resistance. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20: Correct.
  Breaks the initial velocity vector in separate x- and y-components. Note that a_x = 0, and a_y = -9.80 m/s². May either use quadratic equation from ∆y = v_iy·∆t + (1/2)·a_y·(∆t)², to solve for time; or v_fy² - v_iy² = 2·a_y·∆y and then plugging in v_fy into v_fy = v_iy + a_y·∆t to find time. Once time is known, it can then be used to find the horizontal displacement ∆x when the beanbag hits the ground.
  
• r = 16/20:
  Nearly correct, but includes minor math errors. Otherwise carries out systematic decomposition into x and y-components, to kinematic equations, to reduction/substitution using algebra approach.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Still has a methodical approach based on the kinematic equations of motion.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit. May estimate distance from by appealing to trigonometry and straight-line travel.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
p: 7 students
r: 6 students
t: 5 students
v: 19 students
x: 6 students
y: 0 students
z: 0 students

A sample of a "p" response (from student 2325) using the quadratic formula to first determine the time for the beanbag to hit the ground:

A sample of a "p" response (from student 3153) instead solving for the final vertical velocity of the beanbag in order to solve for the time for the beanbag to hit the ground:

Physics clicker question: circular motion free-body diagrams

Physics 5A, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 5.38

Students were asked the following clicker questions (Classroom Performance System, einstruction.com) in the middle of their learning cycle:

Use these free-body diagrams for the following questions:


[0.6 participation points.] Which free-body diagram represents a passenger (upside-down) at the top of a vertical loop, traveling fast enough that there is still contact with the seat?

Sections 0906, 0907
(A) : 1 student
(B) : 10 students
(C) : 10 students
(D) : 9 students
(E) : 1 student
(F) : 8 students

Correct answer: (F)
At the top of the circular arc, the net force points inwards (downwards), which is comprised of both the downwards normal force of the seat on the passenger, and the weight force of the Earth on the passenger.

[0.6 participation points.] Which free-body diagram represents a passenger (upside-down) at the top of a vertical loop, traveling just fast enough that there is barely contact with the seat?

Sections 0906, 0907
(A) : 0 students
(B) : 0 students
(C) : 2 students
(D) : 1 student
(E) : 35 student
(F) : 1 student

Correct answer: (E)
At the top of the circular arc, the net force points inwards (downwards), which is comprised only the downwards weight force of the Earth on the passenger.

Uniform circular motion: wall of death

Rhett "Rotten" Giordano, New Orleans Superdome Bike Expo
http://www.650motorcycles.com/83expoGrinder.jpg

Demonstration of how the (upwards) static friction force prevents the bike from sliding down the "Wall of Death," while the (inwards pointing) normal force provides the net force required for uniform circular motion.

Uniform circular motion: centripetal net force

Li Wei, liweiart.com
047-01, "Life in the high I" (detail)
Beijing July 1, 2004

Demonstration of the inward (centripetal) net force required for uniform circular motion.

Astronomy clicker question: jovian weather patterns

Astronomy 10, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q6.1

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the end of their learning cycle:

[0.3 points.] Which one of the following choices best explains why Saturn's belt-zones and cyclonic spot cloud features are less prominent than Jupiter's?
(A) Saturn supplies less tidal heating than Jupiter.
(B) Saturn retains much less heat than Jupiter.
(C) Saturn is farther from the Sun than Jupiter.
(D) Saturn has much less liquid metallic hydrogen than Jupiter.
(E) Saturn's rings are much more prominent than Jupiter's.

Correct answer: not revealed yet (see discussion).

Initial responses below:

Student responses
Section 1073
(A) : 6 students
(B) : 12 students
(C) : 3 students
(D) : 10 students
(E) : 2 students

The energy source of jovian planet belt-zone and cyclone weather patterns is core heat. A cooler core would result in less prominent weather patterns. The same question was asked again, with no explanation from the instructor.

[0.3 points.] Which one of the following choices best explains why Saturn's belt-zones and cyclonic spot cloud features are less prominent than Jupiter's?
(A) Saturn supplies less tidal heating than Jupiter.
(B) Saturn retains much less heat than Jupiter.
(C) Saturn is farther from the Sun than Jupiter.
(D) Saturn has much less liquid metallic hydrogen than Jupiter.
(E) Saturn's rings are much more prominent than Jupiter's.

Correct answer: (B)

Student responses
Section 1073
(A) : 6 students
(B) : 26 students
(C) : 0 students
(D) : 1 student
(E) : 0 students

Erasing slate: study the night sky

"I like to study the night sky!" by Anonymous
Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Latest scribbling on the lift-and-erase slate in the hallway, outside the office door.

Physics quiz question: average speed versus average velocity

Physics 5A Quiz 3, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 3.26

[Version 1]

[3.0 points.] A car travels west at 80 km/h for 1.0 h. It then travels north at 45 km/h for 1.0 h. Which quantity has a larger magnitude for the car during this trip?
(A) The average speed.
(B) The average velocity.
(C) (Both average speed and average velocity have the same magnitude.)
(D) (Not enough information is given to determine this.)

Correct answer: (A)
The average speed is the distance traveled divided by the elapsed time, which is (80 km + 45 km)/2.0 h = 63 km/h. The average velocity is the displacement (straight-line distance from start to finish) divided by the elapsed time, which is sqrt((80 km)^2 + (45 km)^2)/2.0 h = 46 km/h.

Student responses
Sections 0906, 0907
(A) : 5 students
(B) : 10 students
(C) : 6 students
(D) : 0 students

[Version 2]

[3.0 points.] A car travels west at 80 km/h for 1.0 h. It then travels north at 45 km/h for 1.0 h. Which quantity has a smaller magnitude for the car during this trip?
(A) The average speed.
(B) The average velocity.
(C) (Both average speed and average velocity have the same magnitude.)
(D) (Not enough information is given to determine this.)

Correct answer: (B)

Student responses
Sections 0906, 0907
(A) : 7 students
(B) : 6 students
(C) : 7 students
(D) : 0 students

Physics quiz question: friction-slowed book

Physics 205A (formerly Physics 5A) Quiz 3, fall semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problems 4.26, 4.51

A Physics 205A student pushes an 2.00 kg book across the top of a horizontal table. The coefficient of kinetic friction is 0.3. After it is released, the book slides across the table, and because of friction, slows down with an acceleration of magnitude:
(A) 0.6 m/s².
(B) 1 m/s².
(C) 3 m/s².
(D) 6 m/s².

Correct answer (highlight to unhide): (C)

The book has two vertical forces acting on it:

Weight force of Earth on book (downwards, magnitude w = m·g = 19.6 N).
Normal force of floor on book (upwards, magnitude N = 19.6 N).

Because the book is stationary in the vertical direction, these two forces are equal in magnitude and opposite in direction, due to Newton's first law.

The book has only one horizontal force acting on it (as it moves to the right):

Kinetic friction force of floor on book (to the left).

The book is already unstuck and sliding (presumably to the right) after it being released, such that the only horizontal force acting on it is the (constant) kinetic friction force, directed to the left:

f_k = µ_k·m·g = (0.3)(2.00 kg)(9.80 N/kg) = 6 N,

and from Newton's second law, the kinetic friction force (directed to the left) is the sole horizontal force that contributes to the (non-zero) horizontal net force (directed to the left), such that we can solve for the magnitude of the the horizontal acceleration:

ΣF_x = –6 N,

m·a_x = –6 N,

a_x = (–6 N)/m = (–6 N)/2.00 kg) = –3 N/kg = –3 m/s²,

which has a magnitude of 3 m/s² directed to the left.

(Response (A) is µ_k·m; response (B) is µ_k·g/m; and response (D) is the magnitude of the kinetic friction force f_k = µ_k·m·g.)

Student responses
Sections 0906, 0907
(A) : 13 students
(B) : 2 students
(C) : 7 students
(D) : 19 students

Success level: 18%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50

Astronomy quiz question: radioactive dating

Astronomy 10 Quiz 4, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q4.2

[Version 1]

[3.0 points.] Consider three samples (X)-(Z), with differing amounts of unstable isotopes, embedded gaseous decay products, and inert material (which is not involved in the radioactive decay process), schematically shown below.


Which one of the following choices best corresponds to the order of samples from youngest to oldest, as determined by radioactive dating?
(A) Youngest: X, Y, Z: oldest.
(B) Youngest: X, Z, Y: oldest.
(C) Youngest: Y, Z, X: oldest.
(D) Youngest: Y, X, Z: oldest.
(E) Youngest: Z, X, Y: oldest.

Correct answer: (B)

Student responses
Section 0135
(A) : 8 students
(B) : 16 students
(C) : 3 students
(D) : 2 students
(E) : 6 students

[Version 2]

[3.0 points.] Consider three samples (X)-(Z), with differing amounts of unstable isotopes, embedded gaseous decay products, and inert material (which is not involved in the radioactive decay process), schematically shown below.


Which one of the following choices best corresponds to the order of samples from youngest to oldest, as determined by radioactive dating?
(A) Youngest: X, Y, Z: oldest.
(B) Youngest: X, Z, Y: oldest.
(C) Youngest: Y, Z, X: oldest.
(D) Youngest: Y, X, Z: oldest.
(E) Youngest: Z, X, Y: oldest.

Correct answer: (E)

Student responses
Section 1073
(A) : 1 student
(B) : 5 students
(C) : 8 students
(D) : 6 students
(E) : 24 students