Physics quiz question: area factor increase

Physics 205A Quiz 1, Fall Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 1.11, 1.12

[Version 1]

An architect is redesigning a rectangular doorway. She decides to double the width of the doorway, and increase the height by 50%. By what factor has the area of the doorway increased?
(A) 1.0
(B) 1.5.
(C) 2.5.
(D) 3.

Correct answer: (D)

The original and new areas A in terms of the original and new widths w and heights h of the doorway are given by:

A_1 = w_1*h_1,
A_2 = w_2*h_2.

The new width and new height, in terms of the original width and height are given by:

w_2 = 2.0*w_1 ("doubled"),
h_2 = 1.50*h_1 ("increased by 50%).

Thus the new area, in terms of the original area is:

A_2 = h_2*w_2 = (2.0*w_1)*(1.50*h_1) = 3.0*w_1*h_1 = 3.0*A_1,

corresponding to an increase by a factor of 3.0.

Response (A) is 2.0*0.50 (the result of which, strangely enough, would correspond to a new doorway that has the same area as the original doorway, despite the increases in width and height). Response (B) is the result of 2.0 - 0.50; and response (C) is 2.0 + 0.50.

Student responses
Sections 70854, 70855
(A) : 5 students
(B) : 7 students
(C) : 11 students
(D) : 32 students

Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.65

[Version 2]

An architect is redesigning a rectangular doorway. She decides to increase the width of the doorway by 40%, and increase the height by 25%. By what factor has the area of the doorway increased?
(A) 0.100.
(B) 1.10.
(C) 1.70.
(D) 1.80.

Correct answer: (D)

The new width and new height, in terms of the original width and height are given by:

w_2 = 1.40*w_1 ("increased by 40%"),
h_2 = 1.25*h_1 ("increased by 25%).

Thus the new area, in terms of the original area is:

A_2 = h_2*w_2 = (1.40*w_1)*(1.25*h_1) = 1.80*w_1*h_1 = 1.80*A_1,

corresponding to an increase by a factor of 1.80.

Response (A) is the result of 0.40*0.25; response (B) is (1+ 0.40*0.25); and response (C) is (1+ 0.40 + 0.25).

Student responses
Section 72177
(A) : 3 students
(B) : 1 student
(C) : 2 students
(D) : 9 students

Success level: 60%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.37

Physics quiz question: height factor increase

Physics 205A Quiz 1, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 1.6

[3.0 points.] Hildegaard is 0.99 m tall on her eleventh birthday and 1.13 m tall on her twelfth birthday. By what factor has her height increased?
(A) 0.12.
(B) 0.14.
(C) 1.1.
(D) 14.

Correct answer: (C)

Let h_1 = initial height, and h_2 = final height, such that h_2 is some numerical factor times h_1:

h_2 = factor*h_1,

h_2/h_1 = factor,

1.1 = factor, limited to two significant figures from h_1.

Response (A) is 1 - (h_1/h_2) (which, if multiplied by 100, would give the percent increase in height); response (B) is h_2 - h_1; and response (D) is 100*((1.13/0.99) – 1).

Student responses
Sections 30880, 30881
(A) : 2 students
(B) : 30 students
(C) : 18 students
(D) : 0 students

"Difficulty level": 36%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.49

Physics quiz question: ratio of sides of increased square area

Physics 205A Quiz 1, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 1.49

[3.0 points.] The area of a square plot of land is increased by a factor of 1.5. By what factor did the side of this plot change?
(A) 1.2.
(B) 1.3.
(C) 1.5.
(D) 2.3.

Correct answer: (A)

A_new = 1.5*A_old, where A_new = s_new*s_new, and A_old = s_old*s_old. Thus:

(s_new)/(s_old) = sqrt(A_new)/sqrt(A_old) = sqrt(1.5*A_old/A_old) = sqrt(1.5),

which is 1.224744871..., or to two significant figures, 1.2.

Student responses
Sections 70854, 70855
(A) : 25 students
(B) : 3 students
(C) : 19 students
(D) : 5 students

"Difficulty level": 48%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.7

Physics quiz question: joule heating power

Physics 5A Quiz 1, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 1.72

[3.0 points.] The electrical power P drawn from a generator by a light bulb of resistance R is P = V^2/R, where V is the line voltage. The resistance of bulb B is 75% greater than the resistance of bulb A. What is the ratio P_B/P_A of the power drawn by bulb B to the power drawn by bulb A, if the line voltages are the same?
(A) 0.33.
(B) 0.57.
(C) 1.3.
(D) 1.8.

Correct answer: (B)

P_A = (V_A)^2/R_A, and P_B = (V_B)^2/R_B.

With V_A = V_B, and 1.75*R_A = R_B, then:

P_B /P_A = ((V_B)^2/R_B)/((V_A)^2/R_A) = (V_B/V_A)^2 = (R_A/1.75*R_A)^2 = (1/1.75)^2 = 0.57,

to two significant figures.

The incorrect response (A) is (1/1.75)^2, response (C) is (1/0.75), and (D) is (1/0.75)^2.

Student responses
Sections 4987, 4988
(A) : 8 students
(B) : 17 students
(C) : 13 students
(D) : 12 students

Physics quiz question: radial acceleration

Physics 5A Quiz 1, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 1.51

[3.0 points.] An object of mass m moving at constant speed v around a circle of radius r has a radial acceleration a = mv^2/r. If the speed is increased 12.0%, by what percentage does the radial acceleration increase?
(A) 1.44%.
(B) 13.6%.
(C) 25.4%.
(D) 29.1%.

Correct answer: (C)
a_1 = m*(v_1)^2/r, and a_2 = m*(v_2)^2/r. With v_2 = 1.120*v_1, then:

a_2/a_1 = (m*(v_2)^2/r)/(m*(v_1)^2/r) = (v_2/v_1)^2 = (1.120*v_1/v_1)^2 = (1.120)^2 = 1.2544,

or an increase of 25.4%, to three significant figures (expressed in percent form).

The incorrect response (A) is 100*(0.12)^2.

Student responses
Sections 0906, 0907
(A) : 16 students
(B) : 4 students
(C) : 23 students
(D) : 0 students