Physics midterm problem: copper cylinder suspended in air, and in oil

Physics 205A Midterm 2, Fall Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 9.35

[20 points.] A copper cylinder (density 8.92e+3 kg/m^3) weighs 12.5 N when suspended from a scale in air. When this same cylinder is completely submerged in oil while suspended from a scale, the scale reading is 9.5 N. Find (a) the volume of the cylinder, and (b) the density of the oil. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Applies Newton's first law for the cylinder in air equating tension and weight to find mass, then finds volume V = m/rho_Cu = 1.4e-4 m^3. Applies Newton's first law for the cylinder in oil equating the upwards forces T = 9.5 N and F_B = rho_oil*g*V with the downwards weight (which is still 12.5 N), to solve for rho_oil = (w - T)/(g*V) = 2.1e+3 kg/m^3.
  
• r = 16/20:
  Nearly correct, but includes minor math errors.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Solves for volume using F_B = rho*g*V where F_B is 3.0 N, but rho is the density of water, or copper(!).
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Applies specific gravity definition rho_object/rho_fluid = V_submerged/V_total to solve for the density of the oil and/or the cylinder volume, or uses P_2 = P_1 + rho*g*d.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 72177
p: 4 students
r: 1 students
t: 3 students
v: 5 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7575):