Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 6.85
A 0.50 kg box is held stationary against a k = 85.0 N/m spring, compressing it a certain distance from its equilibrium position. The box is then released, and moves up a frictionless ramp. When the box is at a height of 0.75 m above the base of the ramp, it has a velocity of 1.3 m/s. How much was the spring compressed from its equilibrium position, before the box was launched? Neglect drag. Show your work and explain your reasoning using the properties of energy conservation. Solution and grading rubric:
- p:
Correct. Identifies relevant terms in energy balance equation (Ktr, Ugrav, Uelas), and solves for xi. - r:
Nearly correct, but includes minor math errors. - t:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. - v:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. At least some attempt at energy conservation, but with missing or misapplied energy terms. - x:
Implementation of ideas, but credit given for effort rather than merit. - y:
Irrelevant discussion/effectively blank. - z:
Blank.
Grading distribution:
p: 12 students
r: 7 students
t: 4 students
v: 8 students
x: 1 students
y: 1 student
z: 1 student
A sample of a "p" response (from student 2325), setting up a "zero-sum" energy balance equation:
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