Physics midterm question: faster vertically swung ball

Physics 205A Midterm 1, fall semester 2019
Cuesta College, San Luis Obispo, CA

A Physics 205A student twirls a ball attached to a string in a vertical circle with constant speed. When the ball is swinging through the lowest part of the circle, the tension force on the ball is 1.8 N. Discuss why the magnitude of the tension force on this ball would have a larger magnitude if the ball had a faster constant speed while swinging through the lowest part of the circle (with the same radius). Explain your reasoning by using free-body diagram(s), the properties of forces and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Complete free-body diagram, and discusses/demonstrates:
  1. while the ball is swinging through the lowest part of the circle, there are two forces acting on the ball:

     Tension force T of hand on the ball (originally 1.8 N, upwards),
     Weight force w of Earth on the ball (constant magnitude of m⋅g, downwards);

  2. Newton's second law for uniform circular motion applies, such that while the ball is swinging through the lowest part of the circle, the net force ΣF (magnitude m⋅v²/r) must point in towards the center of the circular motion--which is vertically upwards; and
  3. increasing the speed v (while m and r are constant) would increase the required upwards net force for uniform circular motion, such that the upwards tension force will be greater than the original 1.8 N
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Some substantive attempt at applying Newton's second law for uniform circular motion.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some attempt at applying Newton's first law or third law for uniform circular motion.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic application of Newton's laws.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01duCk
p: 21 students
r: 11 students
t: 9 students
v: 9 students
x: 3 students
y: 0 students
z: 0 students

A sample "p" response (from student 1478):