Newton’s second law - 2024 PLAYTIME

Question

You are an enterprising physics student who has just been asked to solve Norton’s dome, a thought experiment about a ball rolling down a hill. For 10 points each:

[10e] You begin by computing the tangential gravitational force on a point mass sliding off the dome so that you can plug it into this law, which states that the force on an object is equal to the rate of change of momentum.

ANSWER: Newton’s second law [prompt on F equals m a]

[10m] To your surprise, you discover that solutions to Newton’s second law exist but lack this corresponding property, thus apparently providing an example of indeterminism in physics.

ANSWER: uniqueness

[10h] You realize that the dome’s non-determinacy may be sidestepped by observing that at time zero, net force is undefined. Requiring the ball to remain on the dome may thus be modeled as this kind of constraint, in which some function of the generalized coordinates and time is set equal to zero.

ANSWER: holonomic constraints

<JC, Physics>

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Summary


2025 PLAYTIME @ CWRU	12/10/2024	Y	5	10.00	100%	0%	0%
2025 PLAYTIME @ Claremont	12/10/2024	Y	5	12.00	80%	20%	20%
2025 PLAYTIME @ Florida	12/10/2024	Y	3	13.33	100%	33%	0%
2024 PLAYTIME @ Harvard	04/26/2025	Y	4	20.00	100%	50%	50%
2024 PLAYTIME @ JHU	10/26/2024	Y	4	10.00	75%	25%	0%
2025 PLAYTIME @ Northwest	12/10/2024	Y	4	5.00	50%	0%	0%
2025 PLAYTIME Online	04/26/2025	Y	9	13.33	100%	11%	22%
2025 PLAYTIME @ Sheffield	12/10/2024	Y	7	14.29	100%	29%	14%
2024 PLAYTIME @ UBC	10/05/2024	Y	8	16.25	100%	38%	25%
2024 PLAYTIME @ Virginia Tech	07/11/2025	Y	3	16.67	100%	33%	33%
2024 PLAYTIME @ WashU	10/12/2024	Y	6	11.67	100%	17%	0%

Data


Michigan C	Pittsburgh	10	0	0	10
Michigan D	Michigan B	10	0	0	10
UCSD	Art of Premature Signaling	10	0	0	10
Claremont B	Caltech	10	10	10	30
Claremont A	P.C.‚ Daniel‚ Michel‚ and Jason B	0	0	0	0
UCLA B	girl 15 whale i mean they	10	0	0	10
UCSB	UCLA A	10	0	0	10
Too much from you lately	Billy's Bastion	10	10	0	20
Edwin Laundrorat's Long-Lost Man Unclothès Rat Degrosses	Project2025BC: Make Assyria Great Again	10	0	0	10
Qin Shi Huang's Immortality Poison	Keeping Up With the Cardassians	10	0	0	10
Brandeis	Belmont	10	0	0	10
Brown	BU	10	10	10	30
Lexington	Harvard	10	0	0	10
RIT	MIT	10	10	10	30
Rutgers	George Mason C	10	10	0	20
Alberta	Arizona State University A	0	0	0	0
Arizona State University B	Carleton	10	0	0	10
UW B	UW A	10	0	0	10
Washington Connections	South Dakota School of Mines	0	0	0	0
George Mason A	NYU A	0	0	0	0
CWRU	Haverford A	10	0	0	10
Johns Hopkins A	Maryland B	10	0	0	10
Trip-Hop Quizzer Tricky	Monsieur Hulot's Academic Team	10	10	0	20
mongeese	Quatumvirate	10	0	0	10
Gruh	we need new names	10	0	0	10
Sheffield A	Cambridge	10	10	0	20
Manchester	LSE	10	0	0	10
Edinburgh	Sheffield B	10	0	0	10
Imperial A	Sheffield C	10	0	10	20
Warwick A	Birmingham	10	10	0	20
Imperial B	Warwick B	10	0	0	10
Lancaster	Warwick C	10	0	0	10
Ottawa A	Guelph	10	0	0	10
Waterloo C	Simon Fraser	10	10	0	20
Toronto A	Toronto C	10	0	0	10
Waterloo A	Toronto B	10	10	10	30
Mac A	Toronto D	10	0	0	10
McGill B	Toronto Metropolitan	10	0	0	10
UBC	Toronto E	10	0	0	10
Waterloo B	McGill A	10	10	10	30
MSJ	2 Italians, 2 Poles, All Noles	10	0	0	10
Illinois Orange	Auburn 2026	10	0	0	10
Free Agents 1	evil women enjoyers	10	0	10	20
Goober Gang	Notre Dame + Epic Games	10	0	0	10
Mahjonng Masters	Four Generalists in Search of a Power	10	0	0	10
Egypt Airlines Haters	Mike Dukakis Tank Battalion	10	0	10	20
4 quizbowl pros go Virginia on North Carolina	Even in Blacksburg There I Am	10	10	10	30
Master and Margaritaville	Adrianne Lenker 4 Nobel Lit Prize 2K65	10	0	0	10
Ashurbanipal’s Drag Race	Somehow Paula Deen Returned	10	0	0	10
Chicago A	WashU Bulbasaur	10	0	0	10
Chicago B	Illinois B	10	0	0	10
Illinois A	Iowa State	10	0	0	10
SIUE	Illinois C	10	0	0	10
Missouri	Truman State	10	0	0	10
WashU Charmander	WashU Squirtle	10	10	0	20
Ohio State B	Oberlin	10	0	0	10
Ohio State D	Ohio State A	10	0	0	10
Michigan A	Ohio State C	10	0	0	10