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A Winter Cover for a Violin Case

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A Winter Cover for a Violin Case

Test case covers for an outdoor winter concert and judge them against a cooling-rate rule.

Part 1: Round 1 on the cold patio

Read the passage and use Tables 1 and 2 to answer questions 1–5.

Playing at the Tree Lighting

1Every December, the Lakeshore Youth Orchestra plays at the town's tree lighting. The players ride a warm bus to the town square, carry their cases across a cold plaza and wait about 40 minutes beside the stage before they unpack. Last year, several violins came out of their cases badly out of tune, and one had a new crack in its varnish.

2Violin maker Mr. Augustin Ferreol visited the orchestra's engineering club. He explained that many violin makers advise keeping a violin from cooling quickly, because wood and varnish can shrink by different amounts when they cool fast. A hard case alone slows the cooling a little, but the club decided to design a cover that zips around the case.

3Club leader Yasmin Okonjo-Reyes wrote four requirements for the cover. The air inside the case must still be 12 °C or warmer after 40 minutes outside. The air inside must never drop more than 3 °C in any 10-minute period. The cover may add at most 500 g to the case. The materials may cost at most $20.

4To test each design, the club placed a violin-shaped wooden block with a thermometer inside a case. The case sat in the warm music room until the air inside read 21 °C. Then the club carried it out to the school patio on an evening when the air was −4 °C and a light wind was blowing, and they read the thermometer every 10 minutes. Every design used the same case, block and thermometer.

Table 1: Round 1 Designs (start 21 °C, air −4 °C)
Design	Cover	Added mass (g)	Cost	Inside at 40 min (°C)
A	No cover (case alone)	0	$0	4
B	Fleece cover	250	$12	9
C	Fleece cover with a foil layer	300	$15	11
D	Closed-cell foam cover, 1 cm	450	$18	13
E	Closed-cell foam cover, 2 cm	800	$24	16

Table 2: Air Inside the Case Every 10 Minutes (°C)
Time (min)	A	B	C	D	E
0	21	21	21	21	21
10	13	16	17	19	19
20	8	13	14	17	18
30	5	11	12	15	17
40	4	9	11	13	16

1.

Use Table 2.

During the 40 minutes, the air inside the case with no cover (Design A) cooled by °C.

2.

Use Table 2. Circle each design that meets the rule "never drop more than 3 °C in any 10-minute period."

3.

Design C ended at 11 °C, just under the 12 °C goal. Suppose a better thermometer showed it really ended at 12 °C. Use Table 2. Would Design C then meet the requirements in paragraph 3?

A. No, because it cooled by 4 °C in the first 10 minutes, more than the rule allows.B. Yes, because it would meet the end goal, the mass limit and the cost limit.C. Yes, because it cooled by 2 °C or less in each of the last two periods.D. No, because its foil layer adds more than 500 g to the case.

4.

Use Table 2. Look at the first 10 minutes only.

In the first 10 minutes, the air in Design A cooled times as many degrees as the air in Design D.

5.

Use paragraph 4 and Table 1. The fleece cover (B) and the 1 cm foam cover (D) are about the same thickness, yet the air in Design B ended 4 °C colder. Fleece is made of loose fibers with open spaces between them. Closed-cell foam is made of tiny sealed bubbles of air. Which is the best explanation?

A. The foam made its own thermal energy from the wind, which kept the air in Design D warmer.B. The fleece took in the cold from the patio and passed that cold into the case with the block.C. Wind pushed cold air through the fleece's open spaces, so warm air near the case was carried off faster.D. The fleece was lighter, and a lighter cover lets cold soak into the case faster than a heavier one.

Part 2: Round 2, improving Design D

The club changed Design D in two ways and tested again on a night with the same −4 °C air and light wind. Use Table 3 and Part 1 to answer questions 6–11.

Table 3: Round 2 (start 21 °C, air −4 °C)
Design	Change to Design D	Added mass (g)	Cost	Largest 10-min drop (°C)	Inside at 40 min (°C)
D	None	450	$18	2	13
D2	Foil layer inside the foam	480	$19	2	15
D3	Zipper flap left open 5 cm	450	$18	4	10

6.

The club wants the design that meets every requirement in paragraph 3 and keeps the air inside the case the warmest after 40 minutes. Use Tables 1, 2 and 3. Which design should the orchestra use?

A. Design C, because its foil layer reflects energy and it costs $4 less than Design D2B. Design D2, because it ended at 15 °C, dropped 2 °C at most and stays within both limitsC. Design E, because it ended at 16 °C, the warmest result in Round 1D. Design D, because it ended at 13 °C and has the lowest cost of the foam designs

7.

Use Table 3. Compare Design D2 with Design D.

The foil layer kept the air inside °C warmer at 40 minutes and added g of mass.

8.

Design D3 is Design D with the zipper flap left open 5 cm. Which statement best explains its result?

A. Cold flowed in through the gap, and the cold took the place of the case's thermal energy.B. The open flap let the foam give off its stored thermal energy into the night air.C. The gap made the cover lighter, and lighter covers hold less thermal energy in the case.D. Warmer air inside could flow out through the gap as colder air flowed in, carrying energy away.

9.

Match each part of Design D2 to the way it most likely slows thermal energy transfer out of the case.

10.

In June, the orchestra plays outdoors on a 34 °C afternoon. The violins leave an air-conditioned bus at 22 °C. How would the Design D2 cover most likely affect the air inside a case while the players wait?

A. It would slow thermal energy moving into the case, so the inside would warm more slowly.B. It would speed up thermal energy moving into the case, because foil gathers sunlight.C. It would warm the inside faster, because foam stores the afternoon's thermal energy.D. It would keep cold inside the case, so the inside would cool below 22 °C as the players waited.

11.

The orchestra director says, "The fleece cover (Design B) is good enough. The air in the case was still well above freezing after 40 minutes." Do you agree? Write a claim, give evidence from Tables 1 and 2, and explain your reasoning about how thermal energy moves out of the case.