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(a) If H(t) is the temperature of the spring at time t (minutes), explain what the differential equation dH --k(H – 20) dt means in everyday terms. (b) What is the sign of k in the equation? (c) Solve the differential equation under the assumption that the spring starts at 1000° C. If the spring cools to 90° C in 2 minutes, how long will it take to cool to 60° C?

(a) If H(t) is the temperature of the spring at time t (minutes), explain what the differential equation dH --k(H – 20) dt means in everyday terms. (b) What is the sign of k in the equation? (c) Solve the differential equation under the assumption that the spring starts at 1000° C. If the spring cools to 90° C in 2 minutes, how long will it take to cool to 60° C?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The solution to (c) is (in minutes) (2 decimal places)

4. A steel spring is heated then quenched in a bucket of water at 20° C. (Dr. Robinson likes doing metalwork... and fire...) (a) If H(t) is the temperature of the spring at time t (minutes), explain what the differential equation dH = -k(H – 20) dt means in everyday terms. (b) What is the sign of k in the equation? (c) Solve the differential equation under the assumption that the spring starts at 1000° C. If the spring cools to 90° C in 2 minutes, how long will it take to cool to 60° C?
Transcribed Image Text:4. A steel spring is heated then quenched in a bucket of water at 20° C. (Dr. Robinson likes doing metalwork... and fire...) (a) If H(t) is the temperature of the spring at time t (minutes), explain what the differential equation dH = -k(H – 20) dt means in everyday terms. (b) What is the sign of k in the equation? (c) Solve the differential equation under the assumption that the spring starts at 1000° C. If the spring cools to 90° C in 2 minutes, how long will it take to cool to 60° C?
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