The position of a 0.64-kg mass attached to a spring and undergoing simple harmon

Question

The position of a 0.64-kg mass attached to a spring and undergoing simple harmonic motion is given by x = (0.160 m) cos [(35 rad/s)t]. The spring constant of the spring is closest to: How long will it take to transfer 5.5 MJ of heat through a 2.25 m2 pane of 3 mm thick glass (k-0. S4 J/sm degree C) if the temperature difference is 12 degree C. A water heater is operated by a solar power. If the solar collector has an area of 6m2, and the intensity delivered by sunlight is 550 W/m2, how long does it takes to increase the temperature of 1000kg of water from 20 degree C to 60 degree C?

Explanation / Answer

14

Mass m = 0.64 kg
Position function x = 0.16 cos (35t)
Compare this with x = A cos (wt + phi) we get

A= 0.16

k= m/A = 0.64/0.16 =4

2)

use

dQ/dt = -k A dT/dx

where:
dQ/dt is the rate of heat tansfer
k is the conductivity of the material
A is the cross-sectional area
dT/dx is the temperature gradien

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