A spherical balloon has a radius of 6.95m and is filled with helium. The density of helium is 0.179 kg/m3, and the density of ai

The visible spectrum extends from 390 nm to 700 nm. It consists of the colors red (620 - 750 nm), orange (590 - 620 nm), yellow (570 - 590 nm), green (495 - 570 nm), blue (450 - 495 nm), and violet (380 - 450 nm), so a wavelength of 449 nm would correspond to a violet hue.

0.00066518 Nm

The formula used is known as the Law of Universal Gravitation. The gravitational constant G is 6.67×10⁻¹¹ Nm²/kg². The Earth's mass is <span>5.972 ×10</span>²⁴ kg. The mass of the rocket is negligible in comparison to Earth’s mass, hence it is unnecessary for our calculations. Plugging in the values:

F = (6.67×10⁻¹¹ Nm²/kg²)(5.972 ×10²⁴ kg)/(4000 miles*(1.609 km/1 mile))²
F = 9616423.08 N

The work done is given by
W = Fd
W = (9616423.08 N)(2000 miles*1.609 km/mile)
W = 9.095×10¹⁰ Joules

Assuming: For a first-order instrument with a sensitivity of 0.4 mV/K and a time constant of 25 ms, the initial temperature is 273 K and the final temperature is 473 K. Initially, the volume is 0.4 mV/K multiplied by 273 K, equating to 109.2 V. The final volume is calculated as 0.4 mV/K multiplied by 473 K, resulting in 189.2 V. The response of the instrument over time for a rapid rise in temperature is as follows: Considering y as the function of time, we have y(t) = 109.2 + (189.2 - 109.2)(1 - ) mV. This simplifies to y(t) = (109.2 + 80(1 - )) mV. You can graph the response y(t) over time. The response graph of y(t) over time is displayed in the diagram below. The unit for y(t) is mV. To determine the 90% rise time for y(t90) along with the error fraction, you set 90% of 189.2 mV, thus: 0.9 × 189.2 mV = 170.28 mV. When rewritten, we get 170.28 mV = (109.2 + 80(1 - )) mV. This leads to 170.28 mV - 109.2 mV = 80(1 - )) mV, yielding 61.08 mV as 80(1 - )) mV. Thus, 0.7635 mV = (1 - )) mV. When calculating time, we find that t = 1.44 × 25 × 10⁻³ s = 0.036 s, which converts to 36 ms. Thus, the error fraction works out to be 0.1 or 10%.

145.43 N