Suppose you conduct an experiment and determine that g = 9.74 m/s² . If you assume that g = 9.81 m/s? at the surface of the earth, how far from the surface are you? Give your answer in units of Re, the radius of the Earth. (Re = 6378 km)

Newton's theory of gravity, together with the Cavendish experiment to measure the value of Newton's constant G, determines the acceleration due to gravity at the surface of a sphere. For example, the acceleration due to gravity at the surface of Earth is g 9.81 m/s^2. Calculate the acceleration due to gravity at the surface of the sun, which has mass 1.989x10 30 kg and 6.96x108 m. radius = (in m/s^2) A: 112.2 OB: 140.2 OC: 175.3 OD: 219.1 OE: 273.9 OF: 342.3 OG: 427.9 OH: 534.9

The depth of water at a beach changes every 12 hours because of the tides. This forms a periodic function. You get up early on one of the days of spring break and start measuring the depth. The depth at 8AM (t=0)is 7 feet, which is a high point. The low at 2PM is 1 foot deep. According to your model, detemine the height of the tide at 5PM. (Give the VALUE only. Do not include the unit of measurement in your answer.) 4

Idealize the Earth as a perfect sphere of radius R = 6371 km. If you could measure distances with an error of ±1 meter, how large a circle would you have to draw on the Earth’s surface to convince yourself that the Earth is spherical rather than flat?  Note that (or prove yourself) on the surface of a sphere, a circle of radius r will have a circumference of C = 2πR sin(r/R).    Round your answer to the nearest whole number. Hint: recall that you can approximate sin(x) with a Taylor series expansion: sin(x) \approx≈ x - x3/3! Answer value

The length of cell A is 8×10^5 m. The length of cell B is 0.000004 m. What is the ratio of cell​ A's length to cell​ B's length? Use pencil and paper. Is it easier to find the ratio when the numbers are expressed in scientific notation or in standard​ form? Explain your reasoning.

a) Observations and trigonometry can be used to determine that Earth's moon has an orbital period of 27.32 days and a mean orbital radius of 384,400 km. Using this information, calculate the mass of the Earth. 2 M = 47² ² 2 C M= 4+1 (30214100000) 667 e

One mole of Gold (Au) atom has a mass of 197 g. We know that the density of gold is 19.30 g/cm3 in room temperature. Using those numbers, answer the following questions: a) What is the mass of a single gold atom in kg? b) Assume that gold atoms sit in a perfect cubic crystal structure. Estimate the distance between two gold atoms in meters.   c) If we have a gold cube of 6 cm on each side, how many atoms can we fit along the edge of each side of the cube?  d) What would be the mass, in kilograms, of the gold cube we discussed in part (c) (measuring 6 cm on each side)?

In this problem you will measure the gravitational constant in a series of “observational experiments,” making use of Newton’s law of gravitation and second law of motion as well as Kepler’s third law of planetary motion Suppose a rocket is launched as described in part (d) with an initial speed of vi = 494 m/s and attains a peak altitude of H = 12.7 km above the surface of Earth. Taking ME = 5.95×1024 kg and Ri = 6.41×106 m, what is the measured value of the gravitational constant, in units of N⋅m2/kg2?

The International Space Station (ISS) is a space station orbiting the earth above the ground. If the radius of the earth is 3,958.8 miles, mass of earth is 5.972 x 10 24 kg,  the period of the ISS at the orbit around the earth is 10.934 hours, can you calculate what is the distance from the ISS to the surface of the earth, in unit of miles? Use G=6.674 x 10 -11 Nm2/kg2. Write your answer in pure numbers, for example, 4567.8. Please keep at least on digit after the decimal point.

A room has dimensions of 9.8 meters by 8.3 meters by 3.5 meters. Air has a mass density of 1.3 kilograms per cubic meter. Using 9.8 meters per second squared for "g", the acceleration due to gravity, calculate the weight of air in the room in Newtons.