Schwarzschild radius RS of a black hole is the maximum distance from the black hole’s center at which light cannot escape its gravitational field. The quantity RS (with dimensions of length) is dependent on the mass of the black hole M, the speed of light c, and the gravitational constant G. Based on the dimensions of these four parameters, predict an equation for the Schwarzschild radius. Hint: G has dimensions of [L3/MT2]

In 1999, NASA lost the Mars Climate Orbiter because one group of engineers used metric units in their calculations while another group used English units. Consequently, the orbiter descended too far into the Martian atmosphere and burned up. Suppose that the orbiter was to have established orbit at 157 km and that one group of engineers specified this distance as 1.57 x 10³ m. Suppose further that a second group of engineers programmed the orbiter to go to 1.57 x 10³ ft. The $125 million Mars Climate Orbiter was lost in the Martian atmosphere in 1999 because two groups of engineers failed to communicate with each other about What was the difference in kilometers between the two altitudes? Express your answer with the appropriate units. Value Submit HA Provide Feedback Part B Complete previous part(s) Units Request Answer ?

Problem 13:   In this problem, the symbols M, L, and T represent the dimensions mass, length, and time, respectively. Consider the physical quantities s, v, a, and t with dimensions [s] = L, [v] = LT-1, [a] = LT-2, and [t] = T. (Here, the square bracket means “the dimensions of” so, for example, [s] represents the dimensions of the quantity s.) Part (a)  What is the simplest expression involving only a and s that has the same dimensions as v2?  expression = ______ Part (b)  What is the simplest expression involving only v and t that has the same dimensions as a?  expression = ______ Part (c)  What is the simplest expression involving only v and t that has the same dimensions as s?  expression = ______ Part (d)  What is the simplest expression involving only a and t that has the same dimensions as s? expression = ______

(a) Compute the mass of the earth from knowledge of the earth-moon distance (3.84 * 10^8 m) and of the lunar period (27.3 days). (b) Then calculate the average density of the earth. The average radius of the earth is 6.38 * 10^6 m.

A high tech company uses a satellite to measure the size of features on the surface of the earth. They use this technology to measure a particular rectangular field and find it's length to be 444 ± 1.8 in meters and it's width to be 198 ± 1.63 in meters. They plan to report the perimeter (sum of two lengths and two widths) of the field as P± SP in units of yards. (1 meter = 1.094 yards) What is SP?

A rectangular box with mass 16.5 g is said to have dimensions of 2.8 cm x 1.7 cm * 0.4 cm . Calculate the density of this rectangular box, in g/cm^ 3 . The volume of a rectangular box is length times width times depth (I^ * W^ * d) .

Newton's universal law of gravitation can be stated as the force F of gravitation between two objects varies jointly as the masses m, and m, of the objects, and Gm,m2 inversely as the square of the distance r between their centers, where G is the constant of proportionality. In other words, F = The weight of an object is the force F on the object due to gravity, where F = mg. State how g (the acceleration due to gravity) varies with respect to the mass m, of the spherical body on which the object lies, and the radius of that body (assume all of the mass is at its center.). The acceleration due to gravity, g, varies as the spherical body's mass, and as

An expression for buoyant force is FB = ρgV, where FB has dimensions [MLT−2], ρ (density) has dimensions [ML−3], and g (gravitational field strength) has dimensions [LT−2].   The correct interpretation of V is that it represents velocity or volume?

This time the quantities will be different, again randomly chosen by the computer.  The mass will be much smaller for a different reason. The shell is thin, but has a definite thickness.  Calculate the (volume) density of the shell, in g/cm3.  Here are the numbers: R = 27 cm M = 800 grams thickness = 0.4 mm

A bacteria colony which is unrestricted in its growth will grow out in a circular manner. The population ?(?) of the colony at time t is directly proportional to the area of the circle. Suppose that a particular bacteria grows in such a way that the population is 1.3 times larger each day, and that initially (t=0) the colony has a diameter of 4 centimeter and a population of 7 million. a) Find the Population and Diameter of the colony on the fifth day. b) Find the Rate of Change of the Population and Diameter of the colony on the fifth day. c) Unrestricted growth models are often impractical as values will quickly become unreasonable. On what day does our model predict that the area of the bacteria colony will be 1 square mile?