1st EditionHolt McDougal562 explanations
1st EditionKenneth R. Miller, Levine2,591 explanations
1st EditionKenneth R. Miller, Levine2,875 explanations
1st EditionPrentice Hall440 explanations
BIOLOGYThe work required to launch an object from the surface of Earth to outer space is given by W=$\int _ { R } ^ { \infty } F ( x ) d x$, where R=6370 km is the approximate radius of Earth, F(x)=$G M m / x ^ { 2 }$ is the gravitational force between Earth and the object, G is the gravitational constant, M is the mass of Earth, m is the mass of the object, and GM=$4 \times 10 ^ { 14 } \mathrm { m } ^ { 3 } / \mathrm { s } ^ { 2 }$. a. Find the work required to launch an object in terms of m. b. What escape velocity $v_e$ is required to give the object a kinetic energy $\frac { 1 } { 2 } m v _ { e } ^ { 2 }$ equal to W? c. The French scientist Laplace anticipated the existence of black holes in the 18th century with the following argument: If a body has an escape velocity that equals or exceeds the speed of light, c=300,000 km/s, then light cannot escape the body and it cannot be seen. Show that such a body has a radius R$\leq 2 G M / c ^ { 2 }$. For Earth to be a black hole, what would its radius need to be?
