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ApplicationsEscape velocity The gravitational attraction F
Chapter 9, Problem 35PE(choose chapter or problem)
Problem 35PE
Applications
Escape velocity The gravitational attraction F exerted by an airless moon on a body of mass m at a distance s from the moon’s center is given by the equation where g is the acceleration of gravity at the moon’s surface and R is the moon’s radius (see accompanying figure). The force F is negative because it acts in the direction of decreasing s.
a. If the body is projected vertically upward from the moon’s surface with an initial velocity v0 at time t = 0, use Newton’s second law, F = ma, to show that the body’s velocity at position s is given by the equation
Thus, the velocity remains positive as long as The velocity is the moon’s escape velocity. A body projected upward with this velocity or a greater one will escape from the moon’s gravitational pull.
b. Show that if then
Questions & Answers
QUESTION:
Problem 35PE
Applications
Escape velocity The gravitational attraction F exerted by an airless moon on a body of mass m at a distance s from the moon’s center is given by the equation where g is the acceleration of gravity at the moon’s surface and R is the moon’s radius (see accompanying figure). The force F is negative because it acts in the direction of decreasing s.
a. If the body is projected vertically upward from the moon’s surface with an initial velocity v0 at time t = 0, use Newton’s second law, F = ma, to show that the body’s velocity at position s is given by the equation
Thus, the velocity remains positive as long as The velocity is the moon’s escape velocity. A body projected upward with this velocity or a greater one will escape from the moon’s gravitational pull.
b. Show that if then
ANSWER:
SOLUTION:
Step 1 of 3:
In this question, (a) If the body is projected vertically upward from the moon’s surface with an initial velocity at time , use Newton’s second law, , to show that the body’s velocity at position is given by the equation
(b) Show that if then
