Question

on is a short free short free-response question. Show your work for each part of the 2R Note: Figures not drawn to scale. An astronaut stands on the surface of a spherical asteroid that has a weak gravitational telo but no atmosphere. The astronaut throws a small rock straight upward, as shown at left above The rock travels upward until it reaches a distance of 2R from the center of the asteroid, where R is the asteroid's radius, and then falls back down to the asteroid's surface (a) The dots below represent the rock immediately after being thrown and when it is a distance 2R from the asteroid's center. On each dot, draw and label the forces (not components) exerted on the rock at the indicated time. Each force must be represented by a distinct arrow starting on, and pointing away from the appropriate dot. Note: Draw the relative lengths of all vectors to reflect the relative magnitudes of all the forces at both times. ROCK IMMEDIATELY ROCK AT A DISTANCE 2 R AFTER BEING THROWN FROM ASTEROID'S CENTER - - - - - ----+-- i 1 - i ---- 1 1 1 --+---+--- 1 1 1 1 - -- ---- - -- ----- -- - - - -- - - -- - - - - - - - - -- i ! - ! - - - - - ! - ! ! !

Answer 1

W is the weight of the rock on the asteroid

= GMm /R , M mass of asteroid , m mass of rock

F , force applied by the astronaut on the rock

weight of the rock W always acts down ward, towards the center of the asteroid, the rock moves up until its upward velocity becomes 0 and then falls back

First throw : initial velocity v₀₁

when thrown up with initial velocity v₀₁ , the rock experiences acceleration downward

a = - GM/(R+h)² , h is the height of the rock, after time t₁ h = R, the velocity becomes 0 due to -ve acceleration and then it falls back towards the center.

gravitation force exerted on the rock F = GMm/(R+h)² , as the rock gets farther form the asteroid, the force decreases.

at t=0 , F = GMm/R² after t₁ , the rock reaches a height h = R

gravitational force F = GMm/4R²

For the second throw, the initial velocity is more then the escape velocity for the asteroid and it has sufficient KE to escape the gravitational pull of the asteroid, the rock has a const velocity after escaping the gravitational pull of the asteroid.

if the initial speed of the rock v > (2GM/R)^1/2 , the rock can escape from the asteroid, once it escapes from the gravitational pull , ther is no force acting on the rock and it moves with const. velocity.