Two skaters, a man and a woman, are standing on ice. Neglect any friction betwee

Question

Two skaters, a man and a woman, are standing on ice. Neglect any friction between the skate blades and the ice. The mass of the man is 78 kg, and the mass of the woman is 58 kg. The woman pushes on the man with a force of 65 N due east. Determine the acceleration (magnitude and direction) of the following. (a) the man a_man = (b) the woman a_woman At a time when mining asteroids has become feasible, astronauts have connected a line between their 3400-kg space tug and a 6150-kg asteroid. Using their ship's engine, they pull on the asteroid with a force of 490 N. Initially the tug and the asteroid are at rest, 450 m apart. How much time does it take for the ship and the asteroid to meet? S On earth, two parts of a space probe weigh 10000 N and 4400 N. These parts are separated by a to distance of 24 m and may be treated as uniform spherical objects. Find the magnitude of the gravitational force that each part exerts on the other out in space far from any other objects N

Explanation / Answer

Solution 1).

from the 3rd Law of Newton the woman pushes on the man=theforce the man exerts back to the women

(a) the acceleration of the man:

a = F/m = 65/78 = 0.833 m/s2 , the direction due east

(b) for the women

a = F/m = 65/58 = 1.12 m/s2 , due West

Solution 2).

accelerationof asteriod

a = F/m = 490/6150 = 0.0796 m/s^2

acceleration of tug

at = 490/3400 = 0.144 m/s^2

a = aA+at = 0.0796+0.144 = 0.2236 m/s^2

X = Vot+(1/2)at^2

450 = 0+(1/2)*0.2236*t^2

t^2 = 450/0.1118

t = sqrt(4025)

t = 63.44 s

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