A vertical spring (ignore its mass), whose spring stiffness constant is 950 N/m, is attached to a table and is compressed down 0.150 m. (a) What upward speed can it give to a 0.30-kg ball when released? (b) How high above its original position (spring compressed) will the ball fly?
Solution Step 1 of 3 The quantities like orbital period, speed and acceleration of the satellite revolving around the earth, does not depend on the mass of the satellite. It depends on the mass of the central body around which the satellite is revolving and the radius of the orbit. Orbital speed Objects that travel in uniform circular motion around the Earth are said to be "in orbit". The velocity of this orbit depends on the distance from the object to the center of the Earth. The velocity has to be just right, so that the distance to the center of the Earth is always the same. Such a velocity is known as orbital velocity. The orbital speed of the satellite is given by, Since in uniform circular motion, Centripetal force = Gravitational force on satellite by earth mv 2 r = Gr2m Where m and M is the mass of the satellite and earth, r is the distance of satellite from earth center, G is gravitational constant and v is the orbital speed of the satellite. Solving for speed, G Mm v = mr GM v = r………………….1 Where v is the orbital speed, r is the radius of the orbit, G is gravitational constant and M is the mass of the earth. Step 2 of 3 Generally for the object that perform uniform circular motion, the orbital time period is given by, T = (2r/v) Where 2r is the circumference of the orbit of radius r and v is the speed, T is orbital period. Solving for r, r = (vT/2).....................................2 USing equation 2 in equation 1, v = GM (vT/2) v = 2GM vT Rearranging for time period, 2 2GM v = vT 2GM T = v