A 10.0 kg block falls 30.0 m onto a vertical spring whose lower end is fixed to a platform. When the spring reaches its maximum compression of 0.200 m, it is locked in place. The block is then removed and the spring apparatus is transported to the Moon, where the gravitational acceleration is g/6. A 50.0 kg astronaut then sits on top of the spring and the spring is unlocked so that it propels the astronaut upward. How high above that initial point does the astronaut rise ?

A spaceship is orbiting the earth in a circular orbit at a height equal to radius of the earth (R_(c) = 6400 km) from the surface of the earth. An astronaut is on a space walk outside the spaceship. He is at a distance of l = 200 m from the ship and is connected to it with a simple cable which can sustain a maximum tension of10 N. Assume that the centre of the earth, the spaceship and the astronaut are in a line. Mass of astronaut along with all his accessories is 100 kg. Do you think that a weak cable that can only take a load of 10 N, can prevent him from drifting in space ? Make a guess. Estimate the tension in the cable. [Acceleration due to gravity on the surface of [ Earth =9.8m//s^(2) ]

Two astronauts having mass of 75 kg and 50 kg are connected by a rope of length L = 10m and negligible mass. They are in space, orbiting their centre of mass at an angular speed of omega_(0) = 5 rad/s. The centre of mass itself is moving uniformly in space at a velocity of 10 m//s . By pulling on the rope, the astronauts shorten the distance between them to (L)/(2) = 5m . How much work is done by the astronauts in shortening the distance between them ? Assuming that the astronauts are athletic and each of them can generate a power of 500 watt, is it possible for the two astronauts to reduce the distance between them to 5 m , within a minute?

A 80 kg person expends 400 W when walking on a horizontal tracker belt at a speed of 7.2 kph. When the tracker belt is inclined without changing the speed, the person's expended power increases to 600 W. Estimate the angle of incline of the tracker belt by assuming that all of the increased output power goes into overcoming the force of gravity. Assume constant friction by tracker belt in both horizontal and inclined position Take g=10m//s^(2)

At a time when mining asteroids has become feasible, astronauts have connected a line between their 600 kg space ship and a 1200 kg asteroid. Using their ship's engine, they pull on the asteroid with a constant force of 450 N. Initially the space ship and the asteroid are at rest, 225m apart. How much time (in second) does it take for the ship and the asteroid to meet? (Neglect gravitational interaction).

A planet has the same size as that of the earth but its mass is 4 times the mass of the earth. What is the energy required to lift a stone of mass 5 kg vertically upwards through 3 m, on the planet ? [g on the surface of the earth = 10 m//s^(2) ]

A 70.0 kg astronaut pushes to the left on a spacecraft with a force vec(F) in "gravity-free" space. The spacecraft has a total mass of 1.0xx10^(4) kg. During the push, the astronaut accelerates to the right with an acceleration of 0.36" m"//"s"^(2) . Determine the magnitude of the acceleration of the spacecraft.