Imagine that two identical containers, one filled with marbles and the other filled with Styrofoam beads, are released simultaneously from rest from the same height- Earth's surface. (a) Which container, if either, experiences the greater gravitational force? O the container filled with marbles O the container filled with beads Both containers will experience the same gravitational force. Justify your answer. O Since both containers fall to the ground with the same acceleration, both will experience the same gravitational force. O Gravitational force is directly proportional to mass, so the heavier container would experience the greater gravitational force. O Gravitational force is inversely proportional to mass, so the lighter container would experience the greater gravitational force. O Since the acceleration due to gravity is 9.8 m/s2 for each container, both will experience the same gravitational force. (b) Which container, if either, experiences the greater acceleration from gravity? O the container filled with marbles O the container filled with beads O Both containers will experience the same acceleration from gravity. Again, justify your answer. the mass of the falling object, so both containers will experience the same acceleration from gravity. O The acceleration from gravity does not depend O Gravitational acceleration is inversely proportional to mass, so the lighter container would experience the greater acceleration from gravity. O Since the mass of both containers is the same, they both will experience the same acceleration from gravity. O Gravitational acceleration is directly proportional to mass, so the heavier container would experience the greater acceleration from gravity.

Calculate the gravitational constant g, in SI units, for alocation on the surface of the sun.

There is a small sphere of mass m at a height H, from the center of a uniform ring of radius R and mass M. The center of the ring is placed at the origin of a Cartesian coordinate system. The x and y directions line in the plane of the ring, while the z-direction is positive upwards.’  Take the x-axis to be directed towards the right (in the plane of the ring). Write an expression for the x-component of the gravitational force Fx on the mass m, where G is the gravitational constant.

, are: Three point particles are fixed in position in an xy plane. Two of them, particle A of mass 5 g and particle B of mass 11 g, are shown in the figure with a separation of dAB = 0.519 m at angle O = 30°. Particle C, with mass 9 g, is not shown. The net gravitational force acting on particle A due to particles B and Cis 2.71 x 1014 N at an angle of -163.8°. from the positive x axis. What are (a) the x coordinate and (b) the y coordinate of particle C? В dAB A

Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of birth. The only known force a planet exerts on earth is gravitational. (a) Calculate the gravitational force exerted on a 3.00 kg baby by a 90 kg father 0.150 m away at birth (assisting so he is close). N (b) Calculate the force on the baby due to Jupiter if it is at its closest to the earth, some 6.29 × 1011 m away, showing it to be comparable to that of the father. The mass of Jupiter is about 1.90 × 1027 kg. Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.) Additional Materials M Reading

A particle is projected vertically upward in a constant gravitational field with an initial speed Vo. There is a retarding force proportional to the instantaneous speed. Calculate the time it takes to come back to the initial position.

A 4500-kg spaceship is in a circular orbit 180 km above the surface of Earth. It needs to be moved into a higher circular orbit of 390 km to link up with the space station at that altitude. In this problem you can take the mass of the Earth to be 5.97 × 1024 kg.  a) How much work, in joules, do the spaceship’s engines have to perform to move to the higher orbit? Ignore any change of mass due to fuel consumption.

A satellite moves in a circular orbit around Earth at a speed of 4381 m/s. (a) Determine the satellite's altitude above the surface of Earth. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m (b) Determine the period of the satellite's orbit. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. h Need Help? Read It

A 4500-kg spaceship is in a circular orbit 170 km above the surface of Earth. It needs to be moved into a higher circular orbit of 390 km to link up with the space station at that altitude. In this problem you can take the mass of the Earth to be 5.97 × 1024 kg. a)How much work, in joules, do the spaceship’s engines have to perform to move to the higher orbit? Ignore any change of mass due to fuel consumption.

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