Consider a planet orbiting the fixed sun. take the plane of the planet's orbit to be the xy plane, with the sun at the origin, and label the planet's position by polar coordinates (r, (a) show that the problems for chapter 3 103 planet's angular momentum has magnitude = mr2w, where co = 4 is the planet's angular velocity about the sun. (b) show that the rate at which the planet "sweeps out area" (as in kepler's second law) is d a idt = 4r2w, and hence that d a idt = £/2m. deduce kepler's second law.

Mass (kg) force (n) 5 25 10 50 15 75 20 100 a student was trying to find the relationship between mass and force. he placed four different masses on a table and pulled them using a spring scale. the table shows the different masses used in the experiment and the force required to pull each mass. the student concluded that more force was required to pull heavier objects. what comment would you make regarding his conclusion? a) no clear relation can be observed between mass and force from the data. b) there is a direct proportion between the mass and force listed in the table. c) gravity should have been taken into account while performing the experiment. d) there is an inverse proportion between the mass and force listed in the table.