The gravitational constant g was first measured accurately by henry cavendish in 1798. he used an exquisitely sensitive balance to measure the force between two lead spheres whose centers were 0.19 m apart. one of the spheres had a mass of 188 kg, while the mass of the other sphere was 0.63 kg. what was the ratio of the gravitational force between these spheres to the weight of the lighter sphere?

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

A248-g piece of copper is dropped into 390 ml of water at 22.6 °c. the final temperature of the water was measured as 39.9 °c. calculate the initial temperature of the piece of copper. assume that all heat transfer occurs between the copper and the water. remember, the density of water is 1.0 g/m

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