A uniform crate with a mass of 22 kg must be moved up along the 15° incline without tipping. The force P is horizontal. Determine the corresponding magnitude of force P.

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.

The energy of a photon was found to be 3.38 × 10–19 j. planck’s constant is 6.63 × 10–34 j • s. which color of light corresponds to this photon?

Estimate the kinetic energy of mars with respect to the sun as the sum of two terms, that due to its daily rotation about its axis, and that due to its yearly revolution about the sun. (assume mars is a uniform sphere with mass = 6.4×10 to the power of 23 kg, radius = 3.4×10 to the power of 6 m, rotation period = 24.7 hours, orbital period = 686 days and is 2.3×10 to the power of 8 km from the sun.)