Carlin hangs a sign in front of her shop with a cable held a…

Carlin hangs a sign in front of her shop with a cable held away from the building by a lightweight pole. The cable makes an angle of 60 degrees with the wall, and the sign hangs from the edge of the pole, which has a length of 1.5 m and is perpendicular to the wall. Once the sign is hung, Carlin measures a tension in the cable of 150 N. What is the mass of the sign?

Two planets, Fibblestib and Dimble, orbit a single star. The…

Two planets, Fibblestib and Dimble, orbit a single star. The gravitational force from the star on planet Fibblestib is five times the force from the star on planet Dimble. Also, planet Dimble has three times the mass of planet Fibblestib. What is the ratio of the two planets’ orbital radii RFibblestib/RDimble?