You are given the task of designing a dart gun powered by an ideal spring, • The mass, m, of the dart will be 0.030 kg.
• The gun barrel is to be 8.0 cm long.
• When fired horizontally, the dart is to have a velocity, v, of 4.0 m/s as it leaves the barrel of the gun.
What is the required spring constant if the spring is to be compressed the entire 8.0 cm before releasing the dart?


Aforce of 200 n is applied to an input piston of cross-sectional area 2 sq. cm pushing it downward 2.8 cm. how far does the output piston of cross-sectional area 12 sq. cm move upward? show all work.

Arotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. the outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. if the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80 m/s^{2} 2 at the rim?

Determine the maximum r-value of the polar equation r =3+3 cos 0