16. A crate is sitting on the bed of a truck. The truck is moving at 21 km/h. Applying a constant braking force, the truck comes to a stop in 30. m. Find the minimum coefficient of friction between the crate and the bed of the truck if the crate does not slide. The crate has a mass of 10.0 kg.

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

You hang a book bag on a spring scale and place the bag on a platform scale so that the platform scale reads 23.7n and the spring scale reads 13.8n. what is the magnitude of the force that earth exerts on the bag?

The astronauts on the space shuttle flights experienced an acceleration of 29 m/s2 (about 3 "g's") during lift-off. what upward force must the astronaut's seat apply to the astronaut in order to cause this acceleration? assume the astronaut's mass is 70 kg, and compute this force when the acceleration is near the earth's surface so their weight equals latex: mg m g .