Marie and Maria each send a spinning uniform disc towards th…

Marie and Maria each send a spinning uniform disc towards the center of an axle. Marie’s disk has a mass of 0.5 kg with a radius of 15 cm and is spinning about the axle at a rate of 120 rpm. Maria’s disk also has a mass of 0.5 kg, but a radius of 20 cm, and it spins in the same direction as Marie’s at a rate of 150 rpm. The two discs then collide and stick together. What is their final rotational speed in rad/s?

The restoring force a bow provides to an arrow as it is pull…

The restoring force a bow provides to an arrow as it is pulled back can be modeled as a spring force. The archer Gila “nocks” an 18-g arrow by pulling it back a distance of 45 cm. Gila fires the arrow horizontally from a small cliff with a height of 12 m, and when the arrow reaches the bottom, it has a speed of 63 m/s. What is the effective spring constant of the bow as Gila nocks the arrow?

Deadeye Martin fires a 18-g arrow at a speed of 40 m/s at a…

Deadeye Martin fires a 18-g arrow at a speed of 40 m/s at a 150-g apple tossed straight into the air by his friend Jaquette. If the arrow arrow travels straight through the apple at the peak of the apple’s trajectory, and the apple’s speed is 1.8 m/s after the collision, what is the speed of the arrow immediately after hitting the apple?

Hecelina drives her horse to pull her wagon up a long, shall…

Hecelina drives her horse to pull her wagon up a long, shallow hill. The horse and wagon together have a mass of 1800 kg, and the horse provides a constant force of 1000 N directing the wagon up the hill. The hill rises a vertical distance of 8.0 m, and the hill is 85 m long along the slope. With what starting speed must Hecelina drive her horses so that they barely make it to the top of the hill before stopping? Neglect any drag forces.