A cannon initially resting on a frictionless surface of mass m₁ = 800 kg (when unloaded) is loaded with a “shot” of mass m₂ = 10.0 kg. The cannon is aimed at mass m₃ = 7 990 kg, which is connected to a massless spring of force constant k = 4 500 N/m, as in Figure EX5.73a. The cannon is then fired, and the shot inelastically collides with mass m₃ and sticks in it, as shown in Figure EX5.73b. The combined system compresses the spring a maximum distance of d = 0.500 m, as in Figure EX5.73c. (a) Determine the speed of m₂ just before it collides with m₃. (You may assume that m₂ travels in a straight line.) (b) Determine the recoil speed of the cannon. (c) The cannon recoils towards the right, and when it passes point A there is friction (with μ_k = 0.600) between the cannon and the ground. How far to the right of A does the cannon slide before coming to rest? 

A flying squid (family Ommastrephidae) is able to “jump” off the surface of the sea by taking water into its body cavity and then ejecting the water vertically downward. A 0.85-kg squid is able to eject 0.30 kg of water with a speed of 20 m/s. (a) What will be the speed of the squid immediately after ejecting the water. (b) How high in the air will the squid rise? 

The Japanese Flying Squid, otherwise known as Todarodes pacificus, is a invertebrate, and a member of the phylum mollusca, class cephalopoda, and family ommastrephidae. This animal lives in the Northern Pacific ocean. The squid has a siphon–a muscle which takes in water from one side, and pushes it out the other side; in other words: jet propulsion. Squids have ink sacs, which they use as a defense mechanism against possible predators. Squid also have three hearts.

A 45.0-kg girl is standing on a 150-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.50 m/s to the right relative to the plank. (a) What is her velocity relative to the surface of the ice? (b) What is the velocity of the plank relative to the surface of the ice? 

A rifle with a weight of 30 N fires a 5.0-g bullet with a speed of 300 m/s. (a) Find the recoil speed of the rifle. (b) If a 700-N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle. 

A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2-kg physics textbook horizontally toward the north shore at a speed of 5.0 m/s. How long does it take him to reach the south shore?

A 40.0-kg child stands at one end of a 70.0-kg boat that is 4.00 m long. The boat is initially 3.00 m from the pier. The child notices a turtle on a rock beyond the far end of the boat and proceeds to walk to that end to catch the turtle. (a) Neglecting friction between the boat and water, describe the motion of the system (child plus boat). (b) Where will the child be relative to the pier when he reaches the far end of the boat? (c) Will he catch the turtle? (Assume that he can reach out 1.00 m from the end of the boat.)

A 5.00-g bullet moving with an initial speed of 400 m/s is fired into and passes through a 1.00-kg block, as in Figure. The block, initially at rest on a frictionless horizontal surface, is connected to a spring with a spring constant of 900 N/m. If the block moves 5.00 cm to the right after impact, find (a) the speed at which the bullet emerges from the block and (b) the mechanical energy lost in the collision.

Pendulum

A simple pendulum is 5.00 m long. (a) What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s²? (b) What is its period if the elevator is accelerating downward at 5.00 m/s²? (c) What is the period of simple harmonic motion for the pendulum if it is placed in a truck that is accelerating horizontally at 5.00 m/s²? 

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is pulled horizontally so that it stretches the spring 5.00 cm and is then released from rest at t = 0. (a) What is the force constant of the spring? (b) What are the angular frequency ω, the frequency, and the period of the motion? (c) What is the total energy of the system? (d) What is the amplitude of the motion? (e) What are the maximum velocity and the maximum acceleration of the particle? (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. 

Tires

While riding behind a car traveling at 3.00 m/s, you notice that one of the car’s tires has a small hemispherical bump on its rim, as in Figure. (a) Explain why the bump, from your viewpoint behind the car, executes simple harmonic motion. (b) If the radius of the car’s tires is 0.30 m, what is the bump’s period of oscillation?