Projectile Motion and Spring Problems

(1) A mass (m) is pushed against a spring of spring constant k compressing the spring a distance x from the equilibrium position and held in place such that the system is at rest. The system is then released so that the mass is pushed by the spring as the spring is uncompressed. Assuming the coefficient of friction between the mass and the floor is μ, write an algebraic expression for the speed of the mass as the system reaches the equilibrium position.

(2) A 5.00 kg mass is released from rest on a very long frictionless plane inclined at 40.0°. After sliding 8.00 m, the mass hits a spring of spring constant 200. N/m. How much further will the mass slide down the incline until the spring stops compressing?

(3) A 10. 0 kg box strikes a spring (k = 120. N/m) traveling at 2 (3) A 10.0 kg box strikes a spring (k = 120. N/m) traveling at 2.00 m/s. If a force of friction of 5.00 N exists between the box and the floor, by how much will the spring be compressed?

(4) A 10. 0 kg mass falls from a height of 10 (4) A 10.0 kg mass falls from a height of 10.0 m onto an uncompressed spring of spring constant 250. N/m. By how much will the spring compress assuming the 10.0 kg mass maintains contact with the spring as the spring compresses.

(5) A 1. 00 kg mass is projected up a 6. 00 m long rough (μ = 0 (5) A 1.00 kg mass is projected up a 6.00 m long rough (μ = 0.100) plane inclined at 30.0° with an initial speed of 18.0 m/s. The mass still has speed at the top of the incline and undergoes projectile motion. For the projectile motion, find (a) vi (b) vix and viy, (c) the maximum height the mass reaches from the ground, (d) the time of flight, and (e) the range.