mass m = 40 Kg, which was at rest. (Perfectly inelastic shock) and together they go up the channel (inclined surface) without friction,

A cart of mass m₁ = 4 kg is on frictionless surface and compressed against an ideal spring with spring constant k = 158 N/m for a distance of x = 1.08 m. After it is released, it hits a second cart of mass m₂ = 9 kg and bounces back while the second car continues traveling onto a ramp where it reaches a height of h₂ = 0.69 m. Find the magnitude of the velocity of the first cart in m/s immediately after hitting the second cart. Use g = 9.8 m/s² and retain your answer to two decimal places. k m1 m2 Im m1 Loo! m2 I h₂

Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m.  Initially, the spring is unstretched and the bodies are at rest.  If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then  -20 Nm of work was done by the spring on the body A, B system. Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m.  Initially, the spring is unstretched and the bodies are at rest.  If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then  -20 Nm of work was done by the spring on the body A, B system. True False

Consider two cars that can roll on a frictionless track. Initially, both cars are at rest. One car is launched from rest with a spring, and the cars undergo a completely inelastic collision. The spring constant is 850 N/m, and the spring is initially compressed by 0.075 m. The first car has a mass of 0.50 kg and the second has a mass of 1.0 kg. An identical spring is located to the right of the cars. a. The velocity of the first car just before collision. b. The velocities of the cars after collision. c. The distance the spring on the right will be compressed when the cars are completely stopped by the spring.

An ideal spring is attached to the ceiling. While the spring is held at its relaxed length, a wooden block (M = 850 g) is attached to the bottom of the spring, and a ball of clay (m = 210 g) is pressed onto the bottom of the block so that they stick together. The block+clay are gently lowered through a distance of d = 2.7 cm and are then released, at which point they hang motionlessly from the bottom of the spring. After a few minutes have passed, the clay unsticks itself from the block and falls from rest to the ground. 1. What is the resulting period T of the block’s oscillation after the separation occurs? 2. As d approaches 0, what limit does T approach?

A crate of mass m1 slides down a well-lubricated hill of height h, with negligible friction. At the bottom, where it is moving horizontally, it collides with another crate, of mass m2, that initially was sitting at rest and that is attached to a wall by a spring of spring constant k that initially is at its equilibrium length. Assume that the spring itself has negligible mass. a)Given that the distance d that the crates compress the spring is d=0.35 m, calculate the speed v2 of the crates immediately after the collision, in units of meters per second. Use the following values:k=950 N/mm1=2.4 kgm2=2.6 kgμ=0.49g=9.8 m/s2  b)What was the speed of the crate of mass m1 just before the collision with the second block, in meters per second?  c) What is the height h of the hill, in meters?

A crate of mass m1 slides down a well-lubricated hill of height h, with negligible friction. At the bottom, where it is moving horizontally, it collides with another crate, of mass m2, that initially was sitting at rest and that is attached to a wall by a spring of spring constant k that initially is at its equilibrium length. Assume that the spring itself has negligible mass. a)Given that the distance d that the crates compress the spring is d=0.35 m, calculate the speed v2 of the crates immediately after the collision, in units of meters per second. Use the following values:k=950 N/mm1=2.4 kgm2=2.6 kgμ=0.49g=9.8 m/s2  b) What was the speed of the crate of mass m1 just before the collision with the second block, in meters per second?  c)What is the height h of the hill, in meters?

Mickey, a daredevil mouse of mass 0.0201 kg,0.0201 kg, is attempting to become the world's first "mouse cannonball." He is loaded into a spring‑powered gun pointing up at some angle and is shot into the air. The gun's spring has a force constant of 87.5 N/m87.5 N/m and is initially compressed a distance of 0.145 m0.145 m from its relaxed position. If Mickey has a constant horizontal speed of 2.15 m/s2.15 m/s while he is flying through the air, how high ℎh above his initial location in the gun does Mickey soar? Assume ?=9.81 m/s2.

A spring with a spring constant of 383 N/m is initially compressed by a distance of 0.076 m from its equilibrium position. A mass of 0.038 kg is then held against the compressed spring and released from rest while upon a horizontal, frictionless surface. Assuming that the spring then pushes the mass across the surface, with speed does the mass leave the spring? Assume proper SI Units.

A block of mass M = 8 kg rests on a horizontal frictionless floor, and is connected to a vertical wall by a spring of force constant k = 200 N/m. When the spring is in its equilibrium position (neither stretched nor compressed), the block just touches a second lighter block of mass m = 4 kg at rest on the frictionless floor. The spring with mass M attached is now compressed by 0.1 m and released. The two blocks undergo a completely inelastic collision, i.e., they stick together after collision. Draw a diagram and define all relevant variables. Just before the collision, what is the velocity of mass MT Just after the collision, what is the common velocity of the two blocks? (What is the maximum stretching of the spring after the collision?: How long after the collision do the masses reach their first maximum stretch?