A model train set includes two cars that are coupled to- gether. The front car has mass m₁ = 2.5 kg whereas the rear car has mass m₂ 2.2 kg. The two cars are travel- ing with speed v₁ = 3.0 m/s along a track with negligible friction. Suddenly, the two cars become uncoupled, and a compressed spring that was lodged between them pushes the cars apart. (The spring remains attached to the rear car afterward, and its mass has already been included in the m₂ value given earlier.) The front car's speed v₁ is now twice as large as the rear car's speed v2. What is the speed v₁ of the front car? For the representation, be sure to in- clude a before/after diagram of the cars with their velocity vectors properly labeled. =

In the figure, a block slides down an incline. As it moves from point A to point B, which are 5.1 m apart, force Facts on the block with magnitude 2.7 N and directed down the incline. The magnitude of the frictional force acting on the block is 9.7 N. If the kinetic energy of the block increases by 41 J between A and B, how much work is done on the block by the gravitational force as the block moves from A to B? Number i Units

When Crates A and B of mass ma = 38 kg and mB = 74 kg are released from rest, Crate A moves to the right = 0.2 ). The force P = 18 Newtons is always acting on Crate B. The linear spring on a rough surface (u: has a stiffness of k = 480 N and is initially stretched 0.5 meters before the system is released from rest. m Neglect the mass of the pulleys and cables and neglect friction in the pulley bearings. Determine the work done by the external force P (in Joules) when Crate A has moved a distance of 0.5 meters to the right. wwwwm

A block with some mass m is connected to a string that is attached to the ceiling. The block on the end of the string is going around a circular path with a constant radius r and constant speed.  Applying Newton's second law to the x component of force seperately in order to find the expressions for the tension of the string in terms of mass m, angle θ, and constant g.  The x direction includes centripetal acceleration.