(ii) Calculate the amount of energy required to melt 15 kg of ice at 0 °C.
Specific latent heat of fusion of ice = 3.4 x 10J/kg.

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

Estimate the schwarzschild radius (in kilometers) for a mini-black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (assume that the your weight is 50 kg)

Two carts, one of mass 2m and one of mass m, approach each other with the same speed, v. when the carts collide, they hook together. assume that positive momentum is to the right. which graph best represents the momentum of both carts over time, before and after the collision?