Model Energy Transfer Computationally Practice Test

A $10,\text{kg}$ crate starts from rest at the top of a frictionless hill of height $12,\text{m}$. It slides down to the bottom, then travels across a rough horizontal floor where the kinetic friction force is constant at $40,\text{N}$ for $15,\text{m}$, and then goes up a frictionless ramp. Using $g=10,\text{m/s}^2$, what maximum vertical height above the bottom does the crate reach on the ramp? (Track energy through: initial gravitational PE $\to$ KE at bottom $\to$ thermal from friction $\to$ final gravitational PE.)

A $1.5,\text{kg}$ block is launched up a rough incline with initial speed $12,\text{m/s}$. The incline raises the block by a vertical height of $5,\text{m}$ before the block comes to rest. Using $g=10,\text{m/s}^2$, how much energy was converted to thermal energy by friction during the trip up the incline? (Track: initial KE $\to$ gravitational PE + thermal.)