You give a crate of mass m=1.00 kg an initial speed of vi=4.00m/s up an incline of theta= 39°. The crate then slides along the incline, reaches a spring of spring constant k=47 N/m, and compressed the spring by delta_s = 15.0 cm before stopping. What is the distance d in meters along the incline that the crate slides, assuming there is no friction?

The starship enterprise is caught in a time warp and spock is forced to use the primitive techniques of the 20th century to determine the specific heat capacity of an unknown mineral. the 125-g sample was heated to 96.3°c and placed into a calorimeter containing 85.9 g of water at 20.0°c. the heat capacity of the calorimeter was 14.2 j/k. the final temperature in the calorimeter was 24.5°c. what is the specific heat capacity (in j/g°c) of the mineral? enter to 4 decimal places.