A spring is compressed by 50 cm from it's equilibrium length by an unattached block of mass 5.0 kg (the spring constant is 400 N/m). The box is released from rest, slides along a friction-less surface for a time, and then ascends a ramp of length 10 m, which is inclined at an angle of 20 degrees above the horizontal. What is the maximum distance that the box travels up the ramp?

  L = 2.98 m

Explanation:

In this exercise we are told that there is no friction, so we can use energy conservation

Starting point. Compressed spring

        Em₀ = Ke = ½ k x²

Final point. At the highest point of the ramp

        = U = mg h

As there is no friction the energy is conserved

         Emo = Em_{f}

         ½ k x² = mg h

         h = ½ k x² / mg

         h = ½ 400 0.50² / (5.0 9.8)

         h = 1.02 m

This is the height that the body reaches, to calculate the distance traveled on the ramp let's use trigonometry

          sin θ = h / L

         L = h / sin θ

         L = 1.02 / sin 20

         L = 2.98 m

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​