The drawing shows two frictionless inclines that begin at groundlevel ( h = 0 m)

Question

The drawing shows two frictionless inclines that begin at groundlevel (h = 0 m) and slope upward at the sameangle . One track is longer than the other, however.Identical blocks are projected up each track with the same initialspeed v0. On the longer track the block slidesupward until it reaches a maximum height H above theground. On the shorter track the block slides upward, flies off theend of the track at a height H1 above theground, and then follows the familiar parabolic trajectory ofprojectile motion. At the highest point of this trajectory, theblock is a height H2 above the end of thetrack. The initial total mechanical energy of each block is thesame and is all kinetic energy. The initial speed of each block isv0 = 7.52 m/s, and each inclineslopes upward at an angle of =50.0°. The block on the shorter track leaves the trackat a height of H1 = 1.25 m abovethe ground. Find (a) the height H for theblock on the longer track and (b) the total heightfor the block on the shorter track.

Explanation / Answer

Since there's no friction, energy is conserved. For thelonger incline, the initial kinetic energy is converted togravitational potential energy: (1/2)mv02 = m g H, or H = v02/2g Again, because both situations have the same angle and speed, andbecause energy is conserved, both masses will reach the sameheight: H2 = H

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