The following drawing shows two frictionless inclines that begin at ground level (h -0 rn) and slope upward at the same angle 8: Foundations of Physics I Homework, NTU, Singapore

Question

The following drawing shows two frictionless inclines that begin at ground level (h -0 rn) and slope upward at the same angle 8. One track is longer than the other, however. Identical blocks are projected up each track with the same initial speed On the longer track the block slides upward until it reaches a maximum height H above the ground.

On the shorter track, the block slides upward, flies off the end of the track at a height Hi above the ground, and then follows the parabolic trajectory of projectile motion. At the highest point of this trajectory, the block is a height If: above the end of the track. The initial total mechanical energy of each block is the same and Is all kinetic energy. Assume that the air resistance is negligible, and model each block as a point mass.

(1) When the block on the longer track reaches its maximum height, is Its final total mechanical energy all kinetic energy, all potential energy, or some of each? Justify your answer.

(ii) When the block on the shorter track reaches the top of its trajectory after leaving the track, Is its final total mechanical energy all kinetic energy, all potential energy or some of each? Justify your answer.

(iii) Which is the greater height above the ground: H or Hi -IV Why? (You have to provide a qualitative explanation.)

(iv) If the initial speed of each block is 1t = 7.00 m/s, each incline slopes upward at an angle of 6 = 50.0°, and the block on the shorter track leaves the track at a height of Hi = 1.25 m above the ground, find

(a) the height H for the block on the longer track (2 decimal places needed)

(b) the total height Hi -H: for the block on the shorter track (2 decimal places needed)