Classical Mechanics Homework Problems
See attached file for full problem description.
1. Two masses are released at the same height, and fall a very long distance under gravity, till they hit the ground. The masses are subject to air friction, which you should assume has the form —b17 for both masses, even if this mathematical form is not very accurate. Mass A is made of lead. Mass B is made of a much less dense plastic. Both masses have the same size and shape, and therefore have the same friction coefficient b. Which one reaches the ground l ﬁrst?
(A) They both reach the ground at the same time.
(B) Mass B reaches the ground ﬁrst.
(C) Mass A reaches the ground ﬁrst.
2. A mass is thrown upwards on the earth, with an initial velocity vo. It reaches some maximum height he. (Ignore air friction.) The experiment is repeated on the Moon with the same mass and the same 110, and the mass reaches a different height hm, because the acceleration of gravity on the Moon is ~ 1/6 that on the earth. In these two experiments, the potential energy at the maximum height is, respectively, U8 and Um. What is the relationship between U6 and Um?
(A) Ue : Um
(B) U6 = /§Um
(C) Ue = 6Um
(D) Ue = %Um
(E) U6 = §Um
(F) Ue = 36Um
3. A 1 kg projectile is ﬁred (on Earth) with a speed of 10 rn/ s, at an angle 60° above the horizontal. It is subject to gravity, but not friction. Which of the following is the best estimate of its speed when it reaches a point 3 meters higher than the initial position?
A) 8.5 m/s
B) 6.3 m/s
C) 2.0 m/s
D) 1.1 m/s