Due: 1:20pm 2004/10/27
Note: all answers must have 3 significant figures. g = 9.81 m/s2. Use your
calculator or computer if necessary.
[Newton's Second Law]
A human femur will fracture if the compression force is 2.00 * 105 N. A
person of mass 60.0 kg lands on one leg, so that there is a compressional
force on the femur.
(a) How big is the acceleration to produce fracture?
(b) How many times the acceleration of gravity is this?
[Application of Kinematics]
Following problem 1:
(a) The person falls to the ground and rolls right away to minimize the
impact. Assume the acceleration is uniform in 60.0 cm during which he changes
attitude from standing to rolling. What's the minimum velocity v when he
touches the ground to produce the acceleration in 1(a)?
(b) Suppose this person falls from a height h. Neglect the air resistence,
how big is h for producing the velocity in 2(a)? And how much time does it
take to reach the ground from height h?
[Air Resistence]
Following problem 2.
(a) If the air resistence is present and produces a force proportional to
velocity:
Find the time needed to reach the velocity v in problem 2(a). Hint: v(t)
satisfies the equation
and the solution is of the form
Substitute (2) into (1) to solve the parameters vmax and t0, then find t by
setting v(t) equal to v in problem 2(a).
(b) What's the height of this journey?
Hint: Find x(t) by integrating v(t) with respect to t.
[Work and Energy]
Following problem 3.
(a) What is the work done by gravity in the case without resistence?
(b) What is the work done by gravity in the case with resistence?
(c) What is the work done by air resistence in problem 3?
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