1D Kinematics Legacy Problem #21 Guided Solution
Problem*
Captain John Stapp is often referred to as the "fastest man on Earth." In the late 1940s and early 1950s, Stapp ran the U.S. Air Force's Aero Med lab, pioneering research into the accelerations which humans could tolerate and the types of physiological effects which would result. After several runs with a 185-pound dummy named Oscar Eightball, Captain Stapp decided that tests should be conducted upon humans. Demonstrating his valor and commitment to the cause, Stapp volunteered to be the main subject of subsequent testing. Manning the rocket sled on the famed Gee Whiz track, Stapp tested acceleration and deceleration rates in both the forward-sitting and backward-sitting positions. He would accelerate to aircraft speeds along the 1200-foot track and abruptly decelerate under the influence of a hydraulic braking system. On one of his most intense runs, his sled decelerated from 282 m/s (632 mi/hr) to a stop at -201 m/s/s. Determine the stopping distance and the stopping time.
Audio Guided Solution
Some of the habits which a good problem solver practices is a tendency to read the problem carefully and get a good visual picture of what's going on. To extract numerical information from the problem, begin to plot out a strategy and get from the known quantities to the unknown quantities. Now, many students think that you just have to read the problem and jump right into using your calculator and plugging numbers in. But it's really not that simple. Now, here what we do is we read of Colonel Stapp, who is famed for doing studies in deceleration rates and the effect of high G's forces upon human physiology. And in this problem, we're told that he's going to decelerate from 282 meters per second to a stop. So what I get from that little phrase in the sentence is that V0 is 282 meters per second and Vf equals 0. This acceleration occurs at a rate of 201 meters per second per second. So I notice that a equaled 201 meters per second per second. And if you want to put a negative sign in there, you can, because it's a deceleration. A negative sign works great there. Now, we're asked to calculate two things. Find d, d equal to question mark, and find the t. Now, some people may get tripped up by the other information in the problem. It certainly is possible, like a 1,200 foot track. And if you've got a good mental picture of what's going on, you've got a picture of Colonel Stapp starting from rest and then accelerating up to speed and then going for a bit and then decelerating to a braking, to a stop. And our focus here is not on the whole 1,200 feet. Put up on that final section where he's braking to a stop. So the basic idea is that we have in this unit four kinematic equations, each of which have four variables in it. So if you know three of the four, you can calculate the fourth unknown quantity. So what I'm going to do is I'm going to write down vo equals blah, blah, blah, vf equals 0, and a equals blah, blah, blah. I'm going to look for an equation that has in it vo, vf, and a. And my two unknowns are d and t, so I'm going to look for equations that also have that fourth variable d or that fourth variable t. So I think the one I'm going to look for to calculate my d is I'm going to look for the one that goes vf squared equal vo squared plus 2ad. Now, if you notice, we have every quantity in there except for the d. So if I substitute my numbers into that equation, I should be able to solve for d. It matters not that the equation doesn't start off as d equal. I can still solve for d, because it's all one equation, one unknown situation. So I plug 282 in, I square it, I plug 0 in, I square it, I plug negative 201 in, multiply by 2, multiply by d. And I'm going to exercise good algebra. Eventually, I'm going to divide the 282 squared by 2 and divide it by 201, and I'm going to solve for d. And I got my answer. Now, the second part of the problem is to solve for t. So a couple ways to go about that. You can use your definition of acceleration as that delta v over t. Or you can use the kinematic equation that goes vf equal vo plus at. Put 0 in for vf and 2a, 2 in for v original, and put 201 in for a and solve for the unknown quantity t. Good luck.
Solution
Stopping distance: 198 m
Stopping time: 1.40 s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(v_o = \units{0}{\unitfrac{m}{s}}\); \(a = \units{4.2}{\unitfrac{m}{s^2}}\); \(v_f = \units{22.9}{\unitfrac{m}{s}}\); \(d = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of 1D Kinematics at The Physics Classroom Tutorial.