Momentum, Collisions and Explosions Legacy Problem #9 Guided Solution
Problem*
In a study conducted by a University of Illinois researcher, the football team at Unity High School in Tolono, IL was equipped for an entire season with helmets containing accelerometers. Information about every impact in practice and in games was sent to a computer present on the sidelines. The study found that the average force on a top of the head impact was 1770 N and endured for 7.78 milliseconds. Using a head mass of 5.20 kg and presuming the head to be a free body, determine the velocity change experienced in such an impact.
Audio Guided Solution
In this problem, we're told that the typical force that is experienced by a football player during a top-of-the-head impact, the amount of time that that force endures in milliseconds, and the average mass of a football player's head, we're asked to determine the velocity change for this average typical impact. In order to do this, we need to use the impulse equal momentum change equation, the idea that the force times the time is equal to the mass times the velocity change. In this problem, we're given the force and we're given the time, though it's not in a very nice unit, and we're also given the mass of the football player's head. Treating this head as a free body, in other words, ignoring any other forces that act upon the head, like the force of the neck, etc., etc., find the velocity change of the head during such an average impact. So we're going to take 1770 Newtons and multiply by the time in seconds. The time in seconds would not be 7.78, but rather .00778 seconds. That would give us the impulse during this typical collision, and the impulse is equal to the mass times velocity change. The mass here is stated as 5.20 kilograms. So dividing that number by 5.20 kilograms gives me the velocity change, and the value comes out to be about 2.6482, or rounded, 2.65 meters per second.
Solution
2.65 m/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., \(m = 1.50 \unit{kg}\), \(v_i = 2.68 \unit{\meter\per\second}\), \(F = 4.98 \unit{\newton}\), \(t = 0.133 \unit{\second}\), \(v_f = \colorbox{gray}{Unknown}\).
- 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.
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