Newton's Laws Legacy Problem #5 Guided Solution
Problem*
The rising concern among athletic trainers and health advocates (and parents) regarding concussions and multiple concussions among high school football players has prompted numerous studies of the effectiveness of protective head gear and the forces and accelerations experienced by players. One study suggested that there is a 50% chance of concussions for impacts rated at 75 g's of acceleration (i.e., 75 multiplied by 9.8 m/s/s). (The average head impact results in 22 to 24 g's of acceleration.) If a player's head mass (with helmet) is 6.0 kg and considered to be a free body, then what net force would be required to produce an acceleration of 75 g's?
Audio Guided Solution
After the interesting information at the beginning of this problem, we finally get around to asking the question to calculate the net force. What is the net force required to produce an acceleration of about 740 meters per second per second for a head of mass of 6 kilograms, assuming it to be a free body and unaffected by the shoulders and things it's attached to. So here what we wish to do is to find net force from information about M and A, so that's the straightforward calculation of F net equal MA, where the M is 6 kilograms and the A is 740 meters per second per second. Alternatively for that A, you could call it 75 G's, where G is equivalent to 9.8, after all that's where that 740 comes from.
Solution
4400 N (rounded from 4410 N)
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.
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