Momentum, Collisions and Explosions Legacy Problem #3 Guided Solution
Problem*
According to the Guinness Book of World Records, the fastest recorded baseball pitch was delivered by Nolan Ryan in 1974. The pitch was clocked at \(100.9{\unitfrac{\text{mile}}{\text{hour}}}\) (\(45.0\unit{\meter\per\second}\)). Determine the impulse required to give a \(0.145\unit{kg}\) baseball such a momentum.
Audio Guided Solution
Oftentimes, in physics, you find it the case that a problem is not mathematically difficult, but the difficulty in the problem lies in the conceptual nature. This could be an example if you're having difficulty with this problem. We're told that Nolan Ryland throws a pitch and accelerates the .145 kg baseball from at rest position of 45.0 meters per second. Well, we're not actually told that, but we can reason from the context of the problem that a pitcher takes a ball at rest and gives it a final speed when it leaves his hand, the speed here being 45.0 meters per second. The question we're asked is what impulse is delivered to the ball during the pitching motion? Well, if you know that impulse equals momentum change, you can reason through the answer to this question and it becomes an easy mathematical calculation. Because in any sort of situation, when you have an FT or an impulse, that impulse gives the object it acts upon a momentum change, and here the momentum change of the baseball is a momentum change consistent with a .145 kg baseball going from zero meters per second to 45 meters per second. So all we need to do is take the .145 kg and multiply by the velocity change of 45.0 meters per second, and that gives us a momentum change, and the momentum change is equal to the impulse.
Solution
\(6.52\unit{\newton\second}\) (or \(6.52\unit{\kg\meter\per\second}\))
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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