Momentum, Collisions and Explosions Legacy Problem #1 Guided Solution
Problem*
Determine the momentum of …
- …an electron (\(m= \num{9.1e-31} \unit{kg}\)) moving at \(\num{2.18e6}\unit{\meter\per\second}\) (as if it were in a Bohr orbit in the H atom).
- …a 0.45 Caliber bullet (\(m = 0.162 \unit{kg}\)) leaving the muzzle of a gun at \(860\unit{\meter\per\second}\).
- …a \(110 \unit{kg}\) professional fullback running across the line at \(9.2\unit{\meter\per\second}\).
- …a \(360,000 \unit{kg}\) passenger plane taxiing down a runway at \(1.5\unit{\meter\per\second}\).
Audio Guided Solution
This problem involves a straightforward use of the momentum equation that says p, or momentum, equals mass times velocity. The mass and the velocity are given in each of the parts of this problem, and you simply need to multiply, giving careful attention to how you enter the numbers into your calculator, particularly for those which involve scientific notation. Should you enter it correctly and multiply mass times velocity, you'll get the unit of momentum that's listed here on this page. Now the units of momentum are mass units times velocity units, kilograms times meters per second. And so in all the problems you'll notice that we've listed that as our units. There's one conceptual note worth making here, and that is that you'll notice that the momentum of an object depends on both mass and velocity. You might have an object moving really, really fast, like the electron in the Bohr atom, or you might have an object moving really, really slow. But just looking at the speed at which an object moves is not sufficient information in order to determine the relative momentum. You have to look at both speed and mass. In this case, the object that's moving really, really slow has a great mass, and that's the passenger plane. And the object that's moving really, really fast has a minuscule mass, and thus a lesser momentum.
Solution
- \(\num{2.0e-24}\unit{\kg\meter\per\second}\)
- \(140 \unit{\kg\meter\per\second}\) (rounded from \(139 \unit{\kg\meter\per\second}\))
- \(\num{1.0e3}\unit{\kg\meter\per\second}\)
- \(\num{5.4e5}\unit{\kg\meter\per\second}\)
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.
Read About It!
Get more information on the topic of Momentum, Collisions and Explosions at The Physics Classroom Tutorial.