Momentum, Collisions and Explosions Legacy Problem #5 Guided Solution
Problem*
Kara Less was applying her makeup when she drove into South's busy parking lot last Friday morning. Unaware that Lisa Ford was stopped in her lane 30 feet ahead, Kara rear-ended Lisa's rented Taurus. Kara's \(1300\unit{kg}\) car was moving at \(11\unit{\meter\per\second}\) and stopped in \(0.14\unit{s}\).
- Determine the momentum change of Kara's car.
- Determine the impulse experienced by Kara's car.
- Determine the magnitude of the force experienced by Kara's car.
Audio Guided Solution
This is a problem regarding a collision between Kara Less's car and Lisa Ford's car. Kara Less was driving along at 11 meters per second, encountered a collision, and her 1,300 kilogram car came to a stop in 0.14 seconds. What we have is an original velocity of 11 meters per second and a final velocity of 0. That gives us a velocity change of negative 11 meters per second. If we're asked to determine the momentum change of Kara's car, we would have to take the mass and multiply by the velocity change. The 1,300 kilograms multiplied by the negative 11 meters per second gives us a momentum change of 1.43 times 10 to the 4th kilograms times a meter per second. We can round that to two significant figures and that would be our answer. The negative sign in front of the momentum change simply means that momentum was lost. In Part B, we're asked to determine the impulse acting upon Kara's car. Now this is actually an easy question if you understand your concepts. One more example of a case in which the mathematics is rather easy, but the physics is conceptually difficult, though not that difficult. If you understand that in any given collision, the impulse encountered by a car is equal to the momentum change. So in this case, the 1.43 times 10 to the 4th kilograms times meter per second momentum change is equal to the same amount of impulse. The impulse is equal to 1.4 times 10 to the 4th kilograms times meter per second. Or if we prefer, we could use an equivalent set of units to describe this impulse, a newton times a second. Now that we've figured out the impulse, we can now determine the force, because the force is simply equal to the impulse divided by the time, or the momentum change divided by the time. So if we take this 1.43 times 10 to the 4th kilograms meters per second, or newton times a second, and divide by the 0.14 seconds, we'll get an impulse of about 102,143 blah blah blah, newtons. And we can simply round that to 1.0 times 10 to the 5th newtons.
Solution
- \(\num{-1.4e4}\unit{\kg\meter\per\second}\)
- \(\num{-1.4e4}\unit{\newton\second}\)
- \(\num{1.0e5}\unit{\newton}\)
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!
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