Momentum, Collisions and Explosions Legacy Problem #16 Guided Solution
Problem*
A 70.9-kg boy and a 43.2-kg girl, both wearing skates face each other at rest on a skating rink. The boy pushes the girl, sending her eastward with a speed of 4.64 m/s. Neglecting friction, determine the subsequent velocity of the boy.
Audio Guided Solution
A good problem solver reads the problem carefully, developing a mental picture of what's going on, identifies the known and the unknown quantity, and uses conceptual reasoning skills in order to plot out a strategy as to how to get from the known information to the unknown information. Here we have a picture of a boy and a girl who are on the skating rink. They're at rest and they're facing each other. The boy pushes off the girl and the sensor eastward, and the boy, as a result, travels westward. We're given the masses of both boy and girl, and we're given the speed of the girl after this impulse. She was originally moving at zero meters per second and afterwards was moving at 4.64 meters per second. This constitutes a velocity change, and as such, it also constitutes a momentum change. The main principle we'll use to reason towards a solution is that the momentum change of the girl is equal in magnitude to the momentum of the change of the boy in opposite direction. So we're going to calculate the momentum change of the girl, and set it equal to the momentum change of the boy, and solve for the velocity change of the boy. It goes something like this. Calculating the momentum change of the girl is a matter of going mass times velocity change. 43.2 kilograms is the mass, and the velocity change is from zero to 4.64. This is a delta V of 4.64 meters per second. When you determine the momentum change of the girl, you get 200.448 kilograms times meters per second. That's equal to the momentum change of the boy, only his momentum change is opposite that of the girl. The girl gains momentum to the east, and the boy gains momentum to the west. So the 70.9 times the velocity change of the boy, that would be an expression for momentum change, is equal to the 200.448 kilograms meters per second. If you divide each side of that equation by 70.9 kilograms, you can get the velocity change of the boy. It comes out to be 2.8272. Rounding to three significant digits, you'd have 2.83 meters per second west as the final velocity of the boy after this impulse.
Solution
2.83 m/s, West
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.