Momentum, Collisions and Explosions Legacy Problem #15 Guided Solution
Problem*
During an in-class demonstration of momentum change and impulse, Mr. H asks Jerome (102 kg) and Michael (98 kg) to sit on a large 14-kg skate cart. Mr. H asks Suzie (44 kg) to sit on a second 14-kg skate cart. The two carts are placed on low friction boards in the hallway. Jerome pushes off of Suzie's cart. Measurements are made to determine that Suzie's cart acquired a post-impulse speed of 9.6 m/s. Determine the expected recoil speed of Jerome and Michael's cart.
Audio Guided Solution
An effective problem solver reads the problem carefully and gets a mental picture of what's going on. They identify the known and the unknown quantity and then use conceptual reasoning skills in order to determine how to get from the known information to the unknown information. As we read this problem, we read about two massive football players who are sitting on a small skate cart. They're on the floor and they're facing Susie, who's on a second skate cart. Jerome pushes off Susie's cart and gives her a large speed. As a result of that little push on Susie's cart, Jerome and Michael are sent backwards and we're asked to determine the recoil speed of Jerome and Michael's cart. The principle that we're going to use to reason through to a solution is that in any given explosion or collision, the momentum change of one object is equal to and opposite of the momentum change of the other object. Our two objects here are Susie on her cart with a mass of 58 kilograms and Jerome and Michael on his cart with a mass of 214 kilograms. These are the two objects that will encounter the impulse with one another. We're told Susie, after the impulse, is moving at 9.6 meters per second. This is enough information for us to determine the momentum change of Susie and cart. Jerome and Michael on their cart will experience the same momentum change, only in the opposite direction. Knowing their mass, we can determine their velocity change. That's the strategy. Let's execute. So, we want to find the momentum change of Susie's cart. So the mass of Susie on her cart is 58 kilograms and her speed after the collision is 9.6 meters per second. So we go 58 times 9.6 and we get 556.80 kilograms per meter per second. That's the momentum change of Susie and her cart. That's also the momentum change of Jerome and Michael and their cart. So we're going to take their accumulation mass, which is 214 kilograms. That's the 102 plus the 98 plus 14. We're going to say that the 214 kilograms times the delta V of that cart is equal to 556.80 kilograms per meter per second. When you divide through by 214 kilograms, you get a delta V. It comes out to be 2.6019 meters per second. Rounding to two digits, you'd have a velocity change of 2.6 meters per second, and that would be equivalent to the final speed after the impulse.
Solution
2.6 m/s
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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