Momentum, Collisions and Explosions Legacy Problem #21 Guided Solution
Problem*
Ima Rilla Saari rushes to her car in order to hurry home and get dressed for work. Failing to realize the dangers of driving under slick and icy conditions, she collides her 940-kg Mazda Miata into the rear of a 2460-kg pick-up truck which was at rest at the light on Lake Avenue. Ima's pre-collision speed was 12.5 m/s. Determine the post-collision speed of the two entangled cars as they slide across the ice.
Audio Guided Solution
A good problem solver reads the problem carefully and develops a mental picture of what's going on, identifying the known and the unknown quantities, and then uses physics principles and conceptual reasoning skills to determine how to find the final answer from the original information. Here we have a picture of Ayma Rilasari moving along in her car on slick, icy conditions. We're given the mass of her car, and we're given the speed at which she was moving before the collision. The mass of the car was 940 kilograms, and she was moving with a pre-collision speed of 12.5 meters per second. She rear-ends a pickup truck, and the two cars entangle together and slide with the same speed across the ice after the collision. We're asked to determine the speed after the collision. The principle that we'll use is the principle that in a collision, the total momentum of both objects before the collision is equal to the total momentum of both objects after the collision. So here, we know that only the Mazda Miata is moving before the collision, and we can find the momentum of the Mazda Miata. We just multiply the mass of the Miata times its velocity, or 940 times 12.5 meters per second. That gives us the momentum of the system before the collision, and it comes out to be 11,750 kilograms times a meter per second. This 11,750 kilograms meter per second is also equal to the post-collision momentum of the two objects. Now, after the collision, both objects are moving with the same velocity. We'll call that velocity v, and if we do, we can express the post-collision momentum as mass times velocity for the Miata, plus mass times velocity for the pickup truck. That's 940 v plus 2460 v. We can combine these terms and get 3400 v. This 3400 v is an expression for the post-collision momentum of both vehicles, and it's equal to the 11,750 kilograms times a meter per second. If we divide through by 3400 kilograms, we would get the v of both the Miata and of the pickup truck after the collision. It comes out to be 3.4559 meters per second. We can round this to two digits, 3.5 meters per second.
Solution
3.5 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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