Newton's Laws Legacy Problem #3 Guided Solution
Problem*
With fuel prices for combustible engine automobiles increasing, researchers and manufacturers have given more attention to the concept of an ultralight car. Using carbon composites, lighter steels and plastics, a fuel-efficient car can be manufactured at 540 kg. How much less does an ultralight car weigh compared to a 1450-kg Honda Accord (2007)?
Audio Guided Solution
Here we're given the mass of two different cars. We're given the mass of a fuel efficient car of the future, and we're given the mass of a Honda Accord 2007. And I recognize that these are the masses, not because they come out and they tell me here's the masses, but because they give me the quantities in units of kilograms. The question that I'm being asked is, how much less does the ultralight car weigh than the Honda Accord car? So they're not asking me a question about mass, they're asking me a question about weight. So what I need to do is to take these masses and to transform them or change them or calculate from them the weights of the two cars. And once I get the weights, I can subtract one weight from the other weight. That's one way to solve the problem. So how do I find the weight from the mass? Well, I need an equation for that. An equation that I know is that the weight is equal to m times g, where on earth g is 9.8 newtons per kilogram. Sometimes expressed as 9.8 meters per second per second. Either way works. What I need to do is take the 540 and multiply that by g to get the weight in newtons. And I need to take the Honda Accord's mass of 1450 and multiply it by the value of g to get the weight in newtons there. And then just take the difference there. That will give me how much less the ultralight weight car weighs compared to the Honda Accord.
Solution
8900 N less (rounded from 8918 N)
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., \(v_o = \units{0}{\unitfrac{m}{s}}\); \(a = \units{4.2}{\unitfrac{m}{s^2}}\); \(v_f = \units{22.9}{\unitfrac{m}{s}}\); \(d = \colorbox{gray}{Unknown}\).
- 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.
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