Newton's Laws Legacy Problem #7 Guided Solution
Problem*
Sophia, whose mass is 52 kg, experienced a net force of 1800 N at the bottom of a roller coaster loop during her school's physics field trip to the local amusement park. Determine Sophia's acceleration at this location.
Audio Guided Solution
A good problem solver is going to read a problem and identify what's known and what's being asked for. In this problem, what we know is the mass of Sophia, 52 kilograms. I usually write m equals 52 kgs. We also know the net force equals 1,800 Newtons, so I write down F net equals 1,800 Newtons. What I'm asked to determine is Sophia's acceleration, so I write a equals question mark. That's my unknown. Now, in the strategy plotting stage of a problem, a good problem solver looks for equations that relates the knowns to the unknowns, and the equation of interest here is that F net equals ma, where a is my unknown, so rearranging it algebraically gives me a equals F net over m. Now, I need to substitute the two known values of F net and m into this rearranged equation, and I can calculate acceleration, and the answer will be in units of meters per second per second.
Solution
35 m/s/s (rounded from 34.6 m/s/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., \(v_o = \units{0}{\unitfrac{m}{s}}\); \(a = \units{4.2}{\unitfrac{m}{s^2}}\); \(v_f = \units{22.9}{\unitfrac{m}{s}}\); \(d = \colorbox{gray}{Unknown}\).
- 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.
Read About It!
Get more information on the topic of Newton's Laws at The Physics Classroom Tutorial.