problem solving gresa method

2.6 Problem-Solving Basics for One-Dimensional Kinematics

Learning objectives.

By the end of this section, you will be able to:

• Apply problem-solving steps and strategies to solve problems of one-dimensional kinematics.
• Apply strategies to determine whether or not the result of a problem is reasonable, and if not, determine the cause.

Problem-solving skills are obviously essential to success in a quantitative course in physics. More importantly, the ability to apply broad physical principles, usually represented by equations, to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations, whereas a list of facts cannot be made long enough to contain every possible circumstance. Such analytical skills are useful both for solving problems in this text and for applying physics in everyday and professional life.

Problem-Solving Steps

While there is no simple step-by-step method that works for every problem, the following general procedures facilitate problem solving and make it more meaningful. A certain amount of creativity and insight is required as well.

Examine the situation to determine which physical principles are involved . It often helps to draw a simple sketch at the outset. You will also need to decide which direction is positive and note that on your sketch. Once you have identified the physical principles, it is much easier to find and apply the equations representing those principles. Although finding the correct equation is essential, keep in mind that equations represent physical principles, laws of nature, and relationships among physical quantities. Without a conceptual understanding of a problem, a numerical solution is meaningless.

Make a list of what is given or can be inferred from the problem as stated (identify the knowns) . Many problems are stated very succinctly and require some inspection to determine what is known. A sketch can also be very useful at this point. Formally identifying the knowns is of particular importance in applying physics to real-world situations. Remember, “stopped” means velocity is zero, and we often can take initial time and position as zero.

Identify exactly what needs to be determined in the problem (identify the unknowns) . In complex problems, especially, it is not always obvious what needs to be found or in what sequence. Making a list can help.

Find an equation or set of equations that can help you solve the problem . Your list of knowns and unknowns can help here. It is easiest if you can find equations that contain only one unknown—that is, all of the other variables are known, so you can easily solve for the unknown. If the equation contains more than one unknown, then an additional equation is needed to solve the problem. In some problems, several unknowns must be determined to get at the one needed most. In such problems it is especially important to keep physical principles in mind to avoid going astray in a sea of equations. You may have to use two (or more) different equations to get the final answer.

Substitute the knowns along with their units into the appropriate equation, and obtain numerical solutions complete with units . This step produces the numerical answer; it also provides a check on units that can help you find errors. If the units of the answer are incorrect, then an error has been made. However, be warned that correct units do not guarantee that the numerical part of the answer is also correct.

Check the answer to see if it is reasonable: Does it make sense? This final step is extremely important—the goal of physics is to accurately describe nature. To see if the answer is reasonable, check both its magnitude and its sign, in addition to its units. Your judgment will improve as you solve more and more physics problems, and it will become possible for you to make finer and finer judgments regarding whether nature is adequately described by the answer to a problem. This step brings the problem back to its conceptual meaning. If you can judge whether the answer is reasonable, you have a deeper understanding of physics than just being able to mechanically solve a problem.

When solving problems, we often perform these steps in different order, and we also tend to do several steps simultaneously. There is no rigid procedure that will work every time. Creativity and insight grow with experience, and the basics of problem solving become almost automatic. One way to get practice is to work out the text’s examples for yourself as you read. Another is to work as many end-of-section problems as possible, starting with the easiest to build confidence and progressing to the more difficult. Once you become involved in physics, you will see it all around you, and you can begin to apply it to situations you encounter outside the classroom, just as is done in many of the applications in this text.

Unreasonable Results

Physics must describe nature accurately. Some problems have results that are unreasonable because one premise is unreasonable or because certain premises are inconsistent with one another. The physical principle applied correctly then produces an unreasonable result. For example, if a person starting a foot race accelerates at 0 . 40 m/s 2 0 . 40 m/s 2 for 100 s, his final speed will be 40 m/s (about 150 km/h)—clearly unreasonable because the time of 100 s is an unreasonable premise. The physics is correct in a sense, but there is more to describing nature than just manipulating equations correctly. Checking the result of a problem to see if it is reasonable does more than help uncover errors in problem solving—it also builds intuition in judging whether nature is being accurately described.

Use the following strategies to determine whether an answer is reasonable and, if it is not, to determine what is the cause.

Solve the problem using strategies as outlined and in the format followed in the worked examples in the text . In the example given in the preceding paragraph, you would identify the givens as the acceleration and time and use the equation below to find the unknown final velocity. That is,

Check to see if the answer is reasonable . Is it too large or too small, or does it have the wrong sign, improper units, …? In this case, you may need to convert meters per second into a more familiar unit, such as miles per hour.

This velocity is about four times greater than a person can run—so it is too large.

If the answer is unreasonable, look for what specifically could cause the identified difficulty . In the example of the runner, there are only two assumptions that are suspect. The acceleration could be too great or the time too long. First look at the acceleration and think about what the number means. If someone accelerates at 0 . 40 m/s 2 0 . 40 m/s 2 , their velocity is increasing by 0.4 m/s each second. Does this seem reasonable? If so, the time must be too long. It is not possible for someone to accelerate at a constant rate of 0 . 40 m/s 2 0 . 40 m/s 2 for 100 s (almost two minutes).

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Coulomb’s Law Example Problem 1

q 1 and q 2 is the amount of charge in Coulombs r is the distance in meters between the charges k is the Coulomb’s Law constant = 8.99×10 9 N•m 2 /C 2

The direction of the force depends on the positive or negative charges on the bodies. If the two charges are identical, the force is a repulsive force. If one is positive and the other negative, the force is an attractive force.

This Coulomb’s Law example problem shows how to use this equation to find the charges necessary to produce a known repulsive force over a set distance.

Example Problem: The force between two identical charges separated by 1 cm is equal to 90 N. What is the magnitude of the two charges?

Solution: First, draw a force diagram of the problem.

Define the variables: F = 90 N q 1 = charge of first body q 2 = charge of second body r = 1 cm

The problem says the two charges are identical, so

q 1 = q 2 = q

q = ±1.00×10 -6 Coulombs

This equation has two possible answers. The charges can both be positive or both negative and the answer will be the same for the repulsive Columb force over a distance of 1 cm.

Answer: Two identical charges of ±1.00×10 -6 Coulombs separated by 1 cm produce a repulsive force of 90 N.

For another Coulomb’s law example problem, check out Coulomb Force Example Problem .

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The Grass Strategy – Effectively Developing Thorough Math Answers

GRASS Strategy for Math Problem-Solving

• Given – What information are you given in the word problem? I have students rewrite the information in their notebooks or GRASS sheet. Students accommodated or modified as per their I.E.P. can highlight the given information in one colour.
• Required – What information are you required to find out once you solve this problem?
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• Solution – Solve this problem using the chosen strategy.
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4 thoughts on “The Grass Strategy – Effectively Developing Thorough Math Answers”

Nice job on the GRASS thing. Wish my teachers had used tools like this instead of yelling.

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Moms are taking ‘magic’ mushrooms to manage their parenting stress — but is it safe.

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Motherhood is a tough job — and now some moms are getting help from an unlikely source.

Thousands of mothers are taking microdoses of psychedelic or “magic” mushrooms — officially called psilocybin — to ease their stress and anxiety, according to some reports.

On an Instagram account called “Moms On Mushrooms,” which has over 30,000 followers, users claim mushrooms are improving their mental health.

Others, however, are concerned about the possible health risks and legal issues associated with these psychedelic substances.

Read on for both sides of the issue, including a doctor’s warning. 

Potential benefits

Peggy Van de Plassche, a Canada-based former business and finance executive, quit her job to focus her time and energy on the psychedelic industry.

Van De Plassche is a mom and founder of The Microdose Diet, a holistic program that includes alternative medicines such as psilocybin to “rewire the brain, calm the body, master emotions and raise energy to reach more success.”

She calls microdosing the new “biohack” for mothers to navigate their stress and anxiety around parenting, aging and work.

“Microdosing can help moms find calm and clarity in parenting, improve their emotional resilience, and even help manage postpartum depression,” Van de Plassche said in a statement to Fox News Digital.

There are three potential benefits of microdosing mushrooms, according to Van de Plassche, who is also the author of the book “MORE! The Microdose Diet – The 90-Day Plan for More Success, Passion, and Happiness.”

1. Enhanced emotional and mental well-being

Many women report significant improvements in their emotional and mental health when they begin microdosing psychedelics, according to Van de Plassche.

“These small, sub-hallucinogenic doses can stabilize mood and improve emotional responsiveness,” she told Fox News Digital via email.

“Research and anecdotal evidence suggest that microdosing may help diminish symptoms of depression, anxiety and PTSD, which disproportionately affect women.”

In theory, these substances can balance women’s emotions and make everyday challenges more manageable, claimed Van de Plassche.

One mother posted on Reddit last year about her positive experience with microdosing.

“No exaggeration, microdosing saved my life. I had terrible reactions to everything commonly prescribed to treat PTSD, and as a last resort I started microdosing,” she wrote.

“There was no high or buzz, I just stopped wanting to kill myself,” the individual wrote. “It’s been two years and my kids have a fully functional mom and my world has color.”

2. Increased creativity and problem-solving

“Women in creative fields, as well as those in more traditional sectors, find that microdosing enhances their problem-solving capabilities and creative thinking,” Van de Plassche said.

“This isn’t about generating a ‘high,’ but rather sparking a slight uplift in cognitive flexibility.”

In her view, microdosing helps women “think outside the box,” forge new connections and arrive at better solutions. 

“Whether at work or at home, women can benefit from more creativity with the help of microdosing,” she said.

3. Menopause relief and hormonal balance

Van de Plassche said she believes that microdosing can help women navigate the psychological and physiological symptoms of menopause, such as mood swings, insomnia and fatigue. 

“By modulating the serotonin system in the brain, microdoses of psychedelics might offer a new kind of equilibrium without the side effects associated with traditional hormone replacement therapies,” she told Fox News Digital.

“Microdosing holds particular appeal for women seeking gentle yet effective transformations,” she also said. 

Beyond helping to manage symptoms of aging, microdosing can help women “reclaim a sense of agency” over their minds and spirits, according to Van de Plassche.

What is a microdose?

Microdosing psilocybin involves “regularly taking very small, sub-perceptual doses of LSD or psilocybin,” which is the psychoactive compound found in certain mushrooms, according to Van de Plassche.

The ideal dose, frequency and type of mushroom can vary from one person to the next, she said.

“I have found that 100 milligrams of psilocybin once every three days in the morning on an empty stomach is a great rule of thumb for most,” said Van de Plassche.

Potential risks of microdosing on mushrooms

Some medical professionals warn about a lack of research and safety concerns associated with mushrooms.

“There is not a lot of peer-reviewed research or safety data available for microdosing psychedelics, because these substances are not as well-studied as more traditional interventions,” Dr. Adam D. Scioli, chief medical officer of Caron Treatment Centers in Pennsylvania, told Fox News Digital.

“However, some of what we do know is concerning.”

Microdosing psychedelics can cause a psychotic or manic episode, especially in those with a personal or family history of schizophrenia or bipolar disorder, Scioli warned.

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Other potential risks include paranoia, worsened depression or anxiety, and enhancement of emotions like worry, fear and guilt.

“Individuals microdose to manage emotions or feel better, but they should be aware that you can’t control which emotions you may experience,” Scioli added.

There is also the risk that mushrooms may interact with other depression medications, which could be dangerous or even life-threatening, the expert warned.

For some, the substance could lead to elevated blood pressure or heart rate, or an increased risk of stroke or sudden cardiac arrest.

“Individuals may also experience migraines, vomiting, nausea, loss of consciousness, body temperature dysregulation (too hot or too cold), loss of focus and/or brain fog,” Scioli added.

Until there is more conclusive research, Scioli believes that adults should avoid microdosing with mind-altering substances outside a clinical setting and under the supervision of a board-certified physician.

Some also warn of the psychological impact the practice could have on kids.

One Reddit user wrote, “I think parents shouldn’t be on any kind of drug (alcohol, vapes, grass, shrooms, tobacco, hard drugs…) when taking care of a child, because of how it will damage the health of the child. Kids can also tell when adults aren’t sober. It makes kids feel unsafe.”

Van de Plassche acknowledged that taking mushrooms too often or in excessive amounts can be risky — as can consuming “low-quality” varieties.

Women who are pregnant and breastfeeding should not microdose, she also advised.

“Men and women with dissociative mental health challenges, such as schizophrenia, should also refrain from using psychedelics,” Van de Plassche added.

Are mushrooms legal?

Psilocybin is classified as a Schedule I substance under the Controlled Substances Act, according to the Drug Enforcement Agency (DEA).

That classification means the substance “has a high potential for abuse, no currently accepted medical use in treatment in the United States, and a lack of accepted safety for use under medical supervision,” as stated on the DEA’s website.

“Some states offer psychedelic-assisted therapy, which consists of large doses of psychedelics administered in a medical environment and combined with therapy,” Van de Plassche said.

“Patients usually have to jump through many hoops to access it, and it is very expensive — and mostly not covered by health insurance,” she added.

Availability of the substance varies by state, city and county.

Except for some “open-minded” doctors, Van de Plassche said most health practitioners will redirect patients toward more traditional therapies.

“Microdosing is not a practice embraced by health professionals — yet,” she said. 

“Most microdosers have to opt for ‘civil disobedience’ in order to benefit from the practice.”

In most cases, the substances people use are not standardized or regulated, Scioli reiterated. 

“That means you really don’t know what you’re taking — and what you’re taking may be contaminated with other substances that can be extremely dangerous,” he said.

“There is also no way to tell if you’re taking too much of a substance. What may have little to no effect on one person may be extremely harmful to another person.”

Fox News Digital reached out to the DEA requesting additional comment.

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