# How to solve physics tasks to score highest?

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• vxr
In summary, the conversation is about a student seeking advice for an upcoming physics exam. They discuss the importance of substituting numbers in equations and the use of diagrams in problem-solving. The student also asks if deriving a well-known formula could potentially earn them extra points on the exam.

#### vxr

Hello. I am first year student, taking introductory physics course and next week I have a whole-semester exam. (kinematics, dynamics, rigid body, termodynamics, mechanical waves - that kind of basic stuff).

I don't have a chance to directly ask my teacher following questions, so I figured who else could know better but you guys. :)

I am dealing with fairly simple tasks. (you can view my post history to get the idea)

Often, in the task's description, the initial velocity is ##v_{i} = 0##, or initial height is ##h_{0} = 0##, or final height is ##0##, or final velocity is ##0##, or [...].

Let's say I am dealing with some task, I need to calculate ##v_{h}## (velocity at some height). After calculations I came up with this formula:

##v_{h} = \sqrt{v_{i}^2 - 2gh + 2gh_{i}}##, however the formula: ##v_{h} = \sqrt{v_{i}^2 - 2gh}## will work just as fine as the first one, because in the task it is said that initial height ##h_{i} = 0##.My questions:
1. Which approach, as a general advice, should be better? The first-formula one, which is a little bit more complex, however it'll work for more cases; or the second-formula approach, making it as simple as possible, directly addressing only the task-specific requirements. And not making the formula more general. What is better to score highest points as a general advice?

Perhaps you could imagine such energy-conversion scenario in some task:
##mgh_{i} + \frac{mv_{i}^2}{2} = mgh_{f} + \frac{mv_{f}^2}{2}##

Knowing from the task description that ##v_{f} = 0 \quad \land \quad h_{i} = 0## I can reduce the equation down to:
##\frac{mv_{i}^2}{2} = mgh_{f}##

and thus make it far simpler, but less general. Should I do it or not?

2. How important is sketching the situation (making the drawing) that describes the task? Like draw some falling ball, add some vectors to it etc etc. I indeed do understand that making the drawing is always a good idea and it helps to understand the task. But if I regardless did solve the task correctly, without doing any drawing, would you personally cut me off some grading points because of not making the drawing? How important is it grading-wise, basically?

Sometimes I find myself in a situation where I get the calculations right, the final answer is right, but the drawing might not be the finest representation of task's situation. Hence I feel like it's "risky" for me to make the drawing when I am unsure if my drawing is correct. I feel like I am better off not making the drawing when I am not 100% certain the drawing is correct.

3. Lastly, let's say the task is related to momentum of inertia of a disk. The formula ##I = \frac{1}{2}mR^2## is well known. Do you personally think if I derive this formula (nobody is asking me to do so), I could perhaps get some additional small-tiny-bit of points? ((moment of inertia is just an example))

Thanks for answersing those odd questions and helping me.

edit: thanks for moving my post to appropriate sub-forum :)

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You may have seen my posts and those of others wherein we recommend saving the substitution of numbers until the very end. I would certainly reinforce that recommendation here. Having said that, I should also point out that when you solve a physics problem, you start from a general equation or equations and you adapt these to the particular situation you are dealing with. A good deal of simplification and less tortuous algebra are achieved if you substitute the zeroes and symbols for the usual constants, wherever they are, right from the start.

Example
A ball is released from rest and falls a distance h = 2.00 m. Find the time of flight assuming that g = 10 m/s2 and ignoring air resistance.

General equation: ##y=y_0+v_0t+\frac{1}{2}at^2##
General solution
Solve the quadratic for the time of flight ##t_f## assuming that the origin is where the ball lands
$$0=y_0+v_0t_f+\frac{1}{2}at_f^2$$
$$t_f=\frac{-v_0\pm \sqrt{v_0^2-2ay_0}}{a}$$
Substitute ##a=-10~ \rm{m/s^2},~v_0=0,~y_0=2~\rm{m}## to get
$$t_f=\frac{0\pm \sqrt{0^2-2(-10~ \rm{m/s^2})(2~\rm{m})}}{-10~ \rm{m/s^2}}$$

"Zeroes and usual constants in" solution
Substitute ##v_0 = 0## and ##a=-g## in the general equation.
$$0=y_0-\frac{1}{2}gt_f^2$$
$$t_f^2=\frac{2y_0}{g}\rightarrow t_f=\pm\sqrt{\frac{2y_0}{g}}=\pm\sqrt{\frac{2~\rm{m}}{10~ \rm{m/s^2}}}$$

Which do you think is more error-free and less time consuming?

As for diagrams, you need them to explain the use and definition of the symbols you use, the reference lines for angles, etc. No grader will spend time trying to figure out what your symbols stand for unless you explain them . You most certainly need drawings when you do statics and dynamics problems. Without them you are sure to lose points. They don't need to be very accurate, just show enough to convince the grader that you know what you're talking about. Your drawing will be "incorrect" if your understanding of the problem is incorrect. Omitting the drawing will not bluff the grader to think that you know something when you don't.

vxr