Equations of motion and proper Significant Digits.

In summary, the conversation is about solving for the relative uncertainty of the mass of gravel dumped from a loaded truck and calculating the acceleration using the formula v(final) = v(initial) + at. The relative uncertainty is calculated to be 0.275 and the final answer for the acceleration is either 1.53 X 10^3 m/s^2, 1533 m/s^2, or 1530 m/s^2, depending on the desired number of significant figures.
  • #1
JamesJames
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0

Homework Statement



Solve the following to the proper number of significant figures:

a) A loaded truck has mass (2.12 X 10^4 +/- 6 X 10^2) kg and when empty, it has a mass of (1.72 X 10^4 +/- 5 X 10^2) kg. What is the relative uncertainty of the mass of the gravel dumped from the truck?

The Attempt at a Solution



Ok, so I go through the math and get

Relative Uncertainty = (5 X 10^2 + 6 X 10^2) kg / 4000 = 0.275

My qwuestion is in regards to significant digits. According to me, the # of sig. figs. Here is 1……there is 1 sig. fig. in 5 X 10^2 or 6 X 10^2, whichever you look at, so the answer should be rounded off to one significant figure.

This means that the FINAL answer should be 0.3.

b) v(initial) = 10.5 m/s
v(final) = -7.3 m/s
t = 0.0115 s

Calculate a.

The Attempt at a Solution



I used v(final ) = v(initial) + at and got a = 1533 m/s^2.

Should the correct answer (rounded off to proper number of significant figures) be a = 1.53 X 10^3 m/s^2?

What about 1533 m/s^2 or 1530 m/s^2….would either of these be acceptable OR is the only answer 1.53 X 10^3 m/s^2?
 
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  • #2
Your help would be greatly appreciated. I feel like I am close but just need some help finishing off the problems.
 
  • #3


As a scientist, it is important to always consider the proper number of significant figures in your calculations and final answer. In the first problem, the relative uncertainty should be rounded to one significant figure, resulting in an answer of 0.3. This is because the uncertainty is given to one significant figure and the result should not have more significant figures than the least precise measurement.

In the second problem, the answer should be rounded to three significant figures, resulting in an answer of 1.53 X 10^3 m/s^2. This is because both initial and final velocities are given to three significant figures and the time is given to four significant figures. The final answer should have the same number of significant figures as the least precise measurement, which in this case is the time.

It is important to follow proper significant figure rules in scientific calculations to ensure accuracy and precision in your results. It is also important to properly round off your final answer to the correct number of significant figures to avoid any misleading or incorrect information.
 

1. What are the three equations of motion?

The three equations of motion are the equations used to describe the motion of an object in one, two, or three dimensions. They are the equations for constant acceleration, constant velocity, and constant position.

2. How do I determine the significant digits in an equation of motion?

The significant digits in an equation of motion are determined by the number of digits in the measured quantities used in the equation. The final answer should have the same number of significant digits as the quantity with the least number of significant digits.

3. Can significant digits affect the accuracy of an equation of motion?

Yes, significant digits can affect the accuracy of an equation of motion. If the measured quantities used in the equation have a limited number of significant digits, the final answer will also have a limited number of significant digits. This can lead to a less accurate result.

4. Why is it important to include proper significant digits in equations of motion?

Including proper significant digits in equations of motion is important because it ensures that the final answer is accurate and reflects the precision of the measured quantities used in the equation. It also helps to avoid rounding errors and maintain consistency in calculations.

5. How do I round the final answer in an equation of motion to the correct number of significant digits?

The final answer in an equation of motion should be rounded to the same number of significant digits as the quantity with the least number of significant digits. If the final answer has more significant digits, it should be rounded to the appropriate number of significant digits using rounding rules (e.g. rounding up if the next digit is 5 or above).

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