How to solve dimensions analysis
To solve dimensional analysis, follow the steps below:
1. Identify the given quantity: Start by identifying the physical quantity that is given in the problem. For example, if the problem states that a distance is given in meters, note that the given quantity is distance.
2. Determine the physical dimensions: Identify the physical dimensions associated with the given quantity. In the case of distance, the physical dimensions are length or L.
3. Identify the desired quantity: Determine the physical quantity that you want to find or calculate. This desired quantity should also have certain physical dimensions associated with it. For example, if the problem asks for the time it takes for an object to travel a certain distance, the desired quantity is time, which has the physical dimensions of T.
4. Identify the other physical quantities involved: Look for other physical quantities given in the problem that are relevant to the desired quantity. These quantities should also have their own physical dimensions.
5. Create a dimensional equation: Express the relationship between the given quantity, desired quantity, and any other relevant quantities using a mathematical equation.
6. Match the units: Check that the physical dimensions on both sides of the equation match. If the dimensions do not match, adjust the equation by multiplying or dividing by suitable conversion factors until the dimensions on both sides become equal.
7. Solve for the desired quantity: Use algebraic manipulation to re-arrange the equation and solve for the desired quantity.
8. Check the units: After obtaining the numerical value for the desired quantity, check that the units are consistent with the expected units for that quantity. If the units are correct, the solution is valid. If not, review the steps and check for any errors in calculation or unit conversion.
Remember, dimensional analysis is a powerful tool that helps ensure the consistency and correctness of equations and calculations involving physical quantities.
How convert cm to m
Mm to g
Kg m
Cm to kg
Tonnes to metric tonnes
Tonnes to kg
Metric tonnes to kg
Length to m
Hours to minutes
Minutes to second
Hours to second
To convert between different units, use the conversion factors provided below:
1. cm to m: Divide the length in centimeters by 100 to convert it to meters.
Example: 150 cm = 150 / 100 = 1.5 m
2. mm to g: One millimeter (mm) is equal to one gram (g) in terms of length-to-mass conversion.
Example: 75 mm = 75 g
3. kg m: There is no conversion needed for a quantity given as "kg m" since it represents a unit of momentum, which combines mass and velocity.
4. cm to kg: Converting centimeters (cm) to kilograms (kg) is not a direct conversion because they are different physical quantities. You would need additional information, such as the density or specific gravity of the substance, to perform a conversion from volume (cm) to mass (kg).
5. tonnes to metric tonnes: A tonne is equal to a metric ton. Therefore, there is no conversion needed between these two units.
Example: 5 tonnes = 5 metric tonnes
6. tonnes to kg: To convert tonnes to kilograms, multiply the quantity in tonnes by 1000.
Example: 3 tonnes = 3 * 1000 = 3000 kg
7. metric tonnes to kg: Both metric tonnes and kilograms have the same base unit (grams). To convert from metric tonnes to kilograms, multiply the quantity in metric tonnes by 1000.
Example: 2.5 metric tonnes = 2.5 * 1000 = 2500 kg
8. Length to m: If the length is given in a unit other than meters, use the appropriate conversion factor. For example, if the length is given in centimeters (cm), divide by 100 to convert to meters.
9. Hours to minutes: To convert hours to minutes, multiply the number of hours by 60.
Example: 2 hours = 2 * 60 = 120 minutes
10. Minutes to seconds: To convert minutes to seconds, multiply the number of minutes by 60.
Example: 5 minutes = 5 * 60 = 300 seconds
11. Hours to seconds: To convert hours to seconds, multiply the number of hours by 3600.
Example: 3 hours = 3 * 3600 = 10800 seconds
Remember to always double-check your conversions and make sure they make sense in the context of the problem.
To solve dimensional analysis problems, follow these steps:
1. Understand the problem: Read the problem carefully and identify the quantities given and the quantity you are trying to find.
2. List the known quantities: Write down the given quantities and their units.
3. Identify the unknown quantity: Determine what you are trying to find, and write down the unit it should be in.
4. Identify the conversion factors: Find the conversion factors needed to convert the given units to the desired units. Conversion factors are ratios of equivalent quantities expressed in different units.
5. Set up the dimensional analysis equation: Write down the given quantity along with its units, and set it equal to the unknown quantity with its units, using the appropriate conversion factors.
6. Cancel units: Use the conversion factors to cancel out units that are the same on both sides of the equation. Multiply or divide the quantities as necessary to obtain the desired units.
7. Perform the calculation: Perform the numerical calculation, making sure to cancel out units correctly.
8. Check the answer: Verify that the units of the final answer are correct and make sense based on the problem statement. If necessary, round the answer to the appropriate number of significant figures.
By following these steps, you can successfully solve dimensional analysis problems.