Lesson 2 Work and Energy
Completion requirements
Calculation of Work
How is the amount of work done in a system calculated?
C2.6 Calculator and pencil
Remember that work is done on an object whenever a force moves an object a distance and the distance is in the direction of the force.
Work is a measurement of energy, so its units is the joule (J). It can also be expressed as a unit of newton × metre (N·m).
In previous science studies and in Unit B, you were taught about the importance of expressing your final answer in calculation questions to the correct number of significant digits.
Work is a measurement of energy, so its units is the joule (J). It can also be expressed as a unit of newton × metre (N·m).
In previous science studies and in Unit B, you were taught about the importance of expressing your final answer in calculation questions to the correct number of significant digits.
Guidelines for Significant Digits, Manipulation of Data, and Rounding in Science
- For all non-logarithmic values, regardless of decimal position, any of the digits 1 to 9 is a significant digit; 0 may be significant. For example:
123 0.123 0.002 30 2.30 × 103 2.03
All of these have three significant digits.
- Leading zeros are not significant. For example:
0.12 and 0.012 each have two significant digits.
- All trailing zeros are significant. For example:
200 has three significant digits.
0.123 00 and 20.000 each have five significant digits.
- When adding or subtracting measured quantities, the calculated answer should be rounded to the same degree of precision as that of the least precise number used in the computation if this is the only operation. For example in the following addition:
- When multiplying or dividing measured quantities, the calculated answer should be rounded to the same number of significant digits as are contained in the quantity with the fewest number of significant digits if this is the only operation.
For example:
(1.23)(54.321) = 66.814 83
The answer should be rounded to 66.8.
- When a series of calculations is performed, each interim value should not be rounded before carrying out the next calculation. The final answer should then be rounded to the same number of significant digits as are contained in the quantity
in the
original data with the fewest number of significant digits. For example:
In determining the value of (1.23)(4.321) / (3.45 − 3.21), three calculations are required
The answer should be rounded to 24.8.
-
3.45 − 3.21 = 0.24
-
(1.23)(4.321) = 5.314 83
-
5.314 83 / 0.24 = 22.145 125
[Not 5.31 / 0.24 = 22.125]
The value should be rounded to 22.1.
Note: In the example given, steps a and b yield intermediate values. These values should not be used in determining the number of significant digits.
- When calculations involve exact numbers (counted and defined values), the calculated answer should be rounded based upon the precision of the measured value(s). For example:
12 eggs × 52.3 g/egg = 627.6 g
or
5 mol × 32.06 g/mol = 160.30 g
or
(1 mol)(–1 095.8 kJ/mol) + (2 mol)(40.8 kJ/mol) = –1 014.2 kJ
or
5 mol × 32.06 g/mol = 160.30 g
or
(1 mol)(–1 095.8 kJ/mol) + (2 mol)(40.8 kJ/mol) = –1 014.2 kJ
- When the first digit to be dropped is less than or equal to 4, the last digit retained should not be changed. For example:
1.234 5 rounded to three digits is 1.23.
- When the first digit to be dropped is greater than or equal to 5, the last digit retained should be increased by one. For example:
12.25 rounded to three digits is 12.3.
Examples
- What work is done by a forklift raising a 5 720 N box 1.4 m?
Step 1: List the variables.
Step 2: Identify the correct formula and rearrange if necessary.
W = Fd
Step 3: Substitute the values into the formula.
W = (5 720 N)(1.4 m)
Step 4: Calculate the answer.
W = 8 000 J
The answer must be rounded to two significant digits.
8 000 J cannot be rounded to 2 significant digits, so it must be put into scientific notation.
Move the decimal point to the left until your answer is between 1 and 10.
8 008: Move the decimal three places to the left to become .
Three decimals to the left is indicated by a 103 (“3” for moving three places to the left).
Round the value of 8.008 to two significant digits: 8.0.
The amount of work done by the forklift is 8.0 × 103 J.
- A force of 825 N is needed to push a car across a lot. Two students push the car 32 m.
- How much work is done?
Step 1: List the variables.
Step 2: Identify the correct formula and rearrange if necessary.
W = Fd
Step 3: Substitute the values into the formula.
W = (825 N)(32 m)
Step 4: Calculate the answer.
W = 26 400 J
The answer must be rounded to two significant digits.
26 400 J cannot be rounded to two significant digits, so it must be put into scientific notation.
Move the decimal point to the left until your answer is between 1 and 10.
26 400: Move the decimal four places to the left to become 2.640 0.
Four decimals to the left is indicated by a 104 (“4” for moving four places to the left).
Round the value of 2.640 0 to two significant digits: 2.6.
The amount of work done by the two students is 2.6 × 104 J.
-
After a rainstorm, the force needed to push the car doubled because the ground became softer. How does the amount of work done by the students change?
Step 1: List the variables.
Step 2: Identify the correct formula and rearrange if necessary.
W = Fd
Step 3: Substitute the values into the formula.
W = (825 N)(2)(32 m)
Step 4: Calculate the answer.
W = 52 800 J
The answer must be rounded to two significant digits.
52 800 J cannot be rounded to two significant digits, so it must be put into scientific notation.
Move the decimal point to the left until your answer is between 1 and 10.
52 800: Move the decimal four places to the left to become 5.280 0.
Four decimals to the left is indicated by a 104 (“4” for moving four places to the left).
Round the value of 5.280 0 to two significant digits: 5.3.
The amount of work done by the two students is 5.3 × 104 J.
If the amount of force doubles, then the amount of work done also doubles.
- A delivery clerk must carry a 34 N package from the ground floor to the third floor of an apartment building. If it is determined that he did 306 J of work carrying the package, what height did he carry the package to?
Step 1: List the variables.
Step 2: Identify the correct formula and rearrange if necessary.
W = Fd
To isolate d, you must divide each side by F. To move F to the other side, you must use the opposite operation. Division is opposite to multiplication.
Now, cancel the like terms.
Step 3: Substitute the values into the formula
Step 4: Calculate the answer.
d = 9 m
The answer must be rounded to two significant digits.
The height that the delivery clerk carried the package was 9.0 m.
- How much energy must a person use to push a 25 N rock a distance of 1.72 m?
Work is a measurement of energy. So, the amount of work done to push the rock will be equal to the amount of energy the person must use.
Step 1: List the variables.
Step 2: Identify the correct formula and rearrange if necessary.
W = Fd
Step 3: Substitute the values into the formula.
W = (25 N)(1.72 m)
Step 4: Calculate the answer.
W = 43 J
The answer must be rounded to two significant digits.
The amount of energy the person must use is 43 J.
Read This
Please read page 106 in your Science 10 textbook. Make sure you take notes on your readings to study from later. You should focus on how the amount of work can be calculated using the W = Fd formula. Remember, if you have any questions
or do not understand something, ask your teacher!
Practice Questions
Complete the following practice questions to check your understanding of the concept you just learned. Make sure you write complete answers to the practice questions in your notes. After you have checked your answers, make corrections to your responses
(where necessary) to study from.
- A student pushes a book 65 cm across a desk by applying a constant force of 27 N. How much work does the student do?
Step 2: Identify the correct formula and rearrange if necessary.
W = Fd
W = Fd
Step 3: Substitute the values into the formula.
W = (27 N)(0.65 m)
W = (27 N)(0.65 m)
Step 4: Calculate the answer.
W = 17.55 J
The answer must be rounded to two significant digits.
The amount of work the student does is 18 J.
W = 17.55 J
The answer must be rounded to two significant digits.
The amount of work the student does is 18 J.
Step 1: List the variables.
If you need to review how to do unit conversions, see this video.
If you need to review how to do unit conversions, see this video.
Step 2: Identify the correct formula and rearrange if necessary.
Step 3: Substitute the values into the formula.
Step 4: Calculate the answer.
The answer must be rounded to two significant digits.
The amount of work the student does is
The answer must be rounded to two significant digits.
The amount of work the student does is
- A boy pulls a 12 kg box on a horizontal surface and uses 179 J of work to move the box 4.2 m. How much force did the boy exert on the box?
Step 1: List the variables.
Step 2: Identify the correct formula and rearrange if necessary.
W = Fd
To isolate F, you must divide each side by d. To move d to the other side, you must use the opposite operation.
Now, cancel the like terms.
W = Fd
To isolate F, you must divide each side by d. To move d to the other side, you must use the opposite operation.
Now, cancel the like terms.
Step 3: Substitute the values into the formula.
Step 4: Calculate the answer.
F = 42.619...N
The answer must be rounded to two significant digits.
The force the boy exerted on the box was 43 N.
F = 42.619...N
The answer must be rounded to two significant digits.
The force the boy exerted on the box was 43 N.