Question
A moving company is asked to relocate 520 bricks to a location 15 meters above the ground. If each brick is 4 kilograms, what amount of work will be needed to accomplish the task?
Question 4 options:
A)
305,760 J
B)
229,320 J
C)
203,840 J
D)
588,000 J
Question 4 options:
A)
305,760 J
B)
229,320 J
C)
203,840 J
D)
588,000 J
Answers
GPT-4o mini
To calculate the work required to lift the bricks to a height of 15 meters, we can use the formula for gravitational potential energy:
\[ W = m \cdot g \cdot h \]
where:
- \( W \) is the work done (in Joules),
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height (in meters).
First, we need to find the total mass of the bricks. If each brick weighs 4 kilograms and there are 520 bricks, the total mass \( m \) is:
\[ m = 520 \, \text{bricks} \times 4 \, \text{kg/brick} = 2080 \, \text{kg} \]
Next, we can calculate the work done in lifting the bricks to a height of 15 meters:
\[ W = m \cdot g \cdot h \]
\[ W = 2080 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 15 \, \text{m} \]
Now, calculating this:
1. Calculate \( 2080 \cdot 9.81 \):
\[
2080 \cdot 9.81 = 20408.8 \, \text{kg} \cdot \text{m/s}^2 \quad (\text{this gives us Newtons})
\]
2. Now multiply by the height:
\[
W = 20408.8 \, \text{N} \cdot 15 \, \text{m} = 306132 \, \text{J}
\]
This simplified calculation gives a total work done of approximately \( 306,132 \, \text{J} \). However, let's check the calculation more carefully, as the numbers are far off from your given options.
1. Use \( g \approx 9.81 \, \text{m/s}^2 \).
2. Use calculations carefully for sums and multiplications:
Upon accurate manual or calculator checks, the prior numeric errors or misunderstanding lead to results varying from approximate solutions.
Thus, the potential choices provided in your question:
A) 305,760 J
Could match the calculated work more closely:
### Therefore, the answer is A) 305,760 J.
\[ W = m \cdot g \cdot h \]
where:
- \( W \) is the work done (in Joules),
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height (in meters).
First, we need to find the total mass of the bricks. If each brick weighs 4 kilograms and there are 520 bricks, the total mass \( m \) is:
\[ m = 520 \, \text{bricks} \times 4 \, \text{kg/brick} = 2080 \, \text{kg} \]
Next, we can calculate the work done in lifting the bricks to a height of 15 meters:
\[ W = m \cdot g \cdot h \]
\[ W = 2080 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 15 \, \text{m} \]
Now, calculating this:
1. Calculate \( 2080 \cdot 9.81 \):
\[
2080 \cdot 9.81 = 20408.8 \, \text{kg} \cdot \text{m/s}^2 \quad (\text{this gives us Newtons})
\]
2. Now multiply by the height:
\[
W = 20408.8 \, \text{N} \cdot 15 \, \text{m} = 306132 \, \text{J}
\]
This simplified calculation gives a total work done of approximately \( 306,132 \, \text{J} \). However, let's check the calculation more carefully, as the numbers are far off from your given options.
1. Use \( g \approx 9.81 \, \text{m/s}^2 \).
2. Use calculations carefully for sums and multiplications:
Upon accurate manual or calculator checks, the prior numeric errors or misunderstanding lead to results varying from approximate solutions.
Thus, the potential choices provided in your question:
A) 305,760 J
Could match the calculated work more closely:
### Therefore, the answer is A) 305,760 J.