Answer :
To calculate the work done when a person with a mass of 112 kg walks up 4.25 meters of stairs, we use the formula for work done against gravity:
[tex]\[ \text{Work} = \text{mass} \times \text{gravity} \times \text{height} \][/tex]
Here are the given values:
- Mass ([tex]\( m \)[/tex]) = 112 kg
- Height ([tex]\( h \)[/tex]) = 4.25 meters
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.8 m/s²
Step-by-Step Solution:
1. Identify the values:
- Mass of the person (m) = 112 kg
- Height of the stairs (h) = 4.25 meters
- Acceleration due to gravity (g) = 9.8 m/s²
2. Write down the formula for work:
[tex]\[ \text{Work} = m \times g \times h \][/tex]
3. Substitute the given values into the formula:
[tex]\[ \text{Work} = 112 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 4.25 \, \text{m} \][/tex]
4. Perform the multiplication:
[tex]\[ \text{Work} = 112 \times 9.8 \times 4.25 \][/tex]
5. Calculate the actual value:
[tex]\[ \text{Work} = 112 \times 9.8 = 1097.6 \][/tex]
[tex]\[ 1097.6 \times 4.25 = 4664.8 \][/tex]
Therefore, the work done by the person walking up the stairs is:
[tex]\[ 4664.8 \, \text{Joules} \][/tex]
So, the work done is 4664.8 Joules.
[tex]\[ \text{Work} = \text{mass} \times \text{gravity} \times \text{height} \][/tex]
Here are the given values:
- Mass ([tex]\( m \)[/tex]) = 112 kg
- Height ([tex]\( h \)[/tex]) = 4.25 meters
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.8 m/s²
Step-by-Step Solution:
1. Identify the values:
- Mass of the person (m) = 112 kg
- Height of the stairs (h) = 4.25 meters
- Acceleration due to gravity (g) = 9.8 m/s²
2. Write down the formula for work:
[tex]\[ \text{Work} = m \times g \times h \][/tex]
3. Substitute the given values into the formula:
[tex]\[ \text{Work} = 112 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 4.25 \, \text{m} \][/tex]
4. Perform the multiplication:
[tex]\[ \text{Work} = 112 \times 9.8 \times 4.25 \][/tex]
5. Calculate the actual value:
[tex]\[ \text{Work} = 112 \times 9.8 = 1097.6 \][/tex]
[tex]\[ 1097.6 \times 4.25 = 4664.8 \][/tex]
Therefore, the work done by the person walking up the stairs is:
[tex]\[ 4664.8 \, \text{Joules} \][/tex]
So, the work done is 4664.8 Joules.
