To determine how much work the woman performs by carrying her suitcase up the flight of stairs, we can use the formula for work done against gravity:
[tex]\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \][/tex]
Since the suitcase is being lifted vertically, the angle [tex]\(\theta\)[/tex] between the force (weight of the suitcase) and the direction of the movement is 0 degrees. The cosine of 0 degrees is 1, simplifying our calculation. Therefore:
[tex]\[ \text{Work} = \text{Force} \times \text{Distance} \][/tex]
The force in this case is the weight of the suitcase, which can be calculated by multiplying the mass (m) of the suitcase by the acceleration due to gravity (g):
[tex]\[ \text{Force} = m \times g \][/tex]
Let's plug in the given values:
- The mass [tex]\( m \)[/tex] of the suitcase is 10 kg.
- The acceleration due to gravity [tex]\( g \)[/tex] is [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
- The height [tex]\( h \)[/tex] (distance) of the stairs is 12 meters.
Now, calculate the force:
[tex]\[ \text{Force} = 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 98 \, \text{N} \][/tex]
Then, calculate the work done:
[tex]\[ \text{Work} = 98 \, \text{N} \times 12 \, \text{m} = 1176 \, \text{J} \][/tex]
So, the work performed by carrying the suitcase up the stairs is:
[tex]\[ 1176 \, \text{J} \][/tex]
Thus, the correct answer is:
D. 1176 J
