Sure, let's solve this step by step. We want to find out which one exerts more pressure on the ground: the girl or the elephant. Here are the given values:
- Mass of the girl, [tex]\( m_{\text{girl}} = 50 \)[/tex] kg
- Area of one heel of the girl, [tex]\( A_{\text{girl}} = 1 \)[/tex] cm[tex]\(^2\)[/tex]
- Mass of the elephant, [tex]\( m_{\text{elephant}} = 2000 \)[/tex] kg
- Area of one foot of the elephant, [tex]\( A_{\text{elephant}} = 250 \)[/tex] cm[tex]\(^2\)[/tex]
- Number of elephant's feet = 4
### Step 1: Calculate the gravitational force (weight)
We use the formula for weight:
[tex]\[ F = m \cdot g \][/tex]
where [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
#### For the girl:
[tex]\[ F_{\text{girl}} = 50 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 490 \, \text{N} \][/tex]
#### For the elephant (total force):
[tex]\[ F_{\text{elephant total}} = 2000 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 19600 \, \text{N} \][/tex]
Since the elephant stands on four feet, the force per foot:
[tex]\[ F_{\text{elephant per foot}} = \frac{19600 \, \text{N}}{4} = 4900 \, \text{N} \][/tex]
### Step 2: Calculate the pressure exerted
Pressure is given by:
[tex]\[ P = \frac{F}{A} \][/tex]
#### For the girl:
[tex]\[ P_{\text{girl}} = \frac{490 \, \text{N}}{1 \, \text{cm}^2} = 490 \, \text{N/cm}^2 \][/tex]
#### For the elephant (for one foot):
[tex]\[ P_{\text{elephant}} = \frac{4900 \, \text{N}}{250 \, \text{cm}^2} = 19.6 \, \text{N/cm}^2 \][/tex]
### Step 3: Compare the pressures
Now we compare the pressure exerted by the girl and the elephant.
- The pressure exerted by the girl is [tex]\( 490 \, \text{N/cm}^2 \)[/tex].
- The pressure exerted by the elephant (per foot) is [tex]\( 19.6 \, \text{N/cm}^2 \)[/tex].
Thus, the girl exerts more pressure on the ground than the elephant. The significant difference is due to the much smaller area of the girl's heels compared to the elephant's feet.
### Conclusion
The girl standing on pencil heels exerts more pressure on the ground compared to the elephant standing on its four feet.
