a girl standing appriteexerts apressure of 15000N/m2 on the floor givn tht the ttl area of cntact of shoes and floor is 0.02m2.determine her mass.determine the pressure she would exert on the floor if she stood on one foot
To determine the girl's mass, we can use the formula:
Pressure (P) = Force (F) / Area (A)
Given:
Pressure on the floor (P) = 15000 N/m^2
Area of contact (A) = 0.02 m^2
Rearranging the formula, we can solve for the force:
Force (F) = Pressure (P) * Area (A)
F = 15000 N/m^2 * 0.02 m^2
F = 300 N
Therefore, the girl's mass is 300 kg. (Using the formula F = m * g, where g is the acceleration due to gravity, which is approximately 9.8 m/s^2)
To determine the pressure she would exert on the floor if she stood on one foot, the force would remain the same (300 N). However, the area of contact would be halved since she is now standing on one foot.
Area of contact (new) = 0.02 m^2 / 2
Area of contact (new) = 0.01 m^2
Using the formula P = F/A, where P is the pressure:
Pressure (new) = 300 N / 0.01 m^2
Pressure (new) = 30000 N/m^2
Therefore, the pressure the girl would exert on the floor if she stood on one foot is 30000 N/m^2.
To determine the girl's mass, we can use the equation:
Pressure = Force / Area
Given:
Pressure = 15000 N/m²
Area = 0.02 m²
Rearranging the equation, we can find the force:
Force = Pressure x Area
Force = 15000 N/m² x 0.02 m²
Force = 300 N
Now, we can use the equation F = m x g, where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s²).
300 N = m x 9.8 m/s²
Rearranging the equation to solve for mass:
m = 300 N / 9.8 m/s²
m ≈ 30.61 kg
Therefore, the girl's mass is approximately 30.61 kg.
On one foot, the contact area will be halved (assuming the total contact area of 0.02m² is equally distributed between two feet).
Area of one foot = 0.02m² / 2
Area of one foot = 0.01m²
Now we can determine the pressure she would exert on the floor when standing on one foot:
Pressure = Force / Area
Using the same force of 300 N and the new area of 0.01 m²:
Pressure = 300 N / 0.01 m²
Pressure = 30000 N/m²
Therefore, she would exert a pressure of 30000 N/m² when standing on one foot.