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a woman who weights 5.00x10^2 N is leaning against a smooth vertical wall, as the drawing shows.find the force exerted on her shoulders by the wall and the horizontal (F2) and vertical components of the force (F1) exerted on her shoes by the ground.
the angle is 60 degrees. from her shoes to her stomach is 1.10m and from the neck to the stomach is 0.400m.
Assuming no friction on the wall, only normal forces.
Summing moments about the shoe:
500*1.1-(Fwall)*(.4+1.1)*cos60=0
solve for Fwall
summing vertical forces:
F1-500=0 solve for F1.
summing horizontal forces:
F2-Fwall=0 solve for F2, the friction force on the shoe to keep it from sliding.
To solve this problem, we need to break down the forces acting on the woman into their horizontal and vertical components. Let's start by understanding the forces involved:
1. Weight of the woman: The weight of the woman is given as 5.00x10^2 N. This acts vertically downward.
2. Force exerted by the wall: The wall is smooth, so it does not exert a horizontal force on the woman. However, it applies a vertical force to support her weight.
3. Force exerted by the ground on her shoes: The force exerted by the ground has two components - one vertical (F1) and one horizontal (F2).
To calculate the force exerted by the wall, we need to find the vertical component of the force exerted by the ground. Here's how to find each component:
1. Vertical Component (F1):
To find F1, we need to use trigonometry. The angle is given as 60 degrees, and the distance from her shoes to her stomach is given as 1.10m. We can use the sine function to calculate the vertical component:
F1 = Weight of the woman * sin(angle)
= (5.00x10^2 N) * sin(60 degrees)
2. Horizontal Component (F2):
To find F2, we can use trigonometry again. The angle is given as 60 degrees, and the distance from her neck to her stomach is given as 0.400m. We can use the cosine function to calculate the horizontal component:
F2 = Weight of the woman * cos(angle)
= (5.00x10^2 N) * cos(60 degrees)
Now, you can substitute the values and calculate F1 and F2.