Rigid Objects in Equilibrium and Center of Gravity

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The discussion revolves around a physics problem involving a woman leaning against a wall, requiring calculations for forces acting on her. The calculated normal force exerted by the wall on her shoulder is 198.99 N, and the horizontal force exerted on her shoes by the ground is also 198.99 N. However, there is confusion regarding the vertical component of the force on her shoes, initially calculated as 668.99 N, which includes both horizontal and vertical forces. It is clarified that the vertical component should simply equal her weight of 470 N to maintain equilibrium. The emphasis is on understanding the forces in equilibrium without unnecessary calculations.
helen3743
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Thanks in advance--

Problem:
A woman who weighs 470 x 10^2 is leaning against a smooth vertical wall, as the drawing shows.
a) Find the force FN (directed perpendicular to the wall) exerted on her shoulder by the wall.
b) Find the horizontal component of the force exerted on her shoes by the ground.
c) Find the vertical component of the force exerted on her shoes by the ground.

I answered the problem, but I was wondering if I did it correctly.
I uploaded the drawing.

a) Fn(sin60)r1 = mgr2
Fn(sin60)(1.1+0.4) = 470(cos60)(1.1)
Fn = 198.99 N

b) 198.99 N

c) 198.99N + 470N = 668.99 N

Thanks!
 

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helen3743 said:
a) Fn(sin60)r1 = mgr2
Fn(sin60)(1.1+0.4) = 470(cos60)(1.1)
Fn = 198.99 N

b) 198.99 N
Looks good to me.
c) 198.99N + 470N = 668.99 N
Why are you adding a horizontal force to the weight (a vertical force)?

Hint: You should be able to answer c) without any calculation.
 
Hmm.. So I'm guessing it would be just 470N...?

Thanks again!
 
Hey, no guessing! :smile: The only downward force on her is her weight... so what must the upward component of the floor's force on her be for her to be in equilibrium?
 

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