A woman who weighs 4.33 X10^2 N is leaning against a smooth vertical wall, as the drawing shows.
The height of the wall from her shoulder to her hand is .400m
the angle at which she is laying on the wall is 50 degrees and the rest of the height at which she is leaning against the wall is 1.10 m im trying my best to explain this picture.
(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.
the angle is 50 degrees.... <measured how>
the rest of the height is ...<I have no idea what this means>
To solve this problem, we can break down the forces exerted on the woman into their components. Let's go through each part step by step:
(a) Find the force FN (directed perpendicular to the wall) exerted on her shoulder by the wall.
The force FN can be found using the equilibrium condition. Since the woman is in a static state, the sum of all the forces acting on her must be equal to zero.
First, let's resolve the weight of the woman into its components. The weight is given by the formula:
Weight = mass * acceleration due to gravity
Given that the weight is 4.33 × 10^2 N, we need to convert it to kilograms. Divide the weight by the acceleration due to gravity (approximately 9.8 m/s^2) to obtain the mass of the woman.
Now, let's consider the forces acting in the vertical direction. We have the component of weight acting vertically downwards and the component of FN acting vertically upwards. The vertical components must cancel each other out to ensure vertical equilibrium:
Vertical force components:
FN - (vertical component of weight) = 0
To find the vertical component of weight:
Vertical component of weight = weight * sin(angle)
Where the angle is the angle at which she is leaning on the wall, which is 50 degrees in this case.
By substituting the values into the equation, we can find the vertical component of weight.
Once we have the vertical component of weight, we can rearrange the equation to solve for FN:
FN = (vertical component of weight)
(b) Find the horizontal component of the force exerted on her shoes by the ground.
The horizontal component of the force exerted on her shoes by the ground is equal and opposite to the horizontal component of FN. Therefore, we need to find the horizontal component of FN.
The horizontal component of FN can be calculated using the formula:
Horizontal component of FN = FN * cos(angle)
Where the angle is the angle at which she is leaning on the wall, which is 50 degrees in this case.
Substitute the calculated value of FN into the equation to find the horizontal component of the force exerted on her shoes.
(c) Find the vertical component of the force exerted on her shoes by the ground.
The vertical component of the force exerted on her shoes by the ground can be calculated using the formula:
Vertical component of the force exerted on her shoes = (vertical component of weight) - FN
Substitute the values we've already calculated into the equation to find the vertical component of the force exerted on her shoes.
By following these steps and performing the necessary calculations, you should be able to find the answers to all three parts of the problem.