Question

A woman who weighs \(600 \mathrm{N}\) sits on a chair with her feet on the floor and her arms resting on the chair's armrests. The chair weighs $100 \mathrm{N}\(. Each armrest exerts an upward force of \)25 \mathrm{N}$ on her arms. The seat of the chair exerts an upward force of \(500 \mathrm{N}\). (a) What force does the floor exert on her feet? (b) What force does the floor exert on the chair? (c) Consider the woman and the chair to be a single system. Draw an FBD for this system that includes all of the external forces acting on it.

Short answer

Answer: The force exerted by the floor on the woman's feet is 50 N and the force exerted by the floor on the chair is 100 N.

Step-by-step solution

Calculate the total upward force exerted by the chair on the woman

To find the total upward force exerted by the chair on the woman, simply add the forces exerted by the seat and armrests of the chair. Thus: Total Upward Force = Force_seat + 2 * Force_armrests = \(500 N + 2 * 25 N\) = \(500 N + 50 N\) = \(550 N\)

Find the force exerted by the floor on the woman's feet (a)

Since the woman is in equilibrium (not accelerating), the total upward force acting on her should be equal to the total downward force exerted by her weight. The force exerted by the floor on her feet can be calculated by subtracting the total upward force from her weight: Force_floor_woman = Weight_woman - Total Upward Force = \(600 N - 550 N\) = \(50 N\) The force exerted by the floor on the woman's feet is \(50 N\).

Find the force exerted by the floor on the chair (b)

As the chair is also in equilibrium (not accelerating), the downward force (weight of the chair) should be equal to the upward force exerted by the floor on the chair: Force_floor_chair = Weight_chair = \(100 N\) The force exerted by the floor on the chair is \(100 N\).

Draw a Free Body Diagram for the combined system (c)

In order to draw an accurate Free Body Diagram (FBD) for the combined system, we consider the external forces acting on the woman and chair system. These forces include: 1. The force exerted by the floor on the woman's feet (upward, \(50 N\)) 2. The force exerted by the floor on the chair (upward, \(100 N\)) 3. The weight of the woman (downward, \(600 N\)) 4. The weight of the chair (downward, \(100 N\)) Label these forces appropriately, with vectors pointing in the respective directions (upward and downward). Drawing arrows to indicate these forces, you can create a Free Body Diagram representing the external forces acting on this combined system.