Final answer:
To find the magnitude of the normal force n, one must add the vertical component of the applied force to the weight of the chair. The vertical component is calculated using the sine function, and the normal force equals the weight of the chair plus this component. The normal force exerted by the floor on the chair is found to be 141.16 N.
Step-by-step explanation:
To calculate n, the magnitude of the normal force that the floor exerts on the chair, we need to consider both the weight of the chair and the vertical component of the applied force. Since the chair has a weight of 120 N, this is the force that acts downwards due to gravity. When you push on the chair at an angle, you are applying a force that has both horizontal and vertical components. The vertical component of your push will either add to or subtract from the normal force depending on the direction of the push. As the push is directed at an angle of 36 degrees below the horizontal, it has a downward vertical component.
First, we find the vertical component of the push force by using the sine function (since the angle given is below the horizontal, we use sine to find the opposite side of the angle in the right triangle formed by the force vector). The vertical component of the push force (Fv) is calculated as: Fv = F * sin(θ) where F is the push force and θ is the angle. Therefore, Fv = 36.0 N * sin(36 degrees).
Now, we add this vertical component to the weight of the chair to find the total downward force, which will be opposed by the normal force. Thus, the normal force n is equal to the weight of the chair plus the vertical component of the applied force: n = w + Fv.
By calculating, Fv equals 36.0 N * sin(36 degrees) = 36.0 N * 0.5878 ≈ 21.16 N. The total downward force is 120 N + 21.16 N = 141.16 N. Therefore, the normal force n exerted by the floor on the chair is 141.16 N.