A chair of weight 150 lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of = 38.0 directed at an angle of 41.0 below the horizontal and the chair slides along the floor.Using Newton's laws, calculate , the magnitude of the normal force that the floor exerts on the chair.
Mulitple post. Answered elsewhere
To calculate the normal force, we need to consider the forces acting on the chair in the vertical direction. In this case, there are two forces: the weight of the chair (mg) and the vertical component of the force you applied (F_y).
1. Calculate the weight of the chair (mg):
Given that the weight of the chair is 150 N, we know that the force due to gravity acting on the chair is 150 N. The weight can be calculated using the formula:
Weight (mg) = mass (m) x acceleration due to gravity (g)
Assuming the acceleration due to gravity is 9.8 m/s^2, we can rearrange the formula to solve for mass:
m = Weight (mg) / acceleration due to gravity (g)
m = 150 N / 9.8 m/s^2
2. Calculate the vertical component of the force you applied (F_y):
The force you applied on the chair is 38.0 N at an angle of 41.0° below the horizontal. To find the vertical component of this force, we can use trigonometry. The vertical component (F_y) can be calculated using the formula:
F_y = force (F) x sin(angle)
F_y = 38.0 N x sin(41.0°)
3. Calculate the net vertical force:
The net vertical force (ΣF_y) is the sum of the weight and the vertical component of the force you applied. It can be calculated using the formula:
ΣF_y = mg + F_y
4. Calculate the normal force:
The magnitude of the normal force (N) is equal to the magnitude of the net vertical force (ΣF_y). So the normal force can be calculated by substituting the previously calculated values into the formula:
N = ΣF_y
Now you have all the necessary information to solve for the normal force by following these steps.