A flight attendent pulls her 78.6 N flight bag a distance of 344 m along a level airport floor at a constant velocity. The force she exerts is 44.8 N at an angle of 64.2 degrees above the horizontal.
Find the coefficient of kinetic friction between the flight bag and the floor?
Please furnish calculations.
To find the coefficient of kinetic friction between the flight bag and the floor, we need to consider the forces acting on the bag. There are three forces involved: the force the flight attendant exerts on the bag (44.8 N at an angle of 64.2 degrees above the horizontal), the gravitational force pulling the bag downwards (which can be calculated using the weight of the bag), and the force of kinetic friction.
First, we need to find the weight of the bag. We can calculate it using the formula:
Weight = mass * gravity
Where mass is the mass of the bag, and gravity is the acceleration due to gravity (approximately 9.8 m/s²).
Next, we need to resolve the force the flight attendant exerts on the bag into its horizontal and vertical components. Since we have the magnitude (44.8 N) and angle (64.2 degrees above the horizontal), we can find the horizontal component by multiplying the magnitude by the cosine of the angle, and the vertical component by multiplying the magnitude by the sine of the angle.
Now, since the flight bag is moving at a constant velocity, we know that the net force acting on it is zero. Therefore, the force of kinetic friction must be equal in magnitude and opposite in direction to the horizontal component of the force the flight attendant exerts on the bag.
Finally, we can calculate the coefficient of kinetic friction using the formula:
Coefficient of Kinetic Friction = Force of Kinetic Friction / Normal Force
Where the normal force is the force exerted by the floor on the bag, which is equal in magnitude and opposite in direction to the vertical component of the force the flight attendant exerts on the bag.
Now, let's calculate the coefficient of kinetic friction step-by-step.
1. Calculate the weight of the bag:
Weight = mass * gravity
2. Resolve the force the flight attendant exerts into horizontal and vertical components:
Horizontal Component = Force * cos(angle)
Vertical Component = Force * sin(angle)
3. Since the bag is moving at a constant velocity, the net force acting on it is zero, so the force of kinetic friction is equal in magnitude and opposite in direction to the horizontal component of the force the flight attendant exerts:
Force of Kinetic Friction = -Horizontal Component
4. Calculate the normal force:
Normal Force = Weight - Vertical Component
5. Calculate the coefficient of kinetic friction:
Coefficient of Kinetic Friction = Force of Kinetic Friction / Normal Force
By following these steps and performing the necessary calculations, you should be able to find the coefficient of kinetic friction between the flight bag and the floor.
The exerted force along the floor direction is 44.8 cos 64.2 = 19.5 N
That equals the bag's weight times the kinetic friction coefficient, Uk, since there is no acceleration.
19.5 = 78.6 Uk
Solve for Uk