A stewardess pulls her 70 N flight bag a distance of 200 m along an airport floor at constant speed. The force she exerts is 40 N at an angle of 50 degrees above the horizontal. Find (a) the work she does, (b) the work done by the force of friction, and (c) the coefficient of kinetic friction between her flight bag and the floor.
I only know how to do (a). How would I do (b) and (c).
(a) (5kg)(9.8m/s^2)(sin30)(200m)=5140J
Well, hello there! Let's tackle parts (b) and (c) together, shall we?
To find the work done by the force of friction (b), we can use the formula:
Work = Force of Friction x Distance
Now, the force of friction can be calculated by subtracting the horizontal component of the force she exerts from the weight of the flight bag. So,
Force of Friction = Weight of the Flight Bag - Horizontal Component of the Force
The weight of the flight bag can be found by using the formula:
Weight = mass x gravity
We need to use the given mass of the flight bag and the value of gravity (9.8 m/s^2). Once you calculate the weight, you can find the horizontal component of the force she exerts by using the angle provided.
To calculate the coefficient of kinetic friction (c), we can use another formula:
Force of Friction = Coefficient of Kinetic Friction x Normal Force
The normal force is equal to the weight of the flight bag. So, to find the coefficient of kinetic friction, you just need to divide the force of friction by the weight of the flight bag.
I hope this helps! And remember, if you have any more questions, don't hesitate to ask. Laughter is always the best answer!
To solve parts (b) and (c) of the problem, you'll need to use the concept of work done by a force and the relationship between work, force, distance, and angle.
(b) Work done by the force of friction:
The work done by the force of friction can be calculated by determining the work done by the net force acting on the flight bag. Since the flight bag is moving at a constant speed, the net force is zero. This means that the work done by the force of friction is equal in magnitude but opposite in direction to the work done by the applied force.
The work done by the applied force (as calculated in part (a)) is 5140J. Since the applied force is horizontal, the work done by the force of friction is also 5140J, but in the opposite direction.
(b) Work done by the force of friction = -5140J
(c) Coefficient of kinetic friction:
To find the coefficient of kinetic friction between the flight bag and the floor, you'll need to consider the relationship between the force of friction, the normal force, and the coefficient of friction. The normal force is the perpendicular force exerted by the surface on the object.
In this case, the force of friction is equal in magnitude but opposite in direction to the applied force, which is 40N at an angle of 50 degrees above the horizontal. To find the normal force, you'll need to decompose the applied force into its horizontal and vertical components.
Horizontal component of the applied force = 40N * cos(50 degrees)
Vertical component of the applied force = 40N * sin(50 degrees)
Since the flight bag is at constant speed, the vertical forces are balanced (i.e., the weight of the flight bag is balanced by the normal force), so the vertical component of the applied force is equal in magnitude but opposite in direction to the weight of the flight bag. The weight of the flight bag can be calculated using the formula:
Weight = mass * acceleration due to gravity = 70N
Now, you can find the normal force by setting the vertical component of the applied force equal to the weight:
Vertical component of the applied force = Weight
40N * sin(50 degrees) = 70N
Solve for sin(50 degrees):
sin(50 degrees) = 70N / 40N = 1.75
Now, you can find the coefficient of kinetic friction by dividing the magnitude of the force of friction by the magnitude of the normal force:
Coefficient of kinetic friction = |Force of friction| / |Normal force|
= |Force of friction| / 70N
Since the force of friction is equal in magnitude to the work done by the force of friction (as calculated in part (b)), the coefficient of kinetic friction can be found by dividing the absolute value of the work done by the force of friction by 70 N:
Coefficient of kinetic friction = |Work done by the force of friction| / 70N
= 5140J / 70N
Calculate the value:
Coefficient of kinetic friction ≈ 73.4
Therefore, the coefficient of kinetic friction between the flight bag and the floor is approximately 73.4.