A flight attendant pulls her 70.0 N flight bag a distance of 263 m along a level airport floor at a constant speed. The force she exerts is 41.0 N at an angle of 52.0° above the horizontal.

(a) Find the work she does on the flight bag.

(b) Find the work done by the force of friction on the flight bag.

(c) Find the coefficient of kinetic friction between the flight bag and the floor.

(a) To find the work done by the flight attendant on the flight bag, we use the formula for work:

Work = force * distance * cos(angle)

Given:
Force exerted by the flight attendant = 41.0 N
Distance = 263 m
Angle = 52.0°

Substituting these values into the formula:

Work = 41.0 N * 263 m * cos(52.0°)
Work ≈ 41.0 N * 263 m * 0.6157
Work ≈ 6,504.5 Joules

Therefore, the work done by the flight attendant on the flight bag is approximately 6,504.5 Joules.

(b) To find the work done by the force of friction, we use the formula:

Work = force * distance

Since the force of friction is opposite to the direction of motion, the work done by friction is negative. Therefore:

Work = - force of friction * distance

We need to find the force of friction first. To do that, we can use the component of the force exerted by the flight attendant in the horizontal direction:

Force horizontal = force * cos(angle)

Substituting the given values:

Force horizontal = 41.0 N * cos(52.0°)
Force horizontal ≈ 41.0 N * 0.6157
Force horizontal ≈ 25.247 N

The force of friction is equal in magnitude but opposite in direction to the force exerted by the flight attendant in the horizontal direction. So, the force of friction is 25.247 N in the opposite direction.

Now we can find the work done by the force of friction:

Work = - force of friction * distance
Work = - 25.247 N * 263 m
Work ≈ - 6,640.8 Joules

Therefore, the work done by the force of friction is approximately -6,640.8 Joules.

(c) To find the coefficient of kinetic friction, we can use the formula relating frictional force and the normal force:

Frictional force = coefficient of friction * normal force

In this case, the normal force is equal to the weight of the flight bag, which is given by:

Weight of the flight bag = mass * acceleration due to gravity

The mass of the flight bag is not provided in the given information, so we need to assume a value. Let's assume a mass of 10 kg for the flight bag.

Weight of the flight bag = 10 kg * 9.8 m/s^2
Weight of the flight bag = 98 N

Now we can find the coefficient of kinetic friction:

25.247 N = coefficient of kinetic friction * 98 N
coefficient of kinetic friction ≈ 0.257

Therefore, the coefficient of kinetic friction between the flight bag and the floor is approximately 0.257.

To find the answers to the given questions, we will use the formulas related to work, force, distance, and friction.

(a) To find the work done by the flight attendant on the flight bag, we can use the formula for work:

Work = Force * Distance * cos(theta)

Where:
Force = 41.0 N (the force exerted by the flight attendant on the bag)
Distance = 263 m (the distance the bag is pulled)
Theta = 52.0° (the angle between the force and the horizontal direction)

Plugging in the values, we have:
Work = 41.0 N * 263 m * cos(52.0°)

Now, we can calculate the value of cos(52.0°) using a calculator.

(b) To find the work done by the force of friction on the flight bag, we need to use the work-energy theorem, which states that the work done by all forces on an object is equal to the change in its kinetic energy.

The work done by the force of friction can be calculated as:
Work_friction = Work_total - Work_attendant

Here, Work_total is the work done by all forces on the bag, which is equal to the work done by the flight attendant, and Work_attendant is the work done by the flight attendant calculated in part (a).

(c) To find the coefficient of kinetic friction between the flight bag and the floor, we can use the formula:

Coefficient of kinetic friction = (Force_friction / Normal force)

Where:
Force_friction is the force of friction acting on the bag,
Normal force is the force exerted by the floor on the bag perpendicular to the surface.

The value of the normal force is equal to the weight of the bag, which can be calculated as:
Normal force = Mass * Gravity

Given that the weight of the bag can be calculated as:
Weight = Mass * Gravity

We have the force of friction, Normal force, and Force_friction is equal to the coefficient of kinetic friction multiplied by the Normal force. Thus:

Coefficient of kinetic friction = Force_friction / Normal force

By plugging in the values, we can find the coefficient of kinetic friction between the flight bag and the floor.

physics

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