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.
(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.
at constant speed,
horizontal force*distance=workdone
where horizontal force is 41cos52
workdone= mg*mu solve for mu
To find the work done by the force of friction on the flight bag, we need to determine the frictional force acting on the bag and multiply it by the distance over which it acts.
The force of friction can be calculated using the equation:
Frictional force = Normal force * coefficient of friction
In this case, the normal force is equal to the weight of the flight bag, which can be calculated using:
Normal force = mass * gravitational acceleration
Given that the mass of the bag is not provided, we can assume it to be negligible since only the weight is given. Therefore, the normal force is simply equal to the weight, which is the product of the mass and gravitational acceleration.
Using the formula for the gravitational force:
Weight = mass * gravitational acceleration
Knowing that the gravitational acceleration is approximately 9.8 m/s², we can calculate the weight as:
Weight = 70.0 N
Now, we can substitute the weight value into the equation for the frictional force:
Frictional force = 70.0 N * coefficient of friction
Since the flight attendant is pulling the bag at a constant speed, the force she exerts must be equal to the frictional force. Therefore, the force she exerts is also equal to 70.0 N * coefficient of friction.
Given that the force she exerts is 41.0 N at an angle of 52.0° above the horizontal, we can find the horizontal component of this force using the following equation:
Horizontal component = Force * cos(angle)
Plugging in the values:
Horizontal component = 41.0 N * cos(52.0°)
Now, we can set up an equation:
Horizontal component = 70.0 N * coefficient of friction
Solving this equation for the coefficient of friction, we have:
coefficient of friction = (41.0 N * cos(52.0°)) / 70.0 N
Calculating this expression will give us the coefficient of kinetic friction.
To solve this problem, we need to break it down into smaller steps.
First, let's find the work done by the force of friction on the flight bag.
The work done by a force can be calculated using the formula: Work = Force * Distance * cos(theta)
In this case, the force of friction is opposing the direction of motion, so the angle between the force of friction and the displacement is 180 degrees or π radians.
Given:
Force of friction = ?
Distance = 263 m
Angle between force of friction and displacement = 180 degrees (or π radians)
Now, let's substitute the given values into the formula:
Work = Force * Distance * cos(theta)
Work = Force * 263 m * cos(180 degrees)
Next, let's find the coefficient of kinetic friction between the flight bag and the floor.
The coefficient of kinetic friction can be calculated using the formula: coefficient of kinetic friction = (Force of friction) / (Normal force)
In this case, the normal force is equal to the weight of the flight bag, which can be calculated using the formula: weight = mass * gravity
Given:
Force of friction = ?
Normal force = weight
Weight = mass * gravity
Now, let's substitute the given values into the formula:
coefficient of kinetic friction = (Force of friction) / (Normal force)
coefficient of kinetic friction = (Force of friction) / (weight)
coefficient of kinetic friction = (Force of friction) / (mass * gravity)
Now, let's find the force of friction.
The force of friction can be calculated using the formula: Force of friction = coefficient of kinetic friction * Normal force
Given:
Force of friction = ?
coefficient of kinetic friction = ?
Normal force = weight
weight = mass * gravity
Now, let's substitute the given values into the formula:
Force of friction = coefficient of kinetic friction * Normal force
Force of friction = coefficient of kinetic friction * weight
Force of friction = coefficient of kinetic friction * (mass * gravity)
By solving these equations step by step, we can find the answers to parts (b) and (c) of the question.