A flight attendant pulls her 66 N flight bag a distance of 359 m along a level airport floor at a constant velocity. The force she exerts is 42 N at an angle of 54° above the horizontal.
Work = Fe*CosA * d = 42*Cos54 * 359 =
post it.
To solve this problem, we can break the force vector into its horizontal and vertical components.
The force can be broken down into a horizontal component and a vertical component using trigonometry. The horizontal component is given by:
F_horizontal = F * cos(theta)
Where F is the magnitude of the force (42 N) and theta is the angle (54°).
Calculating the horizontal component:
F_horizontal = 42 N * cos(54°)
F_horizontal ≈ 42 N * 0.5878
F_horizontal ≈ 24.57 N
The horizontal component of the force is approximately 24.57 N.
Now, since the flight attendant pulls her flight bag along the level airport floor at a constant velocity, the net force acting on the bag must be zero. The horizontal component of the force is the only force acting in the horizontal direction, so it must be balanced by the force of kinetic friction.
The force of kinetic friction can be calculated using the equation:
F_friction = μ * F_normal
Where μ is the coefficient of kinetic friction and F_normal is the normal force. Since the airport floor is level, the normal force is equal to the weight of the bag, which can be calculated using the equation:
F_normal = m * g
Where m is the mass of the bag and g is the acceleration due to gravity (approximately 9.8 m/s^2). Rearranging the equation, we have:
m = F_normal / g
Now, we know that the force of kinetic friction is equal to the horizontal component of the force, so:
F_friction = F_horizontal
Substituting the values into the equation:
μ * (m * g) = 24.57 N
Here we have two unknowns, μ and m. We can solve for one of them by using additional information or assumptions. If we assume the coefficient of kinetic friction is given as 0.3, we can solve for m:
0.3 * (m * 9.8 m/s^2) = 24.57 N
Rearranging the equation:
m = 24.57 N / (0.3 * 9.8 m/s^2)
m ≈ 8.54 kg
The mass of the flight bag is approximately 8.54 kg.
Therefore, the flight bag has a mass of approximately 8.54 kg, and the horizontal force exerted by the flight attendant is approximately 24.57 N.