Final Answer:
The coefficient of kinetic friction is 0.66. None of the given options is answer.
Step-by-step explanation:
The coefficient of kinetic friction is a dimensionless quantity that is defined as the ratio of the force of friction between two surfaces in contact to the normal force between the surfaces. The force of friction always opposes the motion of the surfaces, and the coefficient of kinetic friction is a measure of how much the force of friction reduces the motion of the surfaces.
To solve this problem, we will need to use the following equations:
F_net = ma
F_friction = μ_k * F_normal
where:
F_net is the net force on the object
m is the mass of the object
a is the acceleration of the object
F_friction is the force of friction
μ_k is the coefficient of kinetic friction
F_normal is the normal force
We are given that the girl pushes the sled at a constant speed. This means that the net force on the sled is zero. We can use this information to solve for the force of friction.
F_net = 0
F_applied - F_friction = 0
F_applied = F_friction
We are also given that the force applied by the girl is 75 N and the angle of the force is 30 degrees. We can use this information to solve for the horizontal component of the force.
F_horizontal = F_applied * cos(θ)
F_horizontal = 75 N * cos(30°)
F_horizontal = 65.25 N
We are also given that the mass of the sled is 10 kg and the distance traveled is 15 meters. We can use this information to solve for the work done by the force.
W = F_horizontal * d
W = 65.25 N * 15 m
W = 978.75 J
Finally, we can use the work done by the force and the distance traveled to solve for the coefficient of kinetic friction.
μ_k = W / (d * mg)
μ_k = 978.75 J / (15 m * 10 kg * 9.81 m/s²)
μ_k = 0.66
Therefore, the coefficient of kinetic friction is 0.66. None of the given options is answer.