Final answer:
The magnitude of the force in the rope being pulled by the father is 32.53 N.
Step-by-step explanation:
To find the magnitude of the force in the rope being pulled by the father, we need to consider the forces acting on the sled. One force is the force of gravity, which is equal to the weight of the sled, given by W = m*g, where m is the mass of the sled and g is the acceleration due to gravity (approximately 9.8 m/s^2). Another force is the force of friction between the sled and the snow, given by f_friction = μ_k * N, where μ_k is the coefficient of kinetic friction and N is the normal force. Since the sled is on an incline, the normal force is equal to the component of the weight of the sled perpendicular to the incline, which is given by N = m*g*cos(theta), where theta is the angle of the incline.
The force being pulled by the father in the rope can be found by considering the net force on the sled along the incline. The net force is equal to the force being pulled by the father minus the force of friction, given by Net force = F - f_friction. Since the sled is moving up the incline at a constant velocity, the net force is zero. Therefore, we can set the equation Net force = 0 and solve for F:
F - f_friction = 0
F - μ_k * N = 0
F - μ_k * m * g * cos(theta) = 0
Substituting the given values, we have:
F - 0.1 * 100 kg * 9.8 m/s^2 * cos(30 degrees) = 0
F - 32.53 N = 0
F = 32.53 N
Therefore, the magnitude of the force in the rope being pulled by the father is 32.53 N.