Final answer:
The magnitude of the acceleration starting from rest is 9.74 m/s². The magnitude of the acceleration once the sled starts to move can be calculated using the maximum force of static friction. The magnitude of the force in the coupling between the dogs and the sled is 1480 N.
Step-by-step explanation:
(a) To calculate the acceleration starting from rest, we can use Newton's second law, which states that force is equal to mass times acceleration. Each dog exerts a force of 185 N backward, so the total force exerted by all eight dogs is 8 * 185 N = 1480 N. The mass of the dogs is 8 * 19 kg = 152 kg. Plugging these values into the formula F = ma, we get 1480 N = 152 kg * a. Rearranging the equation, we find that the acceleration is a = 1480 N / 152 kg = 9.74 m/s².
(b) Once the sled starts to move, the static friction between the sled and the snow is overcome. The force of maximum static friction can be calculated using the equation F = μs * N, where μs is the coefficient of static friction and N is the normal force. The normal force is equal to the weight of the sled and rider, so N = (210 kg + 19 kg * 8) * 9.8 m/s² = 2057.4 N.
Plugging in this value along with the coefficient of static friction (which is not given in the question) would allow us to calculate the maximum force of static friction. Since the sled is on wet snow, we can assume that static friction is enough to start the sled moving, so the magnitude of the acceleration would be equal to the magnitude of the force of static friction divided by the total mass of the sled and dogs, which is 210 kg + 19 kg * 8 = 382 kg.
(c) To calculate the magnitude of the force in the coupling between the dogs and the sled, we can use Newton's third law, which states that for every action, there is an equal and opposite reaction. The force exerted by the dogs on the sled is equal in magnitude but opposite in direction to the force exerted by the sled on the dogs. So the magnitude of the force in the coupling between the dogs and the sled would be 1480 N.