Answer :
Final answer:
The magnitude of the acceleration when starting from rest is 7.05 m/s². Once the sled starts to move, the magnitude of the acceleration is 4.24 m/s². The coupling force between the dogs and the sled is 133.95 N when the sled is at rest, and 80.56 N when the sled is moving.
Explanation:
To calculate the magnitude of the acceleration, we need to use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration. In this case, each dog exerts a force of 185 N backward on the snow, and there are 8 dogs in total. So the total force exerted on the sled is (185 N/dog) * (8 dogs) = 1480 N. Since the mass of the sled with its rider is 210 kg, we can rearrange the equation to solve for the acceleration: acceleration = force / mass = 1480 N / 210 kg = 7.05 m/s².
Once the sled starts to move, the static friction between the sled and the snow is overcome. The force of static friction can be calculated using the equation: static friction = coefficient of friction * normal force. Since the sled is on a horizontal surface, the normal force is equal to the weight of the sled, which is (mass of sled + mass of rider) * gravitational acceleration = (210 kg + 235 kg) * 9.8 m/s² = 4429 N. Assuming a coefficient of friction of 0.1, the force of static friction is (0.1) * (4429 N) = 442.9 N. So the acceleration once the sled starts to move is given by: acceleration = (force - static friction) / mass = (1480 N - 442.9 N) / 210 kg = 4.24 m/s².
The coupling force between the dogs and the sled can be calculated using the equation: force = mass * acceleration. For the first situation where the sled is at rest, the force is (mass of dogs) * (acceleration). So the coupling force is (19.0 kg/dog) * (7.05 m/s²) = 133.95 N. For the second situation where the sled is moving, the force is (mass of dogs) * (acceleration). So the coupling force is (19.0 kg/dog) * (4.24 m/s²) = 80.56 N.
