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Answer :
Final answer:
To calculate the magnitude of the acceleration of the sled pulled by eight dogs, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The magnitude of the acceleration starting from rest is 5.087 m/s². Once the sled starts to move, the magnitude of the acceleration can be calculated using the coefficient of kinetic friction.
The magnitude of the force in the coupling between the dogs and the sled is 185 N.
Explanation:
To calculate the magnitude of the acceleration of the sled pulled by eight dogs, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the net force is the sum of the forces exerted by the dogs and the force of friction.
The force of friction can be calculated using the coefficient of friction between the sled and the snow, and the normal force, which is equal to the weight of the sled and rider.
(a) To find the magnitude of the acceleration starting from rest, we need to find the net force first. The net force is equal to the sum of the forces exerted by the dogs minus the force of friction.
The force exerted by each dog is 185 N, and there are eight dogs, so the total force exerted by the dogs is 185 N x 8 = 1480 N. The force of friction can be calculated using the coefficient of friction (μ) and the normal force (which is equal to the weight of the sled and rider).
The weight of the sled and rider is the total mass multiplied by the acceleration due to gravity, so the weight is 210 kg x 9.8 m/s² = 2058 N.
The force of friction is then the coefficient of friction multiplied by the normal force, so the force of friction is 0.2 x 2058 N = 411.6 N. Therefore, the net force is 1480 N - 411.6 N = 1068.4 N. Using Newton's second law, we can now calculate the acceleration: acceleration = net force / mass of the sled and rider. So, acceleration = 1068.4 N / 210 kg = 5.087 m/s².
(b) Once the sled starts to move, the force of friction becomes the kinetic friction force, which can be calculated using the coefficient of kinetic friction.
The coefficient of kinetic friction is generally smaller than the coefficient of static friction. So, using the same formula for the net force and Newton's second law, we can calculate the magnitude of the acceleration once the sled starts to move.
(c) The magnitude of the force in the coupling between the dogs and the sled is the same as the force exerted by the dogs, which is 185 N.
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