Final answer:
The acceleration of the sled being pulled by reindeer on snow is calculated as about 1.42 m/s². This is found by subtracting the force of friction from the applied force and then dividing by the total mass of the sled and elves (180 kg).
Step-by-step explanation:
The student's question is about calculating the acceleration of a sled being pulled by reindeer on snow when given the mass of the sled, the mass of the passengers, the coefficient of friction, and the force applied by the reindeer. To solve this problem, one must calculate the total mass of the system, which includes the sled and the elves, and then use the formula for Newton's second law of motion (F = ma), accounting for the force of friction.
First, calculate the total mass of the system:
- Mass of the sled = 150 kg
- Mass of six elves = 6 × 5.0 kg = 30 kg
- Total mass (m) = 150 kg + 30 kg = 180 kg
Next, calculate the force of friction (ffriction) using the coefficient of friction (μ) and the normal force (N), which equals the gravitational force (mg) on a horizontal surface:
- ffriction = μ × N = μ × m × g
- ffriction = 0.11 × 180 kg × 9.8 m/s² ≈ 194.04 N
To find the acceleration (a), subtract the force of friction from the pulling force (Fpull) applied by the reindeer, and then divide by the total mass:
- Fnet = Fpull - ffriction = 450 N - 194.04 N = 255.96 N
- a = Fnet / m = 255.96 N / 180 kg ≈ 1.42 m/s²