A 72kg sled is pulled forward from rest by a snowmobile and accelerates at a rate of 2.0m/s2 [forward] for 5.0s. The force of friction acting on the sled is 120N [backwards]. The total mass of the snowmobile and driver is 450kg. The drag force acting on the snowmobile is 540N [backwards]. Determine the tension in the rope.
To determine the tension in the rope, we need to calculate the net force acting on the sled.
1. Calculate the net force on the sled using Newton's second law: F_net = m * a, where F_net is the net force, m is the mass of the sled, and a is the acceleration.
F_net = 72 kg * 2.0 m/s^2
F_net = 144 N [forward]
2. Calculate the net force on the snowmobile using Newton's second law: F_net = m * a, where F_net is the net force, m is the mass of the snowmobile and driver, and a is the acceleration.
F_net = 450 kg * 2.0 m/s^2
F_net = 900 N [forward]
3. Calculate the friction force on the sled: F_friction = -120 N [backwards].
4. Calculate the drag force on the snowmobile: F_drag = -540 N [backwards].
5. The tension in the rope is equal to the net force on the sled, which must balance the friction and drag forces.
Tension = F_net + F_friction + F_drag
Tension = 144 N [forward] - 120 N [backwards] - 540 N [backwards]
Tension = -516 N + 120 N
Tension = -396 N
Therefore, the tension in the rope is 396 N [backwards].