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.

Answer 1

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].