A 72kg sled is pulled forward from rest by a sn owmobile and accelerates at a rate of 2.0m/ s 2 [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.

Question

GPT 3.5 · Answer

To determine the tension in the rope, we need to find the net force acting on the sled.

First, we calculate the net force using Newton's second law: F_net = m * a.
F_net = (72 kg) * (2.0 m/s^2) = 144 N [forward]

Next, we calculate the force required to overcome friction: F_friction = 120 N [backwards]

Then, we calculate the force required to overcome drag: F_drag = 540 N [backwards]

The net force is the vector sum of all the forces:
F_net = F_tension - F_friction - F_drag

Rearranging the equation, we find:
F_tension = F_net + F_friction + F_drag = 144 N [forward] + 120 N [backwards] + 540 N [backwards]
F_tension = 144 N - 120 N - 540 N = -516 N [forward]

The tension in the rope is 516 N [forward].