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.
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].
To determine the tension in the rope, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
First, let's calculate the net force acting on the sled.
Net force = (mass of the sled) × (acceleration of the sled)
= (72 kg) × (2.0 m/s^2)
= 144 N [forward]
Next, let's consider the forces acting on the sled. The forces are the force of friction and the tension in the rope.
Net force = Tension - Friction
Rearranging the equation, we can solve for tension:
Tension = Net force + Friction
Tension = 144 N [forward] + 120 N [backwards]
= 24 N [forward]
Therefore, the tension in the rope is 24 N [forward].
To determine the tension in the rope, we need to calculate the net force acting on the sled. We can do this by applying Newton's second law:
Net force = mass × acceleration
1. Calculate the net force:
Net force = (mass of the sled + mass of the snowmobile) × acceleration
= (72 kg + 450 kg) × 2.0 m/s^2
= 522 kg × 2.0 m/s^2
= 1044 N
2. Determine the total resistance force:
Total resistance force = Force of friction + Drag force
= 120 N + 540 N
= 660 N [backwards]
3. Calculate the tension in the rope:
Tension in the rope = Net force - Total resistance force
= 1044 N - 660 N
= 384 N
So, the tension in the rope is 384 N.