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 analyze the forces acting on the sled.
The forces acting on the sled are:
1. The force applied by the snowmobile, which is the tension in the rope (T), acting forward.
2. The force of friction (F_friction), which is 120N and acts backwards.
3. The force of drag (F_drag), which is 540N and acts backwards.
4. The force of gravity (F_gravity), which is the weight of the sled and acts downwards.
The force of gravity can be calculated using the formula:
F_gravity = mass_sled * acceleration_due_to_gravity
Let's calculate it:
F_gravity = 72kg * 9.8m/s^2
F_gravity = 705.6N
Now, let's write down the equations of motion for the sled:
ΣF = mass_sled * acceleration
Considering the direction of forces, we have:
ΣF = T - F_friction - F_drag - F_gravity
Plugging in the given values, we can solve for T:
T - 120N - 540N - 705.6N = 72kg * 2.0m/s^2
T - 1365.6N = 144N
T = 144N + 1365.6N
T = 1509.6N
Therefore, the tension in the rope is 1509.6N.