A 72 kg sled is pulled forward from rest by a snowmobile
and accelerates at 2.0 m/s2
[forward] for 5.0 s. The force of
friction acting on the sled is 120 N [backwards]. The total
mass of the snowmobile and driver is 450 kg. The drag
force acting on the snowmobile is 540 N [backwards]. T/I
(a) Determine the tension in the rope.
(b) Calculate the force exerted by the snowmobile that
pushes the sled forward.
(a) To determine the tension in the rope, we first need to find the net force acting on the sled. The net force (F_net) can be calculated using Newton's second law:
F_net = m * a
where m is the mass of the sled (72 kg) and a is the acceleration (2 m/s^2).
F_net = 72 kg * 2 m/s² = 144 N [forward]
Since the force of friction is acting backwards (120 N), we need to subtract this force from the net force:
F_net = 144 N - 120 N = 24 N
Now we know that the tension in the rope is 24 N.
(b) To calculate the force exerted by the snowmobile that pushes the sled forward, we need to consider the net force acting on the whole system:
F_total = m_total * a
where m_total is the total mass of the snowmobile and driver (450 kg) and a is the acceleration (2 m/s²).
F_total = 450 kg * 2 m/s² = 900 N [forward]
We also need to consider the drag force acting on the snowmobile, which is 540 N [backward] and the tension in the rope, which is 24 N [forward]. Therefore, the force exerted by the snowmobile (F_snowmobile) can be calculated as:
F_snowmobile = F_total - (drag force + tension in the rope)
F_snowmobile = 900 N - (540 N + 24 N)
F_snowmobile = 900 N - 564 N
F_snowmobile = 336 N [forward]
The force exerted by the snowmobile that pushes the sled forward is 336 N.