Lazydog and his tractor (1330 kg) are pulling a trailer (530 kg) up a 7° hill. The trailer wheels roll freely. What is the magnitude of the force in the coupling between the tractor and trailer when their velocity is 8.7 m/s up the hill and they are slowing down at a rate of 0.2 m/s2? (N)
The mass of the tractor is irrelevant.
The mass of the trailer, m = 530kg
The inclination, θ = 7°
The net downward force is due to gravity, equal to
F1=mg sin(θ)
The coupling pulls the trailer with a force (tension) of T such that the net force is downwards equal to
F1-T=m(0.2)
Substituting F1, and solving for T
T=F1-m(0.2)
=mg sin(θ)- m(0.2)
thanks a lot
To find the magnitude of the force in the coupling between the tractor and trailer, we need to consider the forces acting on the system.
The key forces involved in this scenario are the force of gravity, the force of friction, and the force in the coupling.
1. Force of gravity (downhill force):
The force of gravity acting on the system is equal to the weight of the tractor and trailer. The weight is given by the formula:
Weight = mass * gravity
For the tractor:
Weight of tractor = mass of tractor * gravity
For the trailer:
Weight of trailer = mass of trailer * gravity
2. Force of friction (uphill force):
The force of friction acts in the opposite direction of motion and is given by the formula:
Force of friction = mass * acceleration
In this case, the acceleration is the rate at which the system is slowing down, which is given as -0.2 m/s^2 (negative because it is slowing down).
Now, let's calculate the forces:
1. Weight of tractor:
Weight of tractor = mass of tractor * gravity
= 1330 kg * 9.8 m/s^2 (acceleration due to gravity)
= 13034 N
2. Weight of trailer:
Weight of trailer = mass of trailer * gravity
= 530 kg * 9.8 m/s^2
= 5194 N
3. Force of friction:
Force of friction = (mass of tractor + mass of trailer) * acceleration
= (1330 kg + 530 kg) * (-0.2 m/s^2)
= -372 N (negative because it acts in the opposite direction of motion)
Now, let's consider the forces in the vertical direction (perpendicular to the hill). Since the trailer wheels roll freely, there is no force in the coupling acting vertically.
Finally, the magnitude of the force in the coupling between the tractor and trailer can be calculated using Newton's second law:
Force in coupling = Net force = (weight of tractor + weight of trailer + force of friction)
Force in coupling = (13034 N + 5194 N - 372 N)
Therefore, the magnitude of the force in the coupling between the tractor and trailer is 18556 N.