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)

Question

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)

Answer 1

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.

First, let's calculate the total weight of the system. The weight is given by the formula:

Weight = mass * acceleration due to gravity

For the tractor:
Weight of tractor = mass of tractor * acceleration due to gravity
= 1330 kg * 9.8 m/s^2
= 13034 N

For the trailer:
Weight of trailer = mass of trailer * acceleration due to gravity
= 530 kg * 9.8 m/s^2
= 5194 N

Next, we need to calculate the component of the weight that acts along the direction of motion (up the hill). This component is given by the formula:

Weight component = Weight * sin(angle of the hill)

For the tractor:
Weight component of tractor = Weight of tractor * sin(angle of the hill)
= 13034 N * sin(7°)
= 1527 N

For the trailer:
Weight component of trailer = Weight of trailer * sin(angle of the hill)
= 5194 N * sin(7°)
= 606 N

Now, let's consider the forces acting along the direction of motion. We have the force in the coupling between the tractor and trailer, and the force of friction acting on the system.

The force of friction opposes the motion and is given by the formula:

Force of friction = mass * acceleration

For the system (tractor + trailer):
Force of friction = (mass of tractor + mass of trailer) * acceleration
= (1330 kg + 530 kg) * (-0.2 m/s^2)
= -372 N

Since the system is slowing down, the force of friction will be in the opposite direction of motion.

Now, we can calculate the magnitude of the force in the coupling between the tractor and trailer by applying Newton's second law:

Force in the coupling - Force of friction = mass * acceleration

For the system (tractor + trailer):
Force in the coupling - (-372 N) = (mass of tractor + mass of trailer) * (-0.2 m/s^2)
Force in the coupling + 372 N = (1330 kg + 530 kg) * (-0.2 m/s^2)
Force in the coupling = (1860 kg) * (-0.2 m/s^2) - 372 N
Force in the coupling = -372 N

Therefore, the magnitude of the force in the coupling between the tractor and trailer is 372 N.