In a tug-of-war, a jeep of mass 1200 kg and a tractor of mass 2200 kg pull on a horizontal rope in opposite directions. At one instant, the tractor pulls on the rope with a force of 1.40×104 N while its wheels push horizontally against the ground with a force of 1.50×104 N. Calculate the instantaneous accelerations of the tractor and of the jeep. Assume the rope does not stretch or break.

Question

In a tug-of-war, a jeep of mass 1200 kg and a tractor of mass 2200 kg pull on a horizontal rope in opposite directions. At one instant, the tractor pulls on the rope with a force of 1.40×104 N while its wheels push horizontally against the ground with a force of 1.50×104 N. Calculate the instantaneous accelerations of the tractor and of the jeep. Assume the rope does not stretch or break.

Answer 1

To calculate the instantaneous accelerations of the tractor and the jeep, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Let's start with the tractor:

1. Calculate the net force acting on the tractor:
The net force is the difference between the force exerted by the tractor on the rope and the force exerted by the wheels on the ground. In this case, we have:
Net force on tractor = Force exerted by tractor on the rope - Force exerted by wheels on the ground
Net force on tractor = 1.40×10^4 N - 1.50×10^4 N
Net force on tractor = -1.00×10^3 N

Note that the negative sign indicates that the net force is in the opposite direction.

2. Calculate the acceleration of the tractor:
Using Newton's second law, we can write:
Net force on tractor = mass of tractor × acceleration of tractor
-1.00×10^3 N = 2200 kg × acceleration of tractor

Rearranging the equation, we find:
Acceleration of tractor = -1.00×10^3 N / 2200 kg
Acceleration of tractor ≈ -0.454 m/s²

Now, let's calculate the acceleration of the jeep:

Since the jeep is being pulled in the opposite direction, the net force acting on it will be the same magnitude as the force exerted by the tractor on the rope (1.40×10^4 N), but in the opposite direction.

3. Calculate the acceleration of the jeep:
Using Newton's second law again, we have:
Net force on jeep = mass of jeep × acceleration of jeep
1.40×10^4 N = 1200 kg × acceleration of jeep

Rearranging the equation, we find:
Acceleration of jeep = 1.40×10^4 N / 1200 kg
Acceleration of jeep ≈ 11.67 m/s²

So, the instantaneous acceleration of the tractor is approximately -0.454 m/s² and the instantaneous acceleration of the jeep is approximately 11.67 m/s².