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A tractor of mass 2000kg pulls a trailer of mass 1500 kg. The total resistance to motion has a constant value of 4000 newtons. One quarter of this resistance acts on this trailer. They are moving right with an average acceleration of 1.0 ms-2. (a) Determine the resistive force acting on the trailer. (b) Calculate the force, F, exerted by the tractor to pull the trailer.

Question

A tractor of mass 2000kg pulls a trailer of mass 1500 kg. The total resistance to motion has a constant value of 4000 newtons. One quarter of this resistance acts on this trailer. They are moving right with an average acceleration of 1.0 ms-2. (a) Determine the resistive force acting on the trailer. (b) Calculate the force, F, exerted by the tractor to pull the trailer.

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Solution

(a) Determine the resistive force acting on the trailer.

The total resistance to motion is given as 4000 N. Since one quarter of this resistance acts on the trailer, we can calculate the resistive force on the trailer by dividing the total resistance by 4.

Resistive force on the trailer = Total resistance / 4 = 4000 N / 4 = 1000 N

So, the resistive force acting on the trailer is 1000 N.

(b) Calculate the force, F, exerted by the tractor to pull the trailer.

The force exerted by the tractor can be calculated using Newton's second law of motion, which states that the force is equal to the mass of an object multiplied by its acceleration.

The total mass being moved by the tractor is the sum of the mass of the tractor and the trailer, which is 2000 kg + 1500 kg = 3500 kg.

The total force required to move this mass with an acceleration of 1.0 ms^-2 is therefore:

F = m * a = 3500 kg * 1.0 ms^-2 = 3500 N

However, there is also a resistive force acting against the motion of the tractor and trailer. The total resistive force is 4000 N, and we have already calculated that 1000 N of this is acting on the trailer. Therefore, the remaining 3000 N is acting on the tractor.

So, the total force exerted by the tractor must overcome both the inertia of the tractor and trailer and the resistive force acting on the tractor. Therefore, the total force exerted by the tractor is:

F_total = F + Resistive force on tractor = 3500 N + 3000 N = 6500 N

So, the force exerted by the tractor to pull the trailer is 6500 N.

This problem has been solved

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