Calculating Tractor Movement & Force: Winter Ditch Rescue

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In summary, a tractor gets stuck in a ditch and the operator attempts to move it by attaching a 10m long chain to a nearby tree and jumping on it. The chain is stretched 1m above the ground and the man weighs 100kg. The angle of the bent chain is 78.7 degrees and the man's weight is 980N. To calculate how far the tractor moves, some geometry and trigonometry is needed. The force on the tractor can be obtained by using Newton's first law at the joint where the man and chain meet on the ground.
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pippintook
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One cold winter day, a tractor gets stuck in a ditch. The operator hooks a tow chain to a nearby tree and attempts to move the tractor by jumping up and down on the chain. If the chain is 10 meters long and is stretched level one meter above the ground, and the tree is stationary, how far does the tractor move when the chain is pressed to the ground? Assume the main is in the middle of the chain. If the man has a mass of 100 kg, what is the force on the tractor when the chain just touches the ground?

I figured that the angle of the bent chain was 78.7 degrees (using tan-1(1/5) and then subtracting that by 90). The weight of the man is 980 N. I'm just not sure how to calculate how far the tractor moves, or the force on the tractor when the chain touches the ground (unless it's just the man's weight, which I doubt). Help please?
 
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  • #2
The original chain length is 10m. Assumig it is fairly rigid, when then it moves down a meter at centreline, it's still 10 m long, but the horizontal distance betwen the truck an tree is now less tham 10m. It requires just a little geometry and trig to get the truck movement. The tractor force can be obtaine by applying Newton 1 at the joint where man and chain meet in the new position at the ground.
 
  • #3


I would approach this problem by first identifying the relevant equations and variables involved. In this scenario, we are dealing with the force exerted by the man on the chain, the distance that the tractor will move, and the force exerted by the chain on the tractor.

To calculate the distance that the tractor will move, we can use the equation for work, which is W = Fd, where W is work, F is force, and d is distance. In this case, the work done by the man on the chain will be equal to the work done by the chain on the tractor. We can also assume that the chain is inelastic, meaning that it does not stretch or compress.

Next, we need to find the force exerted by the chain on the tractor. This can be calculated using the equation F = ma, where F is force, m is mass, and a is acceleration. In this scenario, the acceleration of the tractor will be equal to the acceleration of the man, which is caused by his jumping on the chain. We can also assume that the tractor is initially at rest and that there is no friction between the tractor and the ground.

Using the given information, we can calculate the force exerted by the man on the chain as follows:
F = ma = (100 kg)(9.8 m/s^2) = 980 N

Now, to calculate the distance that the tractor will move, we can rearrange the work equation to solve for d:
d = W/F = (980 N)(10 m) = 9800 J

Therefore, the tractor will move 9800 Joules when the chain is pressed to the ground.

To calculate the force exerted by the chain on the tractor, we can use the same equation for work, but this time solve for F:
F = W/d = (9800 J)/(10 m) = 980 N

This means that the force exerted by the chain on the tractor is also 980 N, which is equal to the force exerted by the man on the chain.

In conclusion, the tractor will move 9800 Joules and experience a force of 980 Newtons when the chain is pressed to the ground. It is important to note that this calculation assumes ideal conditions and does not account for any other external factors that may affect the movement of the tractor, such as friction or the weight of the tractor itself.
 

1. How did the tractor get stuck in the ditch?

The tractor likely got stuck in the ditch due to either operator error or unfavorable terrain conditions. It's possible that the driver made a wrong turn or misjudged the depth of the ditch, causing the tractor to get stuck. Alternatively, the ground may have been too soft or muddy, making it difficult for the tractor's tires to gain traction and navigate through the ditch.

2. What steps can be taken to safely remove the tractor from the ditch?

The first step is to assess the situation and determine the best course of action. If the tractor is in a dangerous or unstable position, it's important to secure the area and call for professional assistance. In less serious cases, the tractor may be able to be towed out using another vehicle or by attaching a winch to a sturdy anchor point. It's important to proceed slowly and carefully to avoid causing further damage to the tractor or the surrounding area.

3. How long does it typically take to remove a tractor stuck in a ditch?

The time it takes to remove a tractor from a ditch can vary depending on the circumstances. In some cases, it may only take a few minutes to tow the tractor out, while in other cases it may take several hours. Factors such as the size and weight of the tractor, the severity of the stuck position, and the availability of equipment and assistance can all affect the time it takes to remove the tractor.

4. What are some common causes of tractors getting stuck in ditches?

Aside from operator error and unfavorable terrain conditions, other common causes of tractors getting stuck in ditches include mechanical failure, poor visibility, and inexperience or lack of training. It's important for tractor operators to regularly maintain their equipment and be aware of their surroundings to prevent getting stuck in a ditch.

5. Can getting a tractor stuck in a ditch cause damage to the equipment?

Yes, getting a tractor stuck in a ditch can cause damage to the equipment. The weight and force of the tractor can put strain on its parts and components, potentially causing them to break or malfunction. Additionally, the process of trying to remove the tractor from the ditch may also cause damage. It's important to carefully assess the situation and proceed with caution to minimize potential damage to the equipment.

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