Will cars with different mass make a loop in a tunnel with same given velocity?

In summary, the conversation centered around the possibility of a car, specifically a Ford F-150, being able to make a complete loop in a tunnel with the same velocity and no acceleration once entering the loop. The argument was based on the conservation of energy and whether the centripetal force would be enough to overcome the increased mass of the car. The conclusion was that while the centripetal force would be greater, the mass of the car also increases in the same way, making it possible for the Ford F-150 to make the loop like the lighter Mercedes.
  • #1
chad_syracuse
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me and my colleague watched Mercedes Benz commercial where its sports car accelerated, went in a tunnel, and made a complete loop around the tunnel by going up against the wall. Now, the debate was on whether a car can manage to make a loop in a same tunnel with same given velocity entering the loop, no acceleration once the car enters the loop, and manage to make a loop with heavier car (say, Ford F-150).
With conservation of energy, it has same mass, gravity, and velocity, it must reach same height. But I think once the car hits 1/4 of the loop, centripetal force pulling down the car is greater so with same velocity Mercedes can make the loop, Ford F-150 may not.
What do you guys think?
 
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  • #2
"centripetal force pulling down the car"? That does not make sense.
Anyway, centripetal force will be larger, but so will the mass that resists velocity changes. All forces scale in the same way.

Imagine a heavier car as two lighter cars directly behind each other. Or even a single car as composed of many different parts. Why should this behave differently?
 

1. What is the relationship between the mass of a car and its ability to make a loop in a tunnel?

The mass of a car has a significant impact on its ability to make a loop in a tunnel. Generally, the higher the mass of the car, the more difficult it will be to make the loop. This is because the car's mass affects its inertia, making it more difficult for the car to change its direction and complete the loop.

2. Can a car with a lower mass make a loop in a tunnel with the same given velocity as a car with a higher mass?

Yes, it is possible for a car with a lower mass to make a loop in a tunnel with the same given velocity as a car with a higher mass. However, the car with the lower mass will need to have a significantly higher velocity in order to successfully complete the loop, as it will need to overcome its lower inertia.

3. How does the speed of the car affect its ability to make a loop in a tunnel?

The speed of the car is a crucial factor in determining whether or not it can make a loop in a tunnel. The higher the speed, the more momentum the car has, making it easier to overcome its inertia and complete the loop. However, if the speed is too high, it can also cause the car to lose control and potentially crash.

4. Is there an optimal mass for a car to make a loop in a tunnel?

There is no specific optimal mass for a car to make a loop in a tunnel, as it depends on various factors such as the shape and size of the tunnel, the velocity of the car, and the skills of the driver. Generally, a car with a lower mass will have an easier time completing the loop, but may also require a higher velocity.

5. What other factors besides mass and velocity can affect a car's ability to make a loop in a tunnel?

Aside from mass and velocity, other factors that can affect a car's ability to make a loop in a tunnel include the shape and size of the tunnel, the angle of the loop, and the type of car (e.g. sports car vs. SUV). The skills and experience of the driver can also play a significant role in successfully completing a loop in a tunnel.

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