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I have a design idea and I'm wondering what forces would be at play.

This is the setting: There is an immovable brick wall. I have a car on dynos (dynos are large rollers that allow a car to speed up/slow down while physically being in place and the car is usually strapped down so it can't move). The car has two electric motors and is applying $X$ torque from each motor onto the wheels of $Y$ diameter. While the car is on the dyno, it is touching the brick wall at the front (AKA distance between car and wall is $0$). How much force would the car apply to the brick wall if the rollers were to suddenly stop?

The way that I've gone about thinking about this problem is by taking the torque of the motors $X$ and multiplying by the radius of the wheel $(Y/2)$ to get the force the wheel is applying to the wall. For if we have two electric motors, we double the force.

After the wall takes the instantaneous force as described in the previous paragraph, the wheels would slip and burn out, reducing the continuous force on the wall.

Should I be taking into account the mass of the car? I thought it wasn't relevant because we are not moving any distance. Am I missing something obvious? Thank you in advance.

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  • $\begingroup$ Re, "...large rollers that allow a car to speed up/slow down..." If you're going to pose physics puzzles, you're going to need to be more careful about saying what you really mean. A car on a dynomometer is not (normally) supposed to move at all. The dyno allows the car's wheels to turn while the car remains stationary. Also, but perhaps not relevant to this question, it can provide controlled resistance to the rotation of the wheels, and it measures the torque and speed at the wheel. $\endgroup$
    – Solomon Slow
    Commented Oct 27, 2021 at 17:26
  • $\begingroup$ P.S., Granite cliff faces and ferrocement bridge piers are relatively "immovable." Brick walls actually are pretty flimsy. The mortar between the bricks has much less tensile strength than you might expect. I once watched a driver trying to back a big trailer into a loading dock in a building with a brick facade. Seemed like he just barely bumped the edge of the door opening, and half of the front of the building collapsed. $\endgroup$
    – Solomon Slow
    Commented Oct 27, 2021 at 17:32

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How much force would the car apply to the brick wall if the rollers were to suddenly stop?

Since the car is touching the wall immediately when the dynos released, exactly as much force as the wheels are imparting to the ground at the moment. That's all there is to it.

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  • $\begingroup$ OK sweet. So mass doesn't affect at all correct? Or say a downward force on the car. These wouldn't affect because mass doesn't affect. $\endgroup$
    – Wonjae Jang
    Commented Oct 27, 2021 at 17:42
  • $\begingroup$ @WonjaeJang so long as there is enough downward force to keep the rollers and wheels from slipping during the stop I don't actually see how the force imparted to the ground comes into this. $\endgroup$
    – candied_orange
    Commented Oct 27, 2021 at 17:49
  • $\begingroup$ awesome, yea thats what I was thinking as well. Thank you for verifying. $\endgroup$
    – Wonjae Jang
    Commented Oct 27, 2021 at 18:42
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The immovable brick wall has no momentum.

The strapped down car has no momentum. Apart from it's rotating wheels.

When you stop the rollers the wheels need to stop as well.

Model the car as incompressible and you get the same force you'd get if you spun up the tires to the same RPMs and set them down next to the wall.

Model the car as compressible and the same force gets exerted, just over more time, less whatever is lost to heat generated deforming the car.

Just to keep things in perspective, I doubt even freeway speeds would give the tires enough force to even scratch the bumper.

For an illustration of how little force the wheels impart when they suddenly change rotational speed I offer Knight Rider mounting his 18 wheeler.

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