In the gaming I'm DMing, the heroes are exploring a trap filled dungeon, and have correctly guessed that there is a giant boulder trap at the end of a certain hallway (based on Rolling Sphere from the DMG, but upgrade because it's a 15-foot sphere instead of a 10-foot). They have an immovable rod, and plan to use it to block the giant boulder.

I'm considering letting it just work because its called an **immovable** rod, and because I like to reward smart play.

The thing is though, that according to the book, the immovable rod actually has a weight limit of 8,000 pounds. I did some quick calculations, and a 15 foot diameter sphere of granite should weigh nearly 300,000 pounds.

That's way more than the rod can hold, but I also figure the stone wouldn't be putting its full weight limit on the rod. I'm pretty sure there's a way to calculate the force of the boulder on the rod, but my physics skills are rusty. (Also intuitively I feel like the current speed should factor into it, not just the acceleration).

Both the rod and the sphere can be thwarted by Strength checks, so I'm thinking about having them make some kind of opposed check against each other or something like that.

I don't just want to do a gotcha on my players. My goals are to have fun encounters and encourage clever gaming. With that in mind what would you do?

From a physics point of view you have two things at play here momentum and force.

First force: The 8000lbs is a force, so we will start with that - it is easy to figure out how much it is holding by multiplying 300,000 by the sin of the grade of the slope ... so some simple math - a 300,000lb bolder will exert 8000lbs of force at rest against a 1.6 degree slope. So if the ground is sloped more than 1.6 degrees the rod can't hold it at rest, if it is less than 1.6 degrees it can hold it.. That is the easy answer, but it does not consider if the boulder has a rolling start.

The force at rest is the only thing you can calculate with straight numbers and weight. If the bolder is rolling there is momentum, specifically it is equal to the speed of the bolder in feet per second times the weight of the bolder (300,000lbs) divided by 32. By one of Newton's laws (second law I think) the force exerted is equal will equal the time-rate change of angular momentum. You nhave to know how fast the boulder is rolling to continue here. You also have to decide, 1. do any peices come flying off the boulder in the collision

**(I could argue the boulder just smashes when it hits the rod, rewarding players for thinkning of it) **2. if the immovable rod snaps, moves or bends when 8000lbs is exceeded. If peices come flying off the boulder when it crashes into the rod but it keeps moving then the remaining weight is what we will deal with.

1. If it snaps it can't stop a rolling boulder.

2. If it moves (slides down the ramp) while continuing to exert 8000lb force on the bolder, you can figure out how far the boulder rolls before stopping as follows: Multiply the weight of the boulder by the sine of the slope. --> W*sin(slope) = F1, F1 is the force needed to support the boulder. Subtract this force from 8000 --> 8000-F1=F2. F2 is the force that will slow down the boulder. If it is negative the bolder can not be stopped and will in fact accelerate. If it is positive the deccelration of the boulder can be calculated as this force times 32 divided by the weight of the boulder --> F2*32/W=d. With the deceleration figured out you can calulate how far the boulder rolls before coming to a stop by squaring the velocity and dividing by twice the deceleration --> S=V*V/(2*d). The answer is the number of feet the boulder rolls before stopping. Note I did this using scalers, not vectors. If you use vectors the signs can change a bit, but the answer should be the same.

3. If it bends you need to figure out the strain performance of the moveable rod and use this to calaculate a moment applied to the boulder, translate this into a force depending on the alingment between the rod and the boulder, integrate this from 0 to 90 degrees of bend to determine if it stops the boulder or just bends down and the boulder rolls over it. There are a lot of numbers you are going to have to make up to do this.