![]() ![]() This might be a tiny bit off due to the discreteness of the simulation, but it should be very close. I searched for the initial angle $\theta(0)$ where the broom and key reach zero on the same simulation step, and found 47.9°. I compared it with a key starting from the corresponding initial height simulated the same way but under constant downward acceleration from gravity. I used a time step of $0.2$ milliseconds, which I think is accurate enough. I doubt that such a second-order differential equation with $cos$ has an analytic solution, so I simulated it numerically. Rather, we need to determine its whole trajectory $\theta(t)$ to find when it reaches zero. The broom will accelerate faster during the smaller angles it passes through on its journey, so it will arrive first. But, this isn't the angle that makes them reach the ground at $h=0$ at the same time. ![]() ![]() I got these plots and estimated the cutoff angle 47.9° by numerically solving the following differential equation in the angle $\theta$, where $\ddot$. If it had started lower, it would win, and if it started higher, it would lose. Note that the broom falls slower at first but catches up at the end to tie. The puzzle doesn't specify the properties of the broom, but I think these are a reasonable interpretation for a physical model.īelow are plots of the height, velocity, and acceleration of the top end of the broom and the key for when the broom starts at 47.9°. This assumes that the end of the broom on the ground doesn't slide, making it act like a hinge, and also that the broom handle is a uniform rod. Choose from our large selection of mop and brush heads that are suitable for use with our range of handles.If the broom's angle to the ground is less than 47.9°, it will hit the ground first. These handles deliver a more robust alternative.Īlways ensure that the handle you use is compatible with and will fit the types of mop or brush head you have. Screw broom handles are fitted with a thread that allows you to screw the handle into the already threaded head of a mop or broom.They offer an easy-to-fit, low cost attachment. Plain broom handles are designed to fit into mop and broom heads that already have a pre-drilled hole for the handle to slot into - simply push the handle into the hole for a secure fit.What types of broom and mop handles are available? For easy storage and additional site safety, we also offer a range of wall brackets keep your brooms and mops tidy, safe and secure. Our range includes products from leading brands such as Vikan, Rubbermaid and RS PRO.Įxtendable telescopic handles give versatility for cleaning in a variety of environments, with adjustable handle lengths enabling you to reach the required height for ceilings and walls or the required reach to clean underneath or between pieces of non-moveable equipment.We provide a choice of materials, lengths, widths and colours, with options also catering for whether you need a standard handle or a more ergonomic design with added grip. We also stock a range of broom and mop heads to fit the handles allowing you to mix and match as required, with several fixings methods available, including: standard, screw-on and squeeze-locking. No matter what industry you work in, RS can meet your needs for cleaning and maintenance with our extensive range of mop and broom handles. ![]()
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