Free fall and harmonic oscillations: Analyzing trampoline jumps

© 2015 IOP Publishing Ltd. Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is obtained in terms of maximum normalized force from the trampoline and the harmonic frequency. A simple expression is obtained for the ratio between air-time and harmonic period, and the maximum g-factor. The results are compared to experimental results, including accelerometer data showing 7g during bounces on a small trampoline in an amusement park play area. Similar results are obtained on a larger garden trampoline, and even larger accelerations have been measured for gymnastic trampolines

Beyond velocity and acceleration: Jerk, snap and higher derivatives

© 2016 IOP Publishing Ltd. The higher derivatives of motion are rarely discussed in the teaching of classical mechanics of rigid bodies; nevertheless, we experience the effect not only of acceleration, but also of jerk and snap. In this paper we will discuss the third and higher order derivatives of displacement with respect to time, using the trampolines and theme park roller coasters to illustrate this concept. We will also discuss the effects on the human body of different types of acceleration, jerk, snap and higher derivatives, and how they can be used in physics education to further enhance the learning and thus the understanding of classical mechanics concepts

Velocity, acceleration, jerk, snap and vibration: Forces in our bodies during a roller coaster ride

© 2020 The Author(s). Published by IOP Publishing Ltd. Changing acceleration and forces are part of the excitement of a roller coaster ride. According to Newton's second law, F = ma, every part of our body must be exposed to a force to accelerate. Since our bodies are not symmetric, the direction of the force matters, and must be accounted for by ride designers. An additional complication is that not all parts of the body accelerate in the same way when the acceleration is changing, i.e. when there is jerk. Softer parts of the body provide varying levels of damping, and different parts of the body have different frequency responses and different resonance frequencies that should be avoided or reduced by the roller coaster designer. This paper discusses the effect of acceleration, jerk, snap and vibration on the experience and safety of roller coaster rides, using authentic data from a dive coaster as an example

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

Studsmattematte - fritt fall och harmonisk svängningsrörelse

Studsmattor finns i många trädgårdar och lekplatser. Under studsandet rör man sig huvudsakligen i vertikalled och under en del av tiden faller man fritt. Här bygger författarna en modell för rörelsen genom att anta proportionalitet mellan kraften från mattan och uttöjningen, vilket leder till harmoniska svängningar för små amplituder

Unexpectedly large charge radii of neutron-rich calcium isotopes

Submitted version. See original publication (doi:10.1038/nphys3645) for final versionInternational audienceDespite being a complex many-body system, the atomic nucleus exhibits simple structures for certain "magic" numbers of protons and neutrons. The calcium chain in particular is both unique and puzzling: evidence of doubly-magic features are known in 40,48Ca, and recently suggested in two radioactive isotopes, 52,54Ca. Although many properties of experimentally known Ca isotopes have been successfully described by nuclear theory, it is still a challenge to predict their charge radii evolution. Here we present the ?rst measurements of the charge radii of 49,51,52Ca, obtained from laser spectroscopy experiments at ISOLDE, CERN. The experimental results are complemented by state-of-the-art theoretical calculations. The large and unexpected increase of the size of the neutron-rich calcium isotopes beyond N = 28 challenges the doubly-magic nature of 52Ca and opens new intriguing questions on the evolution of nuclear sizes away from stability, which are of importance for our understanding of neutron-rich atomic nuclei