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Kinematics of Particles
Published in M Rashad Islam, A K M Monayem H Mazumder, Mahbub Ahmed, Engineering Dynamics, 2022
M Rashad Islam, A K M Monayem H Mazumder, Mahbub Ahmed
So far, we have looked at straight-line motion (horizontal or vertical). Now, in this section, a non-straight-line motion is discussed. If a particle is thrown upward with some angle with respect to the horizon, then the particle's travel path is called the projectile motion. In a Projectile motion an object or a particle (a projectile) is thrown that moves along a curved path under the influence of gravity only (in particular, the effects of air resistance are assumed to be negligible). The curved path can be shown to be a parabola. The only force of significance that acts on the object is gravity, which always acts downward, thus imparting to the object a downward acceleration. Two points to remember:In the horizontal direction, there are no external forces. Therefore, there is no horizontal acceleration. Also, the velocity in the horizontal direction is constant.In the vertical direction, the only force acting on the projectile is gravity.
Uniform acceleration and projectile motion
Published in Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler, Instant Notes in Sport and Exercise Biomechanics, 2019
In the examples above, the body in question was moving in the same direction (e.g. the horizontal motion of a car during the start of a race) or along the same line (e.g. the vertical motion of the COM during a SVJ). However, in many situations (e.g. the flight of a soccer ball or javelin) the body has both a horizontal and a vertical component of velocity at the point of release or take-off, and thus moves horizontally and vertically in flight. The movement of a body or object that is unsupported (i.e. in flight) and only affected by the forces associated with gravity and air resistance is known as projectile motion. If air resistance is ignored, as it often is for bodies of relatively large mass travelling at low speeds, the flight path or trajectory of a projectile follows that of a parabola, which is symmetrical about its highest point. The greater the vertical in relation to the horizontal component of velocity that the projectile has at release or take-off, then the more peaked its trajectory will be (Figure A6.3).
Internal reinforcement mechanisms for gelatin bird projectiles for artificial bird impact tests
Published in Mechanics of Advanced Materials and Structures, 2023
Gang Luo, Fengqi Zhang, Ziming Xu, Haiyang Zhang, Lulu Liu, Wei Chen
The values of V0, V, Lf, Pcz, Sf and M are known from the air-gun parameters and test data, and a0 can be calculated from the relationship between air-chamber pressure and projectile mass. Therefore, the unknown projectile motion time t, acceleration rate of change R, and projectile end acceleration at can be solved for by Eq. (8), and the relationship between projectile speed and motion time can be obtained to provide a basis for the simulation control curve. By solving Eq. (8), the relationships between projectile speed and motion time in the barrel under corresponding launch conditions can be obtained as
A fractionally magnetized flow of force fields and Fermi–Walker conformable derivative on the unit sphere
Published in Waves in Random and Complex Media, 2022
Talat Körpinar, Rıdvan Cem Demirkol, Zeliha Körpınar
In traditional projectile motion and ballistics, the equations defining the motion of the particle are given by the well-known formula of Newton's second law. There are many great efforts to correlate fractional calculus and projectile motion or ballistics by using these equations. For example, Ebaid [10] considered the Caputo derivative to approach the ballistics phenomena and compare experimental with theoretical results. Ozarslan et al. [11] chose to consider the special type of the fractional derivative to focus on the projectile motion of the wind-influenced type by preserving the dimension of the physical quantities analytically. Alharbi et al. [12] investigated the physical features of the projectile motion in a resisting medium by applying the conformable derivative. Lazopoulos and Karaoulanis [13] studied fractional derivative and Leibniz derivative to compare the advantages of these new derivatives over traditional fractional derivatives during the projectile motion. Ahmad et al. [14] presented some special solution families of the projectile motion by giving the comparison of the Riemann-Liouville fractional calculus and Caputo fractional calculus. Sayed et al. [15] investigated the projectile motion by modeling its equations in a quadratic resistant medium and uniform gravitational field in view of the fractional differential transform method.
Droplet and particle methods to investigate turbulent particle laden jets
Published in Aerosol Science and Technology, 2021
Eric Thacher, Tvetene Carlson, Jake Castellini, Michael D. Sohn, Evan Variano, Simo A. Mäkiharju
Droplets and particles can also be categorized based on their dynamics, e.g., by their Stokes number or the continuum from ‘aerosol’ to ‘ballistic’ behavior. An aerosol quickly loses its initial momentum, settles slowly through the local flow over minutes (or hours), and is generally a faithful flow tracer. A ballistic particle or droplet maintains its initial momentum long enough to significantly cross streamlines, and thus mostly follows its own trajectory. We can use projectile motion equations to estimate time for a ballistic particle to reach ground where h is the initial height and g the acceleration due to gravity. Thus a ballistic particle starting at a human nose 165 cm high will settle to the floor in sec. Herein we consider particles that are in between the extremes of ballistic and aerosol dynamics. These ‘mid–range’ droplets and particles have diameters 1–100 μm. Their trajectory is a strong function of both their initial momentum and the local flow field.