Physics
A key point in the analysis of 2D motion is the separation and independent examination of each dimension. For projectile motion, this involves looking at both the horizontal and vertical components. It's important to remember that only the vertical component is affected by gravity's acceleration. The acceleration due to gravity can be approximated as -10m/s². The angled velocity of projectiles needs to be separated into its horizontal and vertical components, utilizing cosine and sine functions in relation to the angle (theta) at which the projectile was launched.
When dealing with two-dimensional motion, projectile motion focuses on horizontal displacement (x), which equals the velocity of the horizontal component times time (t). The vertical displacement takes into account the initial vertical velocity times time, plus the acceleration times time squared over two. Inclined planes, on the other hand, involve the analysis of parallel and perpendicular force components, both affected by gravity. The parallel force of gravity is calculated as the object's mass times the acceleration of gravity times the sine of theta, while the perpendicular force of gravity is calculated as the object's mass times the acceleration of gravity times the cosine of theta.
Lesson Outline
<ul> <li>Two-dimensional motion analysis</li> <ul> <li>Separating horizontal and vertical components</li> </ul> <li>Projectile motion components</li> <ul> <li>Horizontal component</li> <ul> <li>Using cosine for horizontal displacement</li> </ul> <li>Vertical component</li> <ul> <li>Using sine for vertical displacement</li> </ul> </ul> <li>Projectile motion equations</li> <ul> <li>Horizontal displacement equation: x = vt</li> <li>Vertical displacement equation: x = v0t + (at^2/2)</li> </ul> <li>Inclined planes</li> <ul> <li>Separating force components</li> <ul> <li>Parallel and perpendicular components</li> </ul> <li>Force equations for inclined planes</li> <ul> <li>Parallel force of gravity equation: parallel Fg = mg sin θ</li> <li>Perpendicular force of gravity equation: perpendicular Fg = mg cos θ</li> </ul> </ul> </ul>
Don't stop here!
Get access to 29 more Physics lessons & 8 more full MCAT courses with one subscription!
FAQs
Projectile motion and inclined planes both involve the two-dimensional motion of an object. In projectile motion, an object is launched with an initial velocity and moves through the air due to gravity and the force exerted during launch. Inclined planes describe the motion of an object moving on a slanting surface, experiencing both horizontal and vertical forces. In both cases, the motion can be broken down into its horizontal and vertical components, which can be analyzed separately using the principles of physics.
The horizontal and vertical components of projectile motion are essential in understanding the motion of an object, since they help decompose the two-dimensional motion into simpler one-dimensional problems. The initial velocity of an object can be separated into its horizontal and vertical components. The horizontal component remains constant throughout projectile motion, as there are no external forces affecting it. Conversely, the vertical component is affected by gravity, causing acceleration and a change in velocity over time.
The role of acceleration due to gravity in motion on inclined planes is crucial as it influences the motion of an object sliding or rolling down the slope. When an object moves along an inclined plane, only a component of the gravitational force, specifically the one parallel to the surface, impacts its motion. This component is determined by the angle of the slope and the gravitational constant - as the angle increases, so does the component of gravity acting along the incline. This results in an increased acceleration of the object down the slope. Conversely, the steeper the incline, the smaller the component of gravity acting perpendicular to the surface, meaning less friction to oppose the motion. Thus, understanding the role of acceleration due to gravity is vital for predicting and analyzing motion on inclined planes.
MCAT® is a registered trademark of the Association of American Medical Colleges. The United States Medical Licensing Examination (USMLE®) is a joint program of the Federation of State Medical Boards (FSMB®) and National Board of Medical Examiners (NBME®). NAPLEX® is a registered trademark of the National Association of Boards of Pharmacy. PANCE© is a registered trademark of the National Commission on Certification of Physician Assistants. NCLEX® is a registered trademark and service mark of the National Council of State Boards of Nursing, Inc. None of the trademark holders are endorsed by nor affiliated with Sketchy or this website.
