Name: gravity and work on sloped motion
Uploaded: 2023-05-16T08:18:40.000Z
Duration: 1 min 11 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

Energy

PS.PSc.7.3

Work Done Over an Inclined Plane

ゲレンデを滑り降りる人を考えてみてください。スキー板の摩擦による力が氷上で無視できると仮定すると、フリーボディ図を描くことができます。
変位に沿った重力の成分は、人を前方に動かします。変位に垂直な力は動きに関係がないため、行われる作業には寄与しません。
したがって、行われる作業は、単に平行な力成分に変位を掛けたものです。
これを解決する別の方法は、そのコンポーネントの代わりに力ベクトルを取得することです。 
ここでは、力と変位の間の角度が考慮されます。完了した作業の最終的な式は同じであることに注意してください。
ただし、スキーヤーの変位が力の反対方向にあり、静止時に開始および終了する場合、行われる作業は負になります。
傾斜面の角度がゼロの場合、力は変位に対して垂直であるため、人にかかる重力によって行われる仕事はゼロになります。

<ol>
	<li>Halliday, Resnick and Walker (2014), Fundamentals of Physics, 10th Edition, Wiley and Sons Inc.: section 7.3; pages 156–157.</li>
</ol>

傾斜面での作業

重心フレームワークは、剛体上で行われる作業を簡単に記述するのに役立ちます。 剛体の内力は仕事をしないので無視でき、外部力は仕事エネルギー定理で考慮できます。

剛体を動かすために重力によって行われる仕事、または重力に逆らって剛体を動かすために反対の力によって行われる仕事は、重心フレームワークを使用して計算できます。 これは、経路上の重力の線積分であり、重力が運動エネルギーを増加させる場合は正、重力を持ち上げるために重力に逆らって仕事が行われ、運動エネルギーが減少する場合は負と見なされます。 水平運動の場合、重力による仕事または重力に逆らう仕事はゼロです。 つまり、物体の運動エネルギーの変化は、たとえゼロでなくても、純粋に他の力によるものです。

この定式化は、物体が傾斜面上を移動する場合にも同様に成り立ちます。 唯一の違いは、重力の成分のみが平面に沿っており、行われた仕事を計算する際にこの成分のみを考慮する必要があることです。 平面に垂直な重力は、変位中のどの時点でも作用しません。

重心フレームワークは、剛体に対して行われる作業を簡単に説明するのに役立ちます。剛体の内力は機能しないため、それらは...

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Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Work and Kinetic Energy

仕事と運動エネルギー

KEY TERMS AND CONCEPTS

主要用語と概念

gravity and work on sloped motion

Gravity and work on sloped motion can be described with the center-of-mass framework. For a rigid body, internal forces do no work, so they can be ignored. The work-energy theorem then uses only the external forces.

The work done by gravity depends on the path of the body’s center of mass. If gravity helps increase kinetic energy, the work is positive. If an object is lifted against gravity, the work is negative because kinetic energy decreases.

For horizontal motion, the work done by or against gravity is zero. In that case, any change in kinetic energy comes from other forces. The same idea applies to motion over an inclined plane.

On a slope, only the component of gravity parallel to the plane contributes to work. The force perpendicular to the plane does no work during the motion. That is the key difference from horizontal motion and other straight paths.

Gravity and Work on Sloped Motion

work

Work in Physics: Force and Motion

Work in physics connects force, motion, and energy transfer. Work is done when a force acts on an object and that object moves from one position to another. If there is no displacement, no work is done, even if a force is present. The amount of work depends on the force and the direction of motion. For a very small displacement, the work done is written as the dot product of force and displacement vectors. That means work depends on the size of the vectors and the angle between them. You can...

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Work in physics depends on the direction of a force and the way an object moves. Work is done when energy is transferred to an object. It happens when a force acts on a body that moves from one position to another. The work done by a force is defined as the integral of the force with respect to displacement along the path. Forces can change with position, and an object can move along different paths between the same two points. In vector form, the size of a force times the cosine of the angle...

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Potential Energy Examples in Everyday Physics

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Kinetic energy depends on an object’s mass and speed. A heavier object moving at the same speed has more kinetic energy than a lighter one. An object moving faster also has more kinetic energy when the mass stays the same. The transcript also describes several forms of kinetic energy. Mechanical energy is linked to the motion of an object. A bullet fired from a gun and water flowing down a dam are examples of mechanical energy. Electrical energy comes from the flow of electric charges.

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Motion Energy in Collisions

Kinetic energy is the energy of motion. It depends on how fast an object moves, not on the direction of its velocity. In classical mechanics, this idea helps explain how moving bodies affect other bodies during collisions. A classic example is a perfectly elastic, head-on collision between two identical bodies, with one body initially at rest. After the collision, the first body stops, and the second body moves away with the first body's original velocity. This same pattern can be seen in...

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Kinetic Energy, Momentum, and Reference Frames

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Work Done and Kinetic Energy

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Variable Force Work via Graphs and Energy

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work-energy theorem for motion along a curve

work-energy-theorem-for-motion-along-a-curve

Work-Energy Along Curved Paths

The work-energy theorem can be applied to motion along a curved path. A curved path can be treated as many tiny straight paths added together. On each small part, the force can be taken as constant, so the work-energy theorem can be used there. The total result comes from adding the work done along all of those small path segments. The net work is found with an integral, which adds the work from each infinitesimal path. The total change in kinetic energy is the sum of the changes along the way.

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work done over an inclined plane

Gravity and work on sloped motion can be described with the center-of-mass framework. For a rigid body, internal forces do no work, so they can be ignored. The work-energy theorem then uses only the external forces. The work done by gravity depends on the path of the body’s center of mass. If gravity helps increase kinetic energy, the work is positive. If an object is lifted against gravity, the work is negative because kinetic energy decreases. For horizontal motion, the work done by or...

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Calculating Work from Multiple Forces

Calculating work from multiple forces can be done in two ways, and both methods give the same result. One method finds the work done by each force first. The other method finds the net force by adding the force vectors first.

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work done by gravity

Gravity and Positive vs Negative Work

Gravity is one of the four fundamental forces in nature. On Earth, the force between an object and Earth is called gravity. Gravity does work on an object when it moves the object toward Earth’s center. In that case, the work done by gravity is positive. When an external force lifts an object away from Earth’s center, that force works against gravity. The net work done in this case is negative. If an object moves along the Earth with no change in distance toward or away from Earth’s center,...

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power

Power in Work and Motion

Power connects work with the time needed to do it. Work depends on force and displacement. The work-energy theorem also links net work on an object to the change in its kinetic energy between two points on its path. These ideas do not include time directly, but time still matters in many real situations. A sprinter is a clear example. Two runners may reach the same finish speed, so they do the same amount of work. The winner is the one who reaches that speed in less time. Power describes this...

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Power as the Rate of Doing Work

Power describes how fast work is done. In physics, two sprinters can cross the finish line with the same velocity and do the same amount of work, but the one who finishes first has greater power because the work takes less time. Average power is the work done during a time interval divided by that time interval. When the time interval becomes very small, this becomes instantaneous power. That gives the power at a specific moment instead of over a longer stretch of time. Power can also be...

key terms and concepts

Learn how gravity does work on a rigid body moving over an inclined plane, why only the parallel force matters, and when gravity does no work.

Gravity and Work on Sloped Motion | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

PS.Phy.6.2

ohios-learning-standards-and-model-curriculum

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Tennessee Academic Standards

High School

motion-and-stability-forces-and-interactions

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PHYS.PS3.6

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PS.PSc.7.2

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Work is done when energy is transferred from one object to another. In other words, work is when a force acts on something that undergoes a displacement ...

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The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be ...

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PS.PSc.7.4

Analyze energy transfers and transformations within a mechanical system.

Gravity and Work on Sloped Motion

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