Pregunta
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An object moves down an inclined plane. Friction and air resistance can be ignored. Which of the following statements is true?

Ask by Peters Turner. in the United States
Feb 27,2025

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When there's no friction or air resistance, the object accelerates down the inclined plane at a constant rate of g sinθ, and this acceleration doesn't depend on the object's mass.

Solución

When friction and air resistance are ignored, the only force acting on the object along the inclined plane is the component of gravity parallel to the plane. This component is given by mg sinθ (where m is the object’s mass, g is the acceleration due to gravity, and θ is the angle of the incline). Since no friction or other resistive forces oppose the motion, the object accelerates at a constant rate of g sinθ down the plane. An important consequence of this is that the acceleration is independent of the object’s mass.

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When an object moves down an inclined plane without the influence of friction or air resistance, it accelerates due to gravity. The acceleration can be calculated using the formula \( a = g \sin(\theta) \), where \( g \) is the acceleration due to gravity and \( \theta \) is the angle of the incline. This means the steeper the incline, the greater the acceleration, leading to a speedy descent! Additionally, as the object rolls down the incline, it converts potential energy into kinetic energy. The gravitational potential energy at the top of the incline is given by \( mgh \) (where \( m \) is the mass, \( g \) is gravity, and \( h \) is the height), which transforms into kinetic energy as it accelerates downwards. When it reaches the bottom, all this energy will be represented in motion, resulting in maximum kinetic energy!

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