Why does mass not affect sliding speed down an inclined plane?

  • #1
MeesaWorldWide
7
1
Homework Statement
Two kids of different masses are having a toboggan race down a frictionless hill. Which kid reaches the bottom first: the one with less mass or the one with more?
Relevant Equations
F = ma
I think that both kids experience the same acceleration (irrespective of mass) since the only force pushing them downwards is acceleration due to gravity, which is the same for both of them. Thus, since they start sliding down the hill at the same time (assumption), and are accelerating at the exact same rate, they should both reach the bottom at the same time. However, if F = ma and a is the same for both, then the one with more mass will experience a greater total force, which seems like it would make him reach the bottom first... but how is that possible if they both experience the exact same acceleration?
 
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  • #2
I'm not sure I understand your question. The larger mass requires a larger force to move it down the incline. This is not inconsistent with it reaching it the bottom of the incline at the same time as the smaller mass.
 
  • #3
F = ma, but gravitational force is also proportional to mass.
 
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  • #5
What do you mean by why ?
 
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FAQ: Why does mass not affect sliding speed down an inclined plane?

Why does mass not affect sliding speed down an inclined plane?

Mass does not affect sliding speed down an inclined plane because the acceleration due to gravity is constant for all objects, regardless of their mass. The force of gravity acting on an object is proportional to its mass, but this is exactly balanced by the object's inertia, which also depends on mass. As a result, the mass cancels out, leading to the same acceleration for all objects.

How does the angle of the inclined plane affect the sliding speed?

The angle of the inclined plane affects the component of gravitational force acting along the plane. A steeper angle increases this component, leading to greater acceleration and a higher sliding speed. However, this effect is independent of the mass of the object.

What role does friction play in the sliding speed down an inclined plane?

Friction opposes the motion of the object sliding down the inclined plane. While it does affect the sliding speed, it does so independently of the object's mass. The frictional force is proportional to the normal force, which in turn is proportional to the object's mass, leading to the mass canceling out in the equations of motion.

Would sliding speed be different in a vacuum?

In a vacuum, there is no air resistance. While air resistance can affect the sliding speed of objects with different shapes and masses, in a vacuum, all objects would slide down the inclined plane at the same rate regardless of their mass, assuming no other forces like friction are acting.

Can the sliding speed be affected by other factors besides mass and gravity?

Yes, the sliding speed can be affected by factors such as the surface texture of the inclined plane, the coefficient of friction between the object and the plane, and any external forces applied to the object. However, these factors affect the sliding speed independently of the object's mass.

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