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A cylinder and a block are at the top of an inclined ramp. The cylinder rolls down the ramp without slipping; the block falls vertically without friction at the same instant. (a) Which object reaches the bottom first?

Respuesta :

Answer:

we can see that block is accelerating with more acceleration and hence it will reach the bottom first

Explanation:

As we know that cylinder is rolling without slipping on the inclined plane

So the acceleration of the cylinder is given as

[tex]a = \frac{gsin\theta}{1 + \frac{k^2}{R^2}}[/tex]

so we know that

[tex]\frac{k^2}{R^2} = \frac{1}{2}[/tex]

so we have

[tex]a = \frac{gsin\theta}{1 + \frac{1}{2}}[/tex]

[tex]a = \frac{2}{3}g sin\theta[/tex]

Now the acceleration of block which is slipping on the floor

[tex]a = g sin\theta[/tex]

so here we can see that block is accelerating with more acceleration and hence it will reach the bottom first

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