Crossing the Chasm

Classical Mechanics Level 1

A uniform sled of length $l$ is released from a hill of height $h$ . The sled then comes across a chasm of width $d$ .

What is the maximum possible width of the chasm such that the sled is able to cross it?

Note: All surfaces are frictionless.

l

\frac l2

Depends on height

h

It won't be able to cross the gap for any non-zero value of

d

1 solution

Steven Chase
Mar 15, 2017

Once the block has at least half its length hanging off of the edge, the gravitational torque on the block will cause it to tilt into the chasm. Portions of the block will then be below "ground level", so no matter how much speed it has, it will collide with the far side of the chasm and fall in. The critical distance is $d = \frac{l}{2}$ . By the time the block would begin to tilt, part of it has already crossed to the other side, and the normal reaction on the other side ensures that the net torque remains zero.

Isn't there a value of h sufficient to create a velocity great enough such that a tiny 'overlap' at the point of collision would cause rotation about the centre of gravity and the block would flip onto the far surface? Maths vs physics...

Carl Sanders - 4 years, 2 months ago

Interesting idea. Maybe so.

Steven Chase - 4 years, 1 month ago

Would we not need to calculate the velocity of the block at the point where it leaves its surface and then calculate the horizontal distance it would travel before it looses height?

Vijay Shankar - 4 years, 2 months ago

As soon as more than half of the block is hanging off of the edge, it will begin to tilt immediately.

Steven Chase - 4 years, 1 month ago

Crossing the Chasm

1 solution

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