A 24 kg child descends a 5.0 m high slide and reaches the ground with a speed of 2.8 m/s. What is the mass of the child?
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Answer:
Minimum coefficient of kinetic friction between the surface and the block is .
Explanation:
Given:
Mass of the block = M
Spring constant = k
Distance pulled = x
According to the question:
<em>We have to find the minimum co-efficient of kinetic friction between the surface and the block that will prevent the block from returning to its equilibrium with non-zero speed. </em>
So,
From the FBD we can say that:
⇒ Normal force, <em>...equation(i)</em>
⇒ Elastic potential energy, =
<em> ...equation (ii)</em>
⇒ Frictional force, =
<em> ...equation (iii)</em>
⇒ Plugging (i) in (iii).
⇒
Now,
⇒ As we know that the energy lost due to friction is equivalent to PE .
⇒ <em>...considering PE as</em>
or
.
Arranging the equation.
⇒
⇒ <em>...eliminating x from both sides.</em>
⇒ <em>...dividing both sides wit Mg.</em>
Minimum coefficient of kinetic friction between the surface and the block is .
To solve this problem it is necessary to apply the concepts related to the Heisenberg's uncertainty principle. Under this principle we understand the relationship that the minimum range of error in position (x) times the minimum range of error in momentum (p) is, at a minimum, about equal to the Planck constant, mathematically that is,
Replacing with our values we have,
Therefore the least uncertainty in any simultaneous measurement of the momentum component px of this electron is