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2 years ago

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In order for the ball to be able to make a complete circle around the peg, there must be sufficient speed at the top of its arc

such that the centripetal acceleration is large enough to keep the string that. Determine the minimum speed for the ball to achieve a complete circle in terms of L, d, and g. (Hint: use Newton’s 2nd Law and consider what the string tension must be for the ball to just barely get over the top).

1 answer:

Vesna [10]2 years ago

6 0

Answer:

Explanation:

Let T be the tension in the swing

At top point $mg-T=\frac{mv^2}{r}$

where v=velocity needed to complete circular path

r=distance between point of rotation to the ball center=L+\frac{d}{2} (d=diameter of ball)

Th-resold velocity is given by $mg-0=\frac{mv^2}{r}$

To get the velocity at bottom conserve energy at Top and bottom

At top $E_T=mg\times 2L+\frac{mv^2}{2}$

Energy at Bottom $E_b=\frac{mv_0^2}{2}$

Comparing two as energy is conserved

$v_0^2=4gr+gr$

$v_0^2=5gr$

$v_0=\sqrt{5gr}$

$v_0=\sqrt{5g\left ( \frac{d}{2}+L\right )}$

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2 years ago

An airplane flying at 115 m/s due east makes a gradual turn following a circular path to fly south. The turn takes 15 seconds to

ankoles [38]

Answer:

The magnitude of the centripetal acceleration during the turn is $a=12.04\ m/s^2.$

Explanation:

Given :

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Also , the plane turns from east to south i.e. quarter of a circle .

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Now , Velocity ,

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2 years ago

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djverab [1.8K]

Answer:

$v_{2}$ will be less than $v_{1}$ and $P_{2}$ will be greater than $P_{1}$ .

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