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3 years ago

Calculate the force required to accelerate a 600 g ball from rest to 14 m/s in 0.1 s.

Physics

1 answer:

Evgen [1.6K]3 years ago

5 0

Statement:

A force is required to accelerate a 600 g ball from rest to 14 m/s in 0.1 s.

To find out:

The force required to accelerate the ball.

Solution:

Mass of the ball (m) = 600 g = 0.6 Kg
Initial velocity (u) = 0 m/s [it was at rest]
Final velocity (v) = 14 m/s
Time (t) = 0.1 s

Let the acceleration be a.
We know the equation of motion,
v = u + at

Therefore, putting the values in the above formula, we get
14 m/s = 0 m/s + a × 0.1 s
or, 14 m/s ÷ 0.1 s = a
or, a = 140 m/s²

Let the force be F.
We know, the formula : F = ma

Putting the values in the above formula, we get
F = 0.6 Kg × 140 m/s²
or, F = 84 N

Answer:

The force required to accelerate the ball is 84 N and this force acts along the direction of motion.

Hope you could understand.

If you have any query, feel free to ask.

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3 years ago

A 22.0 nF capacitor is connected across an AC generator that produces a peak voltage of 5.80 V. part a

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Answer:

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3 years ago

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The ducks' flight path as observed by someone standing on the ground is the sum of the wind velocity and the ducks' velocity relative to the wind:

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or equivalently,

$\vec v_{D/W}+\vec v_{W/E}=\vec v_{D/E}$

(see the attached graphic)

We have

ducks (relative to wind) = 7.0 m/s in some direction θ relative to the positive horizontal direction, or

$\vec v_{D/W}=\left(7.0\dfrac{\rm m}{\rm s}\right)(\cos\theta\,\vec\imath+\sin\theta\,\vec\jmath)$

wind (relative to Earth) = 5.0 m/s due East, or

$\vec v_{W/E}=\left(5.0\dfrac{\rm m}{\rm s}\right)(\cos0^\circ\,\vec\imath+\sin0^\circ\,\vec\jmath)$

ducks (relative to earth) = some speed v due South, or

$\vec v_{D/E}=v(\cos270^\circ\,\vec\imath+\sin270^\circ\,\vec\jmath)$

Then by setting components equal, we have

$\left(7.0\dfrac{\rm m}{\rm s}\right)\cos\theta+5.0\dfrac{\rm m}{\rm s}=0$

$\left(7.0\dfrac{\rm m}{\rm s}\right)\sin\theta=-v$

We only care about the direction for this question, which we get from the first equation:

$\left(7.0\dfrac{\rm m}{\rm s}\right)\cos\theta=-5.0\dfrac{\rm m}{\rm s}$

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$\theta=\cos^{-1}\left(-\dfrac57\right)\text{ OR }\theta=360^\circ-\cos^{-1}\left(-\dfrac57\right)$

or approximately 136º or 224º.

Only one of these directions must be correct. Choosing between them is a matter of picking the one that satisfies both equations. We want

$\left(7.0\dfrac{\rm m}{\rm s}\right)\sin\theta=-v$

which means θ must be between 180º and 360º (since angles in this range have negative sine).

So the ducks must fly (relative to the air) in a direction 224º relative to the positive horizontal direction, or about 44º South of West.

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