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Eduardwww [97]
3 years ago
7

A cart with mass m vibrating at the end of a spring has an extra block added to it when its displacement is x=+A. What should th

e block's mass be in order to reduce the frequency to half its initial value? Express your answer in terms of the variables m and A.
Physics
1 answer:
Pavel [41]3 years ago
8 0

Answer:

The block's mass should be 3m

Explanation:

Given:

Cart with mass m

From the conservation of energy before mass is added,

  \frac{1}{2} mv^{2} = \frac{1}{2} kA^{2}

Where A = amplitude of spring mass system, k = spring constant

  A = v\sqrt{\frac{m}{k} }

Now new mass M is added to the system,

   \frac{1}{2} (m +M ) v^{2}  = \frac{1}{2}  k A^{2}

  A = v \sqrt{\frac{m +M }{k} }

Here, given in question frequency is reduced to half so we can write,

   f' = \frac{f}{2}

Where f = frequency of system before mass is added, f' = frequency of system after mass is added.

        \omega ' = \frac{\omega}{2}

\sqrt{\frac{k}{m +M} }  = \frac{\sqrt{\frac{k}{m} } }{2}

   \frac{k}{m +M } = \frac{k}{4m}

   M = 3m

Therefore, the block's mass should be 3m

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nikitadnepr [17]

The time spent in the air by the ball at the given momentum is 6.43 s.

The given parameters;

  • <em>momentum of the ball, P = 0.9 kgm/s</em>
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The impulse experienced by the ball is calculated as follows;

Ft = \Delta P

where;

Ft is impulse

\Delta P is change in momentum

The time of motion of the ball is calculated as follows;

t = \frac{\Delta P}{F} \\\\t = \frac{0.9 - 0}{0.14} \\\\t = 6.43 \ s

Thus, the time spent in the air by the ball at the given momentum is 6.43 s.

Learn more here:brainly.com/question/13468390

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2 years ago
One cereal bar has a mass of 37 g. What is the mass of 6 cereal bars? Is that more than or less than 1 kg? Explain your answer.
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The mass is 222g.  No, it is less than 1kg.  There are 1000 grams in a kilogram so it would be 0.222kg.  Hope this Helps :D

7 0
3 years ago
If zak's speed is 3.00 m/s when he starts to slide, what distance d will he slide before stopping? express your answer in meters
OverLord2011 [107]
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8 0
3 years ago
A centrifuge is used to test space pilots. The centrifuge spins with a centripetal acceleration of 3.04g. If the length of the a
uranmaximum [27]

Answer:

approx.= 25\frac{m}{s}

Explanation:

Centripetal acceleration (a) is defined as the square of an object's velocity (V^2) divided by the distance of the object from it's point/axis of revolution (r). So:

a=\frac{V^{2} }{r}

which allows us to solve for the velocity:

V=\sqrt{ar}\\ Since: a=3.04g=(3.04)(9.81),r=21;\\V=\sqrt{(3.04)(9.81)(21)} =25.02...

3 0
3 years ago
A light beam is traveling through an unknown substance. When it exits that substance and enters into air, the angle of reflectio
bogdanovich [222]

Answer:

0.79

Explanation:

Using Snell's law, we have that:

n(1) * sin θ1 = n(2) * sinθ2

Where n(1) = refractive index of air = 1.0003

θ1 = angle of incidence

n(2) = refractive index of second substance

θ2 = angle of refraction

The angle of reflection through the unknown substance is the same as the angle of incidence of air. This means that θ1 = 32°

=> 1.0003 * sin32 = n(2) * sin42

n(2) = (1.0003 * sin32) / sin42

n(2) = 0.79

3 0
3 years ago
Read 2 more answers
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