The multiple reflection of a single sound wave is a/an

A 210 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 2.0 N/cm. The block becomes attached t

Yuliya22 [10]

Answer:

a) $W_{g}=mdx = 0.21 kg *9.8\frac{m}{s^2} 0.10m=0.2058 J$

b) $W_{spring}= -\frac{1}{2} Kx^2 =-\frac{1}{2} 200 N/m (0.1m)^2=-1 J$

c) $V_i =\sqrt{2 \frac{W_g + W_{spring}}{0.21 kg}}}=\sqrt{2 \frac{(1-0.2058)}{0.21 kg}}}=2.75m/s$

d) $d_1 =0.183m$ or 18.3 cm

Explanation:

For this case we have the following system with the forces on the figure attached.

We know that the spring compresses a total distance of x=0.10 m

Part a

The gravitational force is defined as mg so on this case the work donde by the gravity is:

$W_{g}=mdx = 0.21 kg *9.8\frac{m}{s^2} 0.10m=0.2058 J$

Part b

For this case first we can convert the spring constant to N/m like this:

$2 \frac{N}{cm} \frac{100cm}{1m}=200 \frac{N}{m}$

And the work donde by the spring on this case is given by:

$W_{spring}= -\frac{1}{2} Kx^2 =-\frac{1}{2} 200 N/m (0.1m)^2=-1 J$

Part c

We can assume that the initial velocity for the block is Vi and is at rest from the end of the movement. If we use balance of energy we got:

$W_{g} +W_{spring} = K_{f} -K_{i}=0- \frac{1}{2} m v^2_i$

And if we solve for the initial velocity we got:

$V_i =\sqrt{2 \frac{W_g + W_{spring}}{0.21 kg}}}=\sqrt{2 \frac{(1-0.2058)}{0.21 kg}}}=2.75m/s$

Part d

Let d1 represent the new maximum distance, in order to find it we know that :

$-1/2mV^2_i = W_g + W_{spring}$

And replacing we got:

$-1/2mV^2_i =mg d_1 -1/2 k d^2_1$

And we can put the terms like this:

$\frac{1}{2} k d^2_1 -mg d_1 -1/2 m V^2_i =0$

If we multiply all the equation by 2 we got:

$k d^2_1 -2 mg d_1 -m V^2_i =0$

Now we can replace the values and we got:

$200N/m d^2_1 -0.21kg(9.8m/s^2)d_1 -0.21 kg(5.50 m/s)^2) =0$

$200 d^2_1 -2.058 d_1 -6.3525=0$

And solving the quadratic equation we got that the solution for $d_1 =0.183m$ or 18.3 cm because the negative solution not make sense.

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2 years ago

Is diverse families positive or negative

nataly862011 [7]

Think its Positive
hope this helpes

6 0

3 years ago

Which of the following processes most directly helps create soil from rocks?

irina [24]

A. Weathering I think

4 0

2 years ago

Read 2 more answers

All you have to do is find the description for a b c and d words and find the meaning 8 9 10 11 and 12

insens350 [35]

A-11 polar easterlies
b-8 winds blowing between the equator and 30° N and south
c-10
d-9

4 0

3 years ago

Find the kinetic energy of a bullet weighing 0.10 N if its velocity is<br> 2.0 X 103 m/s?

irina1246 [14]

The kinetic energy of the bullet is 20.4 kJ.

<u>Explanation:</u>

Kinetic energy of a bullet will be equal to the product of mass of the bullet with the square of velocity or speed of the bullet and then the half of that product value.

But here the mass of the bullet is not given, instead the weight of the bullet is given in terms of force. So from this, we have to first find the mass of the bullet.

We know that as per Newton's second law of motion, force is directly proportional to the product of mass and acceleration. So here the acceleration will be equal to the acceleration due to gravity as it is weight of the object.

So F = mg

0.10 N = m × 9.8

So ,the mass of the bullet is 0.0102 kg.

Now, we know the mass and velocity of the bullet is given as 2000 m/s.

So,

kinetic energy = $\frac{1}{2}$ × m × v²

kinetic energy = 0.5 × 0.0102 × 2000 × 2000 = 20.4 kJ

Thus, the kinetic energy of the bullet is 20.4 kJ.

5 0

3 years ago