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alexdok [17]
3 years ago
13

A 200-g block is attached to a horizontal spring and executes simple harmonic motion with a period of 0.250 s. The total energy

of the system is 2.00 J. Find (a) the force constant of the spring and (b) the amplitude of the motion.
Physics
1 answer:
m_a_m_a [10]3 years ago
6 0

Answer:

(A) Spring constant will be 126.58 N/m

(B) Amplitude will be equal to 0.177 m

Explanation:

We have given mass of the block m = 200 gram = 0.2 kg

Time period T = 0.250 sec

Total energy is given TE = 2 J

(A) For mass spring system time period is equal to T=2\pi \sqrt{\frac{m}{K}}

So 0.250=2\times 3.14 \sqrt{\frac{0.2}{K}}

0.0398=\sqrt{\frac{0.2}{K}}

Now squaring both side

0.00158=\frac{0.2}{K}

K = 126.58 N/m

So the spring constant of the spring will be 126.58 N/m

(B) Total energy is equal to TE=\frac{1}{2}KA^2, here K is spring constant and A is amplitude

So 2=\frac{1}{2}\times 126.58\times A^2

A^2=0.0316

A = 0.177 m

So the amplitude of the wave will be equal to 0.177 m

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A baseball is hit almost straight up into the air with a speed of 26 m/s . Estimate how high it goes.
Natalka [10]

Answer:

The maximum height of the ball is 34.5 m.

The ball is 5.31 s in the air.

Explanation:

Hi there!

The equations for the height and velocity of the baseball that is hit straight up are as follows:

y = y0 + v0 · t + 1/2 · g · t²

v = v0 + g · t

Where:

y = height of the baseball at time t.

y0 = initial height.

v0 = initial velocity.

t = time.

g =  acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).

v = velocity at time t.

If we place the origin of the frame of reference at the place where the baseball is hit, then, y0 = 0.

To calculate how high it goes, we have to obtain the time at which the ball is at maximum height. At that point, the velocity is 0. Then using the equation of velocity:

v = v0 + g · t

0 = 26 m/s - 9.8 m/s² · t

-26 m/s / -9.8 m/s² = t

t = 2.65 s

The height at that time will be the maximum height:

y = y0 + v0 · t + 1/2 · g · t²        (y0 = 0)

y = 26 m/s · 2.65 s - 1/2 · 9.8 m/s² · (2.65 s)²

y = 34.5 m

The maximum height of the ball is 34.5 m

If it takes the ball 2.65 s to reach the maximum height it will take another 2.65 s to return to the initial position. Then, the time it will be in the air is (2.65 s + 2.65 s) 5.30 s. However, let´s calculate the time it takes the ball to reach the initial position using the equation for height.

At the initial position y = 0. Then:

y = y0 + v0 · t + 1/2 · g · t²        (y0 = 0)

0 = 26 m/s · t - 1/2 · 9.8 m/s² · t²

0 = t (26 m/s - 1/2 · 9.8 m/s² · t)      (t = 0 when the ball is hit)

0 = 26 m/s - 1/2 · 9.8 m/s² · t

-26 / -4.9 m/s² = t

t = 5.31 s     ( the difference with the 5.30 s obtained above is due to rounding the time to 2.65 s).

The ball is 5.31 s in the air.

Have a nice day!

5 0
3 years ago
A juggler is practicing with one ball. It takes 2.4 seconds for the ball to leave her hand and return to her hand. How fast did
nikklg [1K]

The kinematics for the vertical launch we can enter the initial velocity is 11.76 m / s

Given parameters

  • Time t = 2.4 s

To find

  • Initial velocity

Kinematics is the part of physics that establishes the relationships between the position, velocity, and acceleration of bodies.

In this case we have a vertical launch

          y = y₀ + v₀ t - ½ g t²

Where y and y₀ are the final and initial positions, respectively, v₀ the initial velocity, g the acceleration of gravity (g = 9.8 m / s²) and t the time

   

With the ball in hand, its position is zero

         0 = 0 + v₀ t - ½ g t²

         v₀ t - ½ g t² = 0

         v₀ = ½ g t

Let's calculate

         v₀ = ½ 9.8 2.4

         v₀ = 11.76 m / s

In conclusion using kinematics for the vertical launch we can enter the initial velocity is 11.76 m / s

Learn more about vertical launch kinematics here:

brainly.com/question/15068914

5 0
2 years ago
If it takes you 20 joules of work to move a couch 10 meters in 10 seconds, what is the power?
Debora [2.8K]

Answer:

Power = 2 j/s

Explanation:

Power = Work / Time

= 20/10

= 2 j/s

4 0
2 years ago
Will kilogram of hydrogen contains more atoms than kilogram of lead?
Zigmanuir [339]
Yes a kg of hydrogen will have more atoms than a kg of lead, because lead has a higher atomic mass, than hydrogen so it will take more atoms of hydrogen to make a kg than lead
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3 years ago
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