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4 years ago

6

-g With what tension must a rope with length 2.50 m and mass 0.120 kg be stretched for transverse waves of frequency 40.0 Hz to

have a wavelength of 0.750 m?

1 answer:

Alex17521 [72]4 years ago

8 0

Answer:

43.2 N

Explanation:

$\lambda$ = Wavelength = 0.75 m

f = Frequency = 40 Hz

m = Mass of string = 0.12 kg

L = Length of string = 2.5 m

$\mu$ = Linear density = $\dfrac{m}{L}$

Velocity of wave is given by

$v=\lambda f\\\Rightarrow v=0.75\times 40\\\Rightarrow v=30\ m/s$

The tension in string is given by

$T=v^2\mu\\\Rightarrow T=30^2\times \dfrac{0.12}{2.5}\\\Rightarrow T=43.2\ N$

The tension in the string is 43.2 N

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A ball of 0.1kg is thrown straight up into the air with

Contact [7]

a) The momentum of the ball at the maximum height is zero

b) The momentum of the ball at halfway is 1.06 kg m/s

Explanation:

a)

There is only one force acting on the ball during its motion: the force of gravity, acting downward. As a result, the ball hasa constant acceleration downward ( $g=9.8 m/s^2$ , acceleration of gravity), and therefore it is in free fall motion.

This means that the velocity of the ball is given by the equation:

$v=u-gt$

where

v is the velocity at time t

u = 15 m/s is the initial velocity

$g=9.8 m/s^2$

As we see from the equation, the term $-gt$ is negative: this means that as the ball goes higher and higher, its velocity decreases. The point of maximum height is reached when the velocity has become zero (after that point, the velocity changes direction and points downward), so when

$v=0$

The momentum of the ball at any point is given by

$p=mv$

where m = 0.1 kg is its mass. Therefore, at the maximum height, since $v=0$ , the momentum is also zero:

$p=0$

b)

We can use the following suvat equation to find the maximum height reached by the ball:

$v^2-u^2=2as$

where

v = 0 is the velocity at the point of maximum height

u = 15 m/s is the initial velocity

$a=-g=-9.8 m/s^2$ is the acceleration (downward)

s is the vertical displacement (the maximum height)

Solving for s,

$s=\frac{v^2-u^2}{2a}=\frac{0-(15)^2}{2(-9.8)}=11.48 m$

This means that the ball is halfway when its height is

$h'=\frac{s}{2}=\frac{11.48}{2}=5.74 m$

We can find the velocity of the ball v' when it is at h' by using again the same equation:

$v'^2-u^2=2ah'\\v=\sqrt{u^2+2ah'}=\sqrt{(15)^2+2(-9.8)(5.74)}=10.6 m/s$

And therefore, the momentum of the ball here is

$p'=mv'=(0.1)(10.6)=1.06 kg m/s$

Learn more about momentum:

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3 years ago

Motion maps for two objects, Y and Z, are shown.

iragen [17]

Answer:

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3 years ago

If a 4kg Bird is pushed by the window with a force of 60 N how fast is the bird accelerate?

LiRa [457]

Force=60N
Mass=4kg

$\\ \ast\sf\hookrightarrow Force=Mass\times Acceleration$

$\\ \ast\sf\hookrightarrow Acceleration=\dfrac{Force}{Mass}$

$\\ \ast\sf\hookrightarrow Acceleration=\dfrac{60}{4}$

$\\ \ast\sf\hookrightarrow Acceleration=15m/s^2$

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3 years ago

AP Physics I, shouldn't be too hard.

Nana76 [90]

Answer:

The correct option is;

D. The kinetic energy decreases by 3·m₀·v₀²

Explanation:

The given parameters are;

The mass of object X = m₀

The initial velocity of object X = v₀

The mass of object Y = 2·m₀

The initial velocity of object Y = -2·v₀

By conservation of linear momentum, we have;

The total initial momentum = The total final momentum

Therefore, we have;

The total initial momentum = m₀·v₀ - 2·m₀·2·v₀ = The total final momentum

∴ The total final momentum = -3·m₀·v₀

The total mass of the two object after sticking together = 2·m₀ + m₀ = 3·m₀

Therefore, the velocity of the two objects after collision = (The total final momentum)/(Total mass) = -3·m₀·v₀/(3·m₀) = -v₀

The kinetic energy = 1/2 × Mass × (Velocity)²

Therefore, the kinetic energy after collision = 1/2 × (3·m₀) × v₀² = 3·m₀·v₀²/2

The kinetic energy before collision = 1/2 × m₀ × v₀² + 1/2 × (2·m₀) × (2·v₀)² = (1/2 + 4) × (m₀·v₀²)

∴ The kinetic energy before collision = 9·(m₀·v₀²)/2

The change in kinetic energy = The kinetic energy after collision - The kinetic energy before collision = 3·m₀·v₀²/2 - 9·(m₀·v₀²)/2 = -3·m₀·v₀²

Therefore, the kinetic energy decreases by 3·m₀·v₀².

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Connection to Big Idea about Earth: The gravitational force is responsible for many physical properties of Earth and consequently it affects the existence and the properties of living creatures on it. For instance, the existence, the chemical composition and the structure of Earth’s atmosphere was determined by Earth’s gravitational force.

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