5. What's the temperature -10°C in kelvins?

A ball is dropped from rest from the top of a building of height h. At the same instant, a second ball is projected vertically u

uranmaximum [27]

Answer:

a) $t = \sqrt{\frac{h}{2g}}$

b) Ball 1 has a greater speed than ball 2 when they are passing.

c) The height is the same for both balls = 3h/4.

Explanation:

a) We can find the time when the two balls meet by equating the distances as follows:

$y = y_{0_{1}} + v_{0_{1}}t - \frac{1}{2}gt^{2}$

Where:

$y_{0_{1}}$ : is the initial height = h

$v_{0_{1}}$ : is the initial speed of ball 1 = 0 (it is dropped from rest)

$y = h - \frac{1}{2}gt^{2}$ (1)

Now, for ball 2 we have:

$y = y_{0_{2}} + v_{0_{2}}t - \frac{1}{2}gt^{2}$

Where:

$y_{0_{2}}$ : is the initial height of ball 2 = 0

$y = v_{0_{2}}t - \frac{1}{2}gt^{2}$ (2)

By equating equation (1) and (2) we have:

$h - \frac{1}{2}gt^{2} = v_{0_{2}}t - \frac{1}{2}gt^{2}$

$t=\frac{h}{v_{0_{2}}}$

Where the initial velocity of the ball 2 is:

$v_{f_{2}}^{2} = v_{0_{2}}^{2} - 2gh$

Since $v_{f_{2}}^{2}$ = 0 at the maximum height (h):

$v_{0_{2}} = \sqrt{2gh}$

Hence, the time when they pass each other is:

$t = \frac{h}{\sqrt{2gh}} = \sqrt{\frac{h}{2g}}$

b) When they are passing the speed of each one is:

For ball 1:

$v_{f_{1}} = - gt = -g*\sqrt{\frac{h}{2g}} = - 0.71\sqrt{gh}$

The minus sign is because ball 1 is going down.

For ball 2:

$v_{f_{2}} = v_{0_{2}} - gt = \sqrt{2gh} - g*\sqrt{\frac{h}{2g}} = (\sqrt{1} - \frac{1}{\sqrt{2}})*\sqrt{gh} = 0.41\sqrt{gh}$

Therefore, taking the magnitude of ball 1 we can see that it has a greater speed than ball 2 when they are passing.

c) The height of the ball is:

For ball 1:

$y_{1} = h - \frac{1}{2}gt^{2} = h - \frac{1}{2}g(\sqrt{\frac{h}{2g}})^{2} = \frac{3}{4}h$

For ball 2:

$y_{2} = v_{0_{2}}t - \frac{1}{2}gt^{2} = \sqrt{2gh}*\sqrt{\frac{h}{2g}} - \frac{1}{2}g(\sqrt{\frac{h}{2g}})^{2} = \frac{3}{4}h$

Then, when they are passing the height is the same for both = 3h/4.

I hope it helps you!

7 0

3 years ago

An electron and a proton each have a thermal kinetic energy of 3kBT/2. Calculate the de Broglie wavelength of each particle at a

IgorLugansk [536]

Answer:

The de Broglie wavelength of electron βe = 2.443422 × 10⁻⁹ m

The de Broglie wavelength of proton βp = 5.70 × 10⁻¹¹ m

Explanation:

Thermal kinetic energy of electron or proton = KE

∴ KE = 3kbT/2

given that; kb = 1.38 x 10⁻²³ J/K , T = 1950 K

so we substitute

KE = ( 3 × 1.38 x 10⁻²³ × 1950 ) / 2

kE = 4.0365 × 10⁻²⁰ ( is the kinetic energy for both electron and proton at temperature T )

Now we know that

mass of electron M'e = 9.109 × 10⁻³¹

mass of proton M'p = 1.6726 × 10⁻²⁷

We also know that

KE = p₂ / 2m

from the equation, p = √ (2mKE)

{ p is momentum, m is mass }

de Broglie wavelength = β

so β = h / p = h / √ (2mKE)

h = Planck's constant = 6.626 × 10⁻³⁴

∴ βe = h / √ (2m'e × KE)

βe = 6.626 × 10⁻³⁴ / √ (2 × 9.109 × 10⁻³¹ × 4.0365 × 10⁻²⁰ )

βe = 6.626 × 10⁻³⁴ / √ 7.3536957 × 10⁻⁵⁰

βe = 6.626 × 10⁻³⁴ / 2.71176984642871 × 10⁻²⁵

βe = 2.443422 × 10⁻⁹ m

βp = h / √ (2m'p ×KE)

βp = 6.626 × 10⁻³⁴ / √ (2 × 1.6726 × 10⁻²⁷ × 4.0365 × 10⁻²⁰ )

βp = 6.626 × 10⁻³⁴ / √ 1.35028998 × 10⁻⁴⁶

βp = 6.626 × 10⁻³⁴ / 1.16201978468527 × 10⁻²³

βp = 5.702140 × 10⁻¹¹ m

3 0

3 years ago

A sound wave, with speed of 340 m/s has a frequency of 17,000 Hz. What

Fiesta28 [93]

Wavelength = speed / frequency = 340 / 17000 = 0.02 m

6 0

3 years ago

Why is it important to have a balanced centrifuge?

ratelena [41]

It is important to properly balance a centrifuge because an unbalanced machine can damage the rotor, cause catastrophic damage to the machine itself, or even injure or kill lab personnel working in the room. Balancing a centrifuge involves spreading the weight of the samples across the entire rotor.

8 0

4 years ago

A police car in a high-speed chase is traveling north on a two-lane highway at 35.0 m/s. In the southbound lane of the same high

Sati [7]

Answer:

53 m/s

Explanation:

Since we take the positive x-direction to be toward the north, an SUV travelling to the south would have a negative velocity, -18m/s, relative to Earth. Velocity of Earth relative to the SUV would be 18m/s. And velocity of police car relative to Earth would be positive, 35 m/s.

Velocity of police relative to SUV would equal to velocity of police car relative to Earth plus velocity of Earth relative to SUV

= 35 + 18 = 53 m/s

3 0

3 years ago

5. What's the temperature -10°C in kelvins? ​

5. What's the temperature -10°C in kelvins?