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morpeh [17]
3 years ago
5

A beam of hydrogen molecules (h2) is directed toward a wall, at an angle of 55 with the normal to the wall. each molecule in the

beam has a speed of 1.0 km/s and a mass of 3.3 1024 g.the beam strikes the wall over an area of 2.0 cm2, at the rate of 1023 molecules per second.what is the beam’s pressure on the wall?
Physics
1 answer:
cestrela7 [59]3 years ago
8 0

 

The change in momentum of the particle upon hitting the wall is expressed as:

Change in momentum = Δp = 2 m v cosθ

where m = 3.3E-24 g = 3.3E-27 kg, v = 1.0 km/s = 1000 m/s, θ = 55°

 

Dividing both sides by Δt:

Δp / Δt = 2 (Δm / Δt) v cosθ

 

By definition, the force applied to a particle is equal to the change in momentum per second of the particle (by Newton's Second Law). Therefore:

Force on wall = Δp / Δt = 2 (Δm / Δt) v cosθ

 

We can get or calculate the value of  (Δm / Δt) from the given data. That is:

Δm / Δt = m * particles per second = (3.3E-27 kg/particle) (1023 particle/s)

Δm / Δt = 3.3759 E-24 kg/s

 

Therefore the force is:

Total force on wall = 2 (3.3759 E-24 kg/s) (1000 m/s) cos(55)

Total Force on wall = 1.494E-22 N

 

Pressure = Total Force / Area = 1.494E-22 N / 2.0E-4 m^2

Pressure = 7.47E-19  Pascals

 

Therefore the pressure is 7.47*10^-19 Pa.

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Answer:

(a) 196 m/s

(b) 490 m

(c) 3394.82 m

(d) 2572.5 m

Explanation:

First of all, let us know one thing. When an object is thrown in the air, it experiences two forces acting in two different directions, one in the horizontal direction called air resistance and the second in the vertically downward direction due to its weight. In most of the cases, while solving numerical problems, air resistance is neglected unless stated in the numerical problem. This means we can assume zero acceleration along the horizontal direction.

Now, while solving our numerical problem, we will discuss motion along two axes according to our convenience in the course of solving this problem.

<u>Given:</u>

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  • Angle of the initial velocity of projectile with the horizontal = \theta = 30^\circ

<u>Assume:</u>

  • Initial velocity of the projectile = u
  • R = Range of the projectile during the time of flight
  • H = maximum height of the projectile
  • D = displacement of the projectile from the initial position at t = 15 s

Let us assume that the position from where the projectile was projected lies at origin.

  • Initial horizontal velocity of the projectile = u\cos \theta
  • Initial horizontal velocity of the projectile = u\sin \theta

Part (a):

During the time of flight the displacement of the projectile along the vertical is zero as it comes to the same vertical height from where it was projected.

\therefore u\sin \theta t +\dfrac{1}{2}(-g)t^2\\\Rightarrow u\sin \theta t=\dfrac{1}{2}(g)t^2\\\Rightarrow u=\dfrac{gt^2}{2\sin \theta t}\\\Rightarrow u=\dfrac{9.8\times 20^2}{2\sin 30^\circ \times 20}\\\Rightarrow u=196\ m/s

Hence, the initial speed  of the projectile is 196 m/s.

Part (b):

For a projectile, the time take by it to reach its maximum height is equal to return from the maximum height to its initial height is the same.

So, time taken to reach its maximum height will be equal to 10 s.

And during the upward motion of this time interval, the distance travel along the vertical will give us maximum height.

\therefore H = u\sin \theta t +\dfrac{1}{2}(-g)t^2\\\Rightarrow H = 196\times \sin 30^\circ \times 10 + \dfrac{1}{2}\times(-9.8)\times 10^2\\ \Rightarrow H =490\ m

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Part (c):

Range is the horizontal displacement of the projectile from the initial position. As acceleration is zero along the horizontal, the projectile is in uniform motion along the horizontal direction.

So, the range is given by:

R = u\cos \theta t\\\Rightarrow R = 196\times \cos 30^\circ \times 20\\\Rightarrow R =3394.82\ m

Hence, the range of the projectile is 3394.82 m.

Part (d):

In order to calculate the displacement of the projectile from its initial position, we first will have to find out the height of the projectile and its range during 15 s.

\therefore h = u\sin \theta t +\dfrac{1}{2}(-g)t^2\\\Rightarrow h = 196\times \sin 30^\circ \times 15 + \dfrac{1}{2}\times(-9.8)\times 15^2\\ \Rightarrow h =367.5\ m\\r = u\cos \theta t\\\Rightarrow r = 196\times \cos 30^\circ \times 15\\\Rightarrow r =2546.11\ m\\\therefore D = \sqrt{r^2+h^2}\\\Rightarrow D = \sqrt{2546.11^2+367.5^2}\\\Rightarrow D =2572.5\ m

Hence, the displacement from the point of launch to the position on its trajectory at 15 s is 2572.5 m.

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