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Natalka [10]
3 years ago
14

Consider a sound wave moving through the air modeled with the equation s(x, t) = 5.00 nm cos(60.00 m−1x − 18.00 ✕ 103 s−1t). Wha

t is the shortest time (in s) required for an air molecule to move between 2.50 nm and −2.50 nm?
Physics
1 answer:
GaryK [48]3 years ago
4 0

Answer:

Shortest time = 58.18 × 10^(-6) s

Explanation:

We are given;

s(x,t) = 5.00 nm cos((60.00 m^(−1)x) − (18.00 X 10³ s^(−1)t))

Let us set x = 0 as origin.

Now, for us to find the time difference, we need to solve 2 equations which are;

s(x,t) = 5.00 nm cos((60.00 m^(−1)x) − (18.00 X 10³ s^(−1)t1))

And

s(x,t) = 5.00 nm cos((60.00 m^(−1)x) − (18.00 X 10³ s^(−1)t2))

Now, since the wave starts from maxima at time at t = 0, the required time would be the difference (t2 - t1)

Thus, the solutions are;

t1 = (1/(18 × 10³)) cos^(-1) (2.5/5)

And

t2 = (1/(18 × 10³)) cos^(-1) (-2.5/5)

Angle of the cos function is in radians, thus;

t1 = 58.18 × 10^(-6) s

t2 = 116.36 × 10^(-6) s

So,

Required time = t2 - t1 = (116.36 × 10^(-6) s) - (58.18 × 10^(-6) s) = 58.18 × 10^(-6) s

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Throw two balls from the same height at the same time at an initial speed of 20 m/s. One is thrown vertically down, while the ot
labwork [276]

The time difference between their landing is 2.04 seconds.

<h3>Time of difference of the two balls</h3>

The ball thrown vertical upwards will take double of the time taken by the ball thrown vertically downwards.

Time difference, = 2t - t = t

t = √(2h/g)

where;

  • h is the height of fall
  • g is acceleration due to gravity

Apply the principle of conservation of energy;

¹/₂mv² = mgh

h = v²/2g

where;

  • v is speed of the ball

h = (20²)/(2 x 9.8)

h = 20.41 m

<h3>Time of motion</h3>

t = √(2 x 20.41 / 9.8)

t = 2.04 s

Thus, the time difference between their landing is 2.04 seconds.

Learn more about time of motion here: brainly.com/question/2364404

#SPJ1

6 0
2 years ago
an object at rest starts accelerating if it travels 30 meters to end up going 10 m/s what was it’s acceleration
vfiekz [6]

First we have to calculate the time taken to travel the distance 30 m, is

t = \frac{distance}{velocity} = \frac{30 \ m}{10 \ m/s } =  3 \ s.

Now from equation of motion,

v = u + at

Given, v = 10 \ m/s .

As object starts from rest, so  u = 0.

Substituting these values in above equation, we get

 10 \ m/s = 0 + a \times 3 \ s \\\\ a = \frac{10}{3}  = 3.33 \ m/s^2.

Thus, the acceleration is 3.33 \ m/s^2

3 0
3 years ago
in the figure shown, if the mass of the block is 4kg and the coefficient of static friction is 0.5 and the coefficient of kineti
Elan Coil [88]

Answer:

Ff = 19.6 N

Explanation:

So since its saying whats the minimum F to move the block, we will use static friction (0.5).

We will use the equation for force of friction, which is Ff = uFn

Ff = (0.5)(4)(9.8)

Ff = 19.6 N

this is the minumum force needed to move the block, as that is the frictional force. You would need to apply a minimum force of 19.6 N to move the block

3 0
3 years ago
A box mass of 24kg is being pulled horizontally on a rough surface by an applied force of 585N. The coefficient of kinetic frict
Elan Coil [88]

the normal force is the force applied opposite to the weight of the was box. So the normal force is equal to the weight of the box = 24 kg *(9.81 m/s2) = 235.44 N

the acceleration of the box be solve using newtons 2nd law of motion:

F = ma

a = F/ m = 585 N/ 24 kg = 24.38 m/s2

8 0
3 years ago
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Consider two wheels with fixed hubs. The hub cannot move, but the wheel can rotate about it. The hubs are fixed to a stationary
kykrilka [37]

Answer:

Magnitude of force on wheel B is 4 N

Explanation:

Given that

I=mr^2

For wheel A

m= 1 kg

d= 1 m,r= 0.5 m

F=1 N

We know that

T= F x r

T=1 x 0.5 N.m

T= 0.5 N.m

T= I α

Where I is the moment of inertia and α is the angular acceleration

I_A=1 \times 0.5^2\ kg.m^2

I_A=0.25\ kg.m^2

T= I α

0.5= 0.25 α

\alpha = 2\ rad/s^2

For Wheel B

m= 1 kg

d= 2 m,r=1 m

I_B=1 \times 1^2\ kg.m^2

I_B=1 \ kg.m^2

Given that angular acceleration is same for both the wheel

\alpha = 2\ rad/s^2

T= I α

T= 1 x 2

T= 2 N.m

Lets force on wheel is F then

T = F x r

2 = F x 1

So F= 2 N

Magnitude of force on wheel B is 2 N

3 0
3 years ago
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