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1 year ago

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An object undergoing simple harmonic motion has a maximum displacement of 6.2 m at t=0.0 s. if the angular frequency of oscillat

ion is 1.6 rad/s what is the objects displacement when t=3.5 s A) 3.1 m B) 5.6 m C) 4.8 m D) 3.7 m

1 answer:

Law Incorporation [45]1 year ago

4 0

Answer:

C

Explanation:

From above question we know that

A = 6.2 m

f = 1.6 rad/s

t = 3.5 s

x =?

We know that,

x = Acos(2pie ft)

Putting all values in above eq.

x = 6.2 x cos(2x3.142x1.6x3.5)

x = - 4.8

Displacement can never be negative so ignore - sign.

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Emmy kicks a soccer ball up at an angle of 45° over a level field. She watches the ball's trajectory and notices that it lands,

Elenna [48]

Let $u$ be the initial velocity of the soccer ball at an angle of inclination of $\theta_0$ with the positive x-axis.

Given that:

$\theta_0=45^{\circ}$

The horizontal distance covered by the projectile=20 m

Time of flight, $t_f=2$ seconds

Acceleration due to gravity, $g= 10 m/s^2$ downward.

As "north" and "up" as the positive x ‑ and y ‑directions, respectively.

So, $g= -10 m/s^2$

As the acceleration due to gravity is in the vertical direction, so the horizontal component of the initial velocity remains unchanged.

The x-component of the initial velocity, $u_x=u\cos\theta_0$ .

The horizontal distance covered by the projectile $= u_x\times t_f$

$\Rightarrow u_x\times t_f=20$

$\Rightarrow u_x\times 2=20$

$\Rightarrow u_x=10$ m/s

So, the horizontal component of the velocity is 10 m/s which is constant and the graph has been shown in the figure (i).

Now, $u\cos(45^{\circ})=10$ [as $u_x=u\cos\theta_0$ ]

$\Rightarrow u=10\sqrt{2}$ m/s.

The vertical component of the initial velocity,

$u_y= u\sin\theta_0$

$\Rightarrow u_y=10\sqrt{2}\sin(45^{\circ})$

$\Rightarrow u_y=10$ m/s

Let v be the vertical component of the velocity at any time instant t.

From the equation of motion,

$v=u+at$

where u: initial velocity, v: final velocity, a: constant acceleration, and t: time taken to change the velocity from u to v.

In this case, we have $u=u_y, a= -10 m/s^2$ .

So at any time instant, t.

$v=u_y+(-10)t$

$\Rightarrow v=10-10t$

The vertical component of the velocity, v, is the function of time and related as $v=10-10t$ .

This is a linear equation.

At 2 second, the vertical component of the velocity

v=10-10x2=-10 m/s.

The graph has been shown in figure (ii).

7 0

1 year ago

Which one of the following statements concerning kinetic energy is true? a The kinetic energy of an object always has a positive

hodyreva [135]

a The kinetic energy of an object always has a positive value.

Explanation:

The kinetic energy of an object is the energy possessed by an object due to its motion, and it can be calculated as

$K=\frac{1}{2}mv^2$

where

m is the mass of the object

v is its speed

Let's now analyze each statement:

a The kinetic energy of an object always has a positive value. --> TRUE. In fact, the mass of the object is always positive, and the term $v^2$ is always positive as well, so the kinetic energy is always positive.

b The kinetic energy of an object is directly proportional to its speed. --> FALSE. Looking at the formula, we see that the kinetic energy is proportional to the square of the speed, $K\propto v^2$ .

c The kinetic energy of an object is expressed in watts. --> FALSE. Watts is the units for measuring power, while the kinetic energy is measured in Joules, the units for the energy.

d The kinetic energy of an object is a quantitative measure of its inertia. --> FALSE. The inertia of an object depends only on its mass, not on its speed.

e The kinetic energy of an object is always equal to the object’s potential energy. --> FALSE. The potential energy depends on the altitude from the ground, not from the speed, so the two energies can be different.

Learn more about kinetic energy:

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#LearnwithBrainly

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1 year ago

The plates of a parallel-plate capacitor are 2.50 mm apart, and each carries a charge of magnitude 80.0 nC. The plates are in va

bonufazy [111]

Answer:

10000 V

0.00225988700565 m²

$8\times 10^{-12}\ F$

Explanation:

E = Electric field = $4\times 10^6\ V/m$

d = Gap = 2.5 mm

Q = Charge = 80 nC

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

Potential difference is given by

$V=Ed\\\Rightarrow V=4\times 10^6\times 2.5\times 10^{-3}\\\Rightarrow V=10000\ V$

The potential difference between the plates is 10000 V

Area is given by

$A=\dfrac{Q}{\epsilon_0E}\\\Rightarrow A=\dfrac{80\times 10^{-9}}{8.85\times 10^{-12}\times 4\times 10^6}\\\Rightarrow A=0.00225988700565\ m^2$

The area of the plate is 0.00225988700565 m²

Capacitance is given by

$C=\dfrac{\epsilon_0A}{d}\\\Rightarrow C=\dfrac{8.85\times 10^{-12}\times 0.00225988700565}{2.5\times 10^{-3}}\\\Rightarrow C=8\times 10^{-12}\ F$

The capacitance is $8\times 10^{-12}\ F$

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1 year ago

Let this oscillator have the same energy as a mass on a spring, with the same k and m, released from rest at a displacement of 5

allochka39001 [22]

There are a lot of same examples that you may have worked before, where the mass on a spring uses a classics when it comes to mechanics. So in this system, always put in your mind that there is an enormous quantum standard that one can use in the equation. It should be 2.10x10 raise to a negative sixth. J.

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1 year ago

A wave is represented by the equation y = 0.20 sin [ 0.4π (x – 60t)], where x and y are in cm and t is in s. The velocity of the

Leya [2.2K]

Answer:

v = 60 m/s

Explanation:

It is given that,

A wave is represented by the equation :

$y=0.2\sin [0.4\pi (x-60)t]$

We need to find the velocity of the wave

The general equation of a wave is given by :

$y=A\sin (kx-\omega t)$ ....(1)

Equation (1) can be written as :

$y=0.2\sin (0.4\pi x-24\pi t)$ ...(2)

If we compare equation (1) and (2) we get :

$k=0.4\pi$

$\omega=24\pi$

The velocity of a wave is given by :

$v=\dfrac{\omega}{k}\\\\v=\dfrac{24\pi}{0.4\pi}\\\\v=60\ m/s$

So, the velocity of the wave is 60 m/s.

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1 year ago