Gravity is affected by

A 2.00-kg, frictionless block is attached to an ideal spring with force constant 300 N/m. At t = 0 the spring is neither stretch

r-ruslan [8.4K]

Answer:

a) A = 0.98 m

b) Ф = 90°

c) x = -0.98sin(12.25t)

Explanation:

We know the value of the spring constant which is 300 N/m, the innitial apmplitude, that we will call it xo is 0, at t = 0, and the speed is 12 m/s

The expression for the amplitude under these conditions is:

A = √xo² + vx²/w² (1)

To calculate the angular speed w, we use the following expression:

w = √k/m (2)

Calculating w:

w = √300/2 = 12.25 rad/s

Now, we replace this value into equation 1, along with the other known values and solve for A:

A = √0 + (12)²/(12.25)²

A = 0.98 m

b) In this part, is actually easy, the displacement of x in function of the time is given by:

x = A cos(wt - Ф) (4)

But at t = 0 we have then:

x = xo = A cosФ (5)

Solving for the angle Ф we have:

xo/A = cosФ

Ф = arccos(x0/A) (6)

Replacing the data in (6):

Ф = arccos(0/0.98)

Ф = 90°

c) Equation (4) is the expression for the simple harmonic motion

x = A cos(wt - Ф)

And if we replace here the value of w and the previous angle, we can write an equation for x in function of t:

x = 0.98 cos (12.25t - 90)

x = 0.98 cos(12.25t - 90)

And we have an trigonometric expression for cos that is:

cos(α - π/2) = -sinα

in this case, α will be the value of w = 12.25 rad/s. and 90° is the same as rewritting as π/2, therefore:

cos(α - π/2) = cos(12.25t - 90)

x = -0.98sin(12.25t)

3 0

3 years ago

During physical activity of high intensity, your heart will beat at a percentage of its maximum rate. Whi

Maurinko [17]

Answer:

D

Explanation:

If it is of very high intensity it will be 85-100%

8 0

3 years ago

5. A sled with no initial velocity accelerates at a rate of 5.0 m/s2 down a hill. How

ad-work [718]

Answer:

60 m/s

Explanation:

$a = \frac{vf - vi}{t}$

$5.0 = \frac{vf - 0}{12}$

$5.0 \times 12 = vf$

$60 = vf$

6 0

3 years ago

HOLA, NECESITO AYUDA!

givi [52]

The electrostatic force between the two ions is $2.9\cdot 10^{-10} N$

Explanation:

The electrostatic force between two charged particle is given by Coulomb's law:

$F=k\frac{q_1 q_2}{r^2}$

where

$k=8.99\cdot 10^9 Nm^{-2}C^{-2}$ is the Coulomb's constant

$q_1, q_2$ are the two charges

r is the separation between the two charges

In this problem, the ion of sodium has a charge of

$q_1 = +e = +1.6\cdot 10^{-19} C$

while the ion of chlorine has a charge of

$q_2 = -e = -1.6\cdot 10^{-19}C$

And the distance between the two ions is

$r=282 pm = 282\cdot 10^{-12} m$

Substituting, we find the electrostatic force between the two ions:

$F=(8.99\cdot 10^9) \frac{(1.6\cdot 10^{-19})(-1.6\cdot 10^{-19})}{(282\cdot 10^{-12})^2}=-2.9\cdot 10^{-10} N$

where the negative sign simply means that the force is attractive, since the two ions have opposite charge.

Learn more about electrostatic force:

brainly.com/question/8960054

brainly.com/question/4273177

#LearnwithBrainly

6 0

3 years ago

For each of the problems below, you will need to draw a graph to find the solution.

Gelneren [198K]

Answer:

Final velocity (v) of an object equals initial velocity (u) of that object plus acceleration (a) of the object times the elapsed time (t) from u to v. Use standard gravity, a = 9.80665 m/s2, for equations involving the Earth's gravitational force as the acceleration rate of an object.

Explanation:

3 0

3 years ago