1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Radda [10]
3 years ago
7

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

ed nor compressed and the block is moving in the negative direction at 12.0 m/s. Find (a) the amplitude and (b) the phase angle. (c) Write an equation for the position as a function of time.
Physics
1 answer:
r-ruslan [8.4K]3 years ago
3 0

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)

You might be interested in
Which quantity and unit are INCORRECTLY paired?
liq [111]
Force, the unit is Newton, newton is the force to accelerate a mass. so it should be kg m/s^2

joule (J) is equal to Nm not Ns

the unit of work is J and it is correct.
the unit of power is J/s which is equal to W
the unit of of energy is the same with work, which is J which equivalent to kgm2/s2
5 0
3 years ago
A dense metal sphere is dropped from a 10-meter tower, and at the exact same time an identical metal sphere is thrown horizontal
givi [52]

Answer:

A. Both spheres land at the same time.

Explanation:

The horizontal motion doesn't affect the vertical motion.  Since the two spheres have the same initial vertical velocity and same initial height, they land at the same time.

7 0
3 years ago
Read 2 more answers
A piece of rocky debris in space has a semi major axis of 45.0 AU. What is its orbital period?
KATRIN_1 [288]

Complete Question

Planet D has a semi-major axis = 60 AU and an orbital period of 18.164 days. A piece of rocky debris in space has a semi major axis of 45.0 AU.  What is its orbital period?

Answer:

The value  is  T_R  = 11.8 \  days  

Explanation:

From the question we are told that

   The semi - major axis of the rocky debris  a_R = 45.0\  AU

   The semi - major axis of  Planet D is  a_D  = 60 \  AU

    The orbital  period of planet D is  T_D = 18.164 \  days

Generally from Kepler third law

          T \  \ \alpha \ \ a^{\frac{3}{2} }

Here T is the  orbital period  while a is the semi major axis

So  

        \frac{T_D}{T_R}  =  \frac{a^{\frac{3}{2} }}{a_R^{\frac{3}{2} }}

=>     T_R  = T_D *  [\frac{a_R}{a_D} ]^{\frac{3}{2} }  

=>     T_R  = 18.164  *  [\frac{ 45}{60} ]^{\frac{3}{2} }

=>      T_R  = 11.8 \  days  

   

7 0
3 years ago
Students who embrace an innate mindset might view their poor performance in math as inevitable or beyond their control
PilotLPTM [1.2K]

Answer:

True

Explanation:

4 0
3 years ago
Read 2 more answers
When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of 0.140 m from the center of t
choli [55]

Answer:

Part a)

\tau = 23.1 Nm

Part b)

\tau = 17.05 Foot pound force

Explanation:

As we know that torque is defined as the product of force and its perpendicular distance from reference point

so here we have

\tau = \vec r \times \vec F

now we have

\tau = (0.140)(165)

\tau = 23.1 Nm

Part b)

Now we know the conversion as

1 meter = 3.28 foot

1 N = 0.225 Lb force

now we have

\tau = 23.1 Nm

\tau = 23.1 (0.225 Lb)(3.28 foot)

\tau = 17.05 Foot pound force

3 0
3 years ago
Other questions:
  • A block has acceleration a when pulled by a string. if two identical blocks are glued together and pulled with twice the origina
    9·1 answer
  • A tiger leaps horizotally from a 15.5 m high rock with a speed of 7.5 m/s. How
    5·1 answer
  • Unimpressed with your previous stunt, the director of the new James
    7·1 answer
  • What does Newton’s first law describe
    11·2 answers
  • A gas laser has a cavity length of 1/3 m and a single oscillation frequency of 9.0 x 1014 Hz. What is the cavity mode number?
    13·1 answer
  • Two bodies, one hot and the other cold kept in vacuum.what will happen to the tempreture of bodies after some time.
    14·1 answer
  • If the battery has a voltage of 24 Volts, Find the current when switch is closed.
    5·1 answer
  • PLEASE HELPP<br> Look at the picture
    14·2 answers
  • Jason while driving on Kukum highway at 70 m.s – 1 seeing the traffic light turn red, he applies the brake and comes to rest in
    14·1 answer
  • an object of mass m is rotating about a fixed axis with angular momentum l. its moment of inertia about this axis is i. what is
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!