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
According to the Law of Reflection, the angle of incidence
Elan Coil [88]

Answer:

A

Explanation:

this is because the law of reflection states that the angle of incidence equals to the angle of the reflection.

hope this helps, if not please report it

someone else can try it

8 0
3 years ago
When the saw slices wood, the wood exerts a 104-N force on the blade, 0.128 m from the blade’s axis of rotation. If that force i
Soloha48 [4]

Answer:

Explanation:

When saw slices wood by exerting a force on the wood , wood also exerts a reaction force on the saw in opposite direction which is equal to the force of action that is 104 N.

So torque exerted by wood on the blade

= force x perpendicular distance from the axis of rotation

= 104 x .128

=13.312 Nm.

Since this torque opposes the movement of blade , it turns the blade slower.

5 0
2 years ago
A box is being pushed but two stellar science students, one on each side of the box. Peter is pushing box with a force of 10 N t
Vitek1552 [10]

Answer:

Josh is the strongest

The net force is 5N towards right

5 0
3 years ago
Which of the following is an ionic compound ? A. Gold
quester [9]
Among the given choices, the ionic compound is D. Magnesium Chloride (<span>MgCl2</span>) where magnesium has a +2 charge while chloride has a -1 charge. Ionic compounds are chemical compounds comprising of ions held together by electrostatic forces named as ionic bonding.
7 0
2 years ago
You have two square metal plates with side lengths of (6.50 C) cm. You want to make a parallel-plate capacitor that will hold a
gtnhenbr [62]

Answer:

The necessary separation between  the two parallel plates is 0.104 mm

Explanation:

Given;

length of each side of the square plate, L = 6.5 cm = 0.065 m

charge on each plate, Q = 12.5 nC

potential difference across the plates, V = 34.8 V

Potential difference across parallel plates is given as;

V = \frac{Qd}{L^2 \epsilon_o} \\\\d = \frac{V L^2 \epsilon_o}{Q}

Where;

d is the separation or distance between the two parallel plates;

d = \frac{VL^2 \epsilon_o}{Q} \\\\d =  \frac{34.8*(0.065)^2 *8.854*10^{-12}}{12.5*10^{-9}} \\\\d = 0.000104 \ m\\\\d = 0.104 \ mm

Therefore, the necessary separation between  the two parallel plates is 0.104 mm

6 0
3 years ago
Other questions:
  • 1. Take the speed at which the body moves as 10 m/s 2. Calculate the distance travelled by the body every second 3. Take the tim
    10·1 answer
  • A positive charge Q1 = 30.5 nC is located at the origin. A negative charge Q2 = -3.5 nC is located on the positive x-axis p = 3
    9·2 answers
  • A flat, 101 turn current‑carrying loop is immersed in a uniform magnetic field. The area of the loop is 5.61×10−4 m2, and the an
    10·1 answer
  • How do I work out this question
    12·1 answer
  • Ratio of acceleration due to grabity and universal gravitational constant
    14·1 answer
  • Help Me !! I have an exam.
    10·2 answers
  • A (11.4 A) ohm device is connected to a 115 V outlet. If the cost of the electrical energy is $0.16/kWh, determine the cost of r
    15·1 answer
  • HELP NOW PLS !!
    12·1 answer
  • Please help.<br>Just True or False​
    13·1 answer
  • To win the game, a place kicker must kick a football from 30m from the goal, and the ball must clear the crossbar which is 3.05
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!