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Tju [1.3M]
4 years ago
8

1. A 500-g block is placed on a level, frictionless surface and attached to an ideal spring. At t = 0 the block moves through th

e equilibrium position with speed vo in the –x direction, as shown below. At t =  sec, the block reaches its maximum displacement of 40 cm to the left of equilibrium. a. Determine the value of each of the following quantities. Show all work. • period: • spring constant: b. Using x(t) = A cos(t + o) as the solution to the differential equation of motion: i. Determine the form of the function v(t) that represents the velocity of the block. ii. Evaluate all constant parameters (A, , and o) so as to completely describe both the position and velocity of the block as functions of time. c. Consider the following statement about the situation described above. "It takes the first  seconds for the block to travel 40 cm, so the initial speed vo can be found by dividing 40 cm by  seconds." Do you agree or disagree with this statement? If so, explain why you agree. If not, explain why you disagree and calculate the initial speed vo of the block.
Physics
1 answer:
Thepotemich [5.8K]4 years ago
6 0

Answer:

Pls refer to attached handwritten document for calculation and detailed answer

Explanation:

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Mercury has an average disease to the sun of 0.39 AU. In two or more complete sentences, explain how to calculate the orbital pe
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Answer: 88 Earth days

Explanation:

According to the Kepler Third  Law of Planetary motion <em>“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”. </em>

<em />

In other words, this law states a relation between the orbital period T of a body (moon, planet, satellite) orbiting a greater body in space with the size a of its orbit:

T^{2}=a^{3} (1)

If we assume the orbit is circular and apply Newton's law of motion and the Universal Law of Gravity we have:

T^{2}=\frac{4\pi^{2}}{GM}a^{3} (2)

Where M is the mass of the massive object and G is the universal gravitation constant. If we assume M constant and larger enough to consider G  really small, we can write a general form of this law:

MT^{2}=a^{3} (3)

Where T is in units of Earth years,  a is in AU (<u>1 Astronomical Unit is the average distane between the Earth and the Sun)</u> and  M is the mass of the central object  in units of the mass of the Sun.

This means when we are making calculations with planets in our solar system  M=1.

Hnece, in the case of Mercury:

(1)T^{2}=(0.39 AU)^{3} (4)

Isolating T:

T=\sqrt{(0.39 AU)^{3}} (5)

T=0.243 Earth-years \frac{365 days}{1 Earth-year}=88.6 days \approx 88 days (6)

This means the period of Mercury is 88 days.

7 0
3 years ago
When an object moves, where does the energy come from?
Eddi Din [679]
Ans: Kinetic and potential energies are found in all objects. If an object is moving, it is said to have kinetic energy (KE). Potential energy (PE) is energy that is "stored" because of the position and/or arrangement of the object. The classic example of potential energy is to pick up a brick.
5 0
3 years ago
A positive force on the balance indicates a downward force on the silver sphere while a negative force on the balance indicates
anastassius [24]

The two spheres have opposite charges.

<h3 /><h3 /><h3>What are types charge?</h3>
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When a positive charge points downwards ↓ and the negative charge points upwards ↑, this causes attraction and shows that the two charges are different.

Thus, we can conclude that the two spheres have opposite charges.

Learn more about attraction and repulsion of charges here: brainly.com/question/2396080

7 0
2 years ago
Which of the following is an example of energy changing from one form to another?
Anastaziya [24]

The correct option is

a fire


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6 0
4 years ago
Read 2 more answers
S A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a frictionless, horizontal tr
cestrela7 [59]

The kinetic energy of this block-spring when the block has a speed (v) is given by K.E = 1/2 × (M + m/3)v².

<h3>What is kinetic energy?</h3>

Kinetic energy can be defined as a form of energy that is possessed by a person due to its motion or change in speed (acceleration).

<h3>How to calculate kinetic energy?</h3>

Mathematically, kinetic energy can be calculated by using this formula:

K.E = 1/2 × mv²

Where:

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Since the mass of a segment of this spring is dm = (m/l) dx, the kinetic energy for each of its segment would be given by:

dK = 1/2 × (dm)Vx²

This ultimately implies that, the kinetic energy of this block-spring when the block has a speed (v) is given by:

K.E = 1/2 × Mv² + 1/2 × ¹∫₀((x²v²/l²)m/ldx

K.E = 1/2 × (M + m/3)v².

Read more on kinetic energy here: brainly.com/question/15848455

#SPJ4

6 0
2 years ago
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