A mass of 0.14 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.28 m)cos[(8 rad/s)t]. Determine the following. (a) amplitude of oscillation for the oscillating mass .

Answer:

Explanation:

We can use Ohm's Law to find the resistance R of a wire that carries a current I under a given potential difference:

Answer:

Ohm's law states that I=V/R (Current=volts divided by resistance). Since we're looking for resistance, we'll rewrite it as R=V/I. Then just plug in the numbers; R=84/9, R= 9 1/3 or 28/3. The resistance of the wire is 9.33... or 9 1/3 ohm's, depending on how you wanna write it.

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Answer:

1. 53.415 m

2. 32.373 m/s

3. 30.82 m/s

Explanation:

Let g = 9.81 m/s2. We can use the following equation of motion to calculate the distance traveled by the ball in 3.3s, and the velocity it achieved

1.

2.

3. If the ball is kicked at 0.5 m above the ground then the net distance between the ball and the roof top is

53.415 - 0.5 = 48.415 m

For the ball to at least make it to the roof top at speed v = 0 m/s. We can use the following equation of motion to calculate the minimum initial speed

where v = 0 m/s is the final velocity of the ball when it reaches the rooftop, is the initial velocity, is the distance traveled, g = -9.81 is the gravitational acceleration with direction opposite with velocity

Answer:

Explanation:

Energy falling on 1 m² surface of earth per second = 1050

Energy in one million years on 1 m²

= 1050 x 60 x 60 x 24 x 365 x 10⁶ = 3.311 x 10¹⁶ J

In order to calculate total energy coming out of the surface of the sun , we shall have to sum up this energy for the while spherical surface of imaginary sphere having radius equal to distance between sun and earth.

Area of this surface = 4π R² = 4 X 3.14 X (149.6 X 10⁹ )²

= 2.8 X 10²³ m²

So total energy coming out of the sun = 2.8 x 10²³ x 3.311 x 10¹⁶

= 9.271 x 10³⁹ J

From the formula

E = mc² { energy mass equivalence formula }

m = E / c² =

1.03 x 10²³ kg

mass of earth = 5.972 x 10²⁴

Answer in percentage of mass of earth

=

= 1.72  %

Image is missing, so i have attached it

Answer:

19.04 × 10⁻⁴ T in the +x direction

Explanation:

We are told that the point P which is equidistant from the wires. (R = 5.00 cm). Thus distance from each wire to O is R.

Hence, the magnetic field at P from each wire would be; B = μ₀I/(2πR)

We are given;

I = 2.4 A

R = 5 cm = 0.05 m

μ₀ is a constant = 4π × 10⁻⁷ H/m

B = (4π × 10⁻⁷ × 2.4)/(2π × 0.05)

B = 9.6 × 10⁻⁴ T

To get the direction of the field from each wire, we will use Flemings right hand rule.

From the diagram attached:

We can say the field at P from the top wire will point up/right

Also, the field at P from the bottom wire will point down/right

Thus, by symmetry, the y components will cancel out leaving the two equal x components to act to the right.

If the mid-point between the wires is M, the the angle this mid point line to P makes with either A or B should be same since P is equidistant from both wires.

Let the angle be θ

Thus;

sin(θ) = (1.3/2)/5

θ = sin⁻¹(0.13) = 7.47⁰

The x component of each field would be:

9.6 × 10⁻⁴cos(7.47) = 9.52 × 10⁻⁴ T

Thus, total field = 2 × 9.52 × 10⁻⁴ = 19.04 × 10⁻⁴ T in the +x direction

Final answer:

The magnetic field at point P, which is equidistant from two long parallel wires with equal anti-parallel currents, is calculated using Ampere's law. The net magnetic field is zero because the fields due to each wire cancel each other at that point.

Explanation:

The question concerns the calculation of the magnetic field at a point equidistant from two long parallel wires that carry equal anti-parallel currents. According to the right-hand rule and Ampere's law, each wire generates a magnetic field that circles the wire. For two wires carrying currents in opposite directions, the magnetic fields at the midpoint between the wires will point in opposite directions, thus they will subtract from each other when calculating the total magnetic field at point P.

To find the magnetic field at point P, we use the formula for the magnetic field due to a long straight current-carrying wire: B = (μ₀I)/(2πd), where B is the magnetic field, μ₀ is the permeability of free space (4π x 10-7 T·m/A), I is the current, and d is the distance to the point of interest from the wire. In this case, the distance d will be the radius R = 5.00 cm since point P is equidistant from both wires.

Substituting the values into the formula, the magnetic field due to each wire at point P can be calculated. However, since the currents are anti-parallel, the net magnetic field at P would be the difference between the two fields, which is zero.

The reflected beam experienced a phase change of about 180°.

What is reflection in the glass surface?

According to Snell's law, the light that incident on the glass surface will be reflected and transmitted at an angle equals to the angle of incidence.  

By the observation of refractive index of the glass for the normal incidence only 4% of the light is transmitted or reflected.

The light passing through glass is not only reflected on the front surface, but also on the back. For several times the light will gets reflected back and forth. So, the total reflectance through a glass window can be calculated as

                                    2·R / (1+R).

Thus, A light wave travelling in air is reflected by a glass barrier will undergo a  phase change of 180°, while light travelling in glass will not undergo a phase change if it is reflected by a boundary with air.

Learn more about reflection,

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Answer:

180 degree phase change

Explanation: