During a storm, a tree limb breaks off and comes to rest across a barbed wire fence at a point that is not in the middle between two fence posts. The limb exerts a downward force of 176 N on the wire. The left section of the wire makes an angle of 12.5° relative to the horizontal and sustains a tension of 413 N. Find the (a) magnitude and (b) direction (as an angle relative to horizontal) of the tension that the right section of the wire sustains.

Answer:

Acceleration = 8.27 cm/s²

Explanation:

We are given;

initial velocity; v_i = 10.5 cm/s

Initial position; x_i = 2.72 cm

Time; t = 2.30 s

final position; x_f = 5.00 cm

To find the acceleration, we will make use of the formula;

x_f - x_i = (v_i * t) - (½at²)

Plugging in the relevant values, we have;

5 - 2.72 = (10.5 × 2.3) - (½ × a × 2.3²)

2.28 = 24.15 - 2.645a

24.15 - 2.28 = 2.645a

2.645a = 21.87

a = 21.87/2.645

a = 8.27 cm/s²

Using the kinematic equation, the acceleration of the object was calculated to be approximately8.27 cm/s² given its initial velocity, position, time, and final position.

We are given:

Initial velocity (vᵢ) = 10.5 cm/s

Initial position (xᵢ) = 2.72 cm

Time (t) = 2.30 seconds

Final position () = 5.00 cm

We want to find the acceleration (a) of the object using the kinematic equation:

x₋ᵢ - xᵢ = (vᵢ * t) - (1/2) * a * t²

Now, let's substitute the given values:

5.00 cm - 2.72 cm = (10.5 cm/s * 2.30 s) - (1/2) * a * (2.30 s)²

Simplify the equation:

2.28 cm = 24.15 cm - (1/2) * a * 5.29 s²

Now, isolate 'a' by rearranging the equation:

-1.09 cm = (-1/2) * a * 5.29 s²

To remove the negative sign, multiply both sides by -1:

1.09 cm = (1/2) * a * 5.29 s²

Next, solve for 'a' by multiplying both sides by (2 / 5.29):

a ≈ (1.09 cm) / (2 / 5.29) s²

a ≈ 8.27 cm/s²

So, the acceleration of the object is approximately 8.27 cm/s².

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Final answer:

In plate tectonics theory, transform boundaries occur when two plates slide past each other, divergent boundaries occur when two plates move away from each other, and convergent boundaries occur when two plates collide. A volcano is most likely to occur at a divergent boundary because the plates move away from each other, allowing magma from the mantle to reach the surface and create new crust.

Explanation:

In plate tectonics theory, Transform boundaries occur when two plates slide past each other horizontally, creating earthquakes. Divergent boundaries occur when two plates move away from each other, creating volcanic activity.

Convergent boundaries occur when two plates collide, and depending on the type of plates involved, can result in volcanic activity as one plate is forced beneath the other.

A volcano is most likely to occur at a divergent boundary because the plates move away from each other, allowing magma from the mantle to reach the surface and create new crust.

The Richter scale indicates the magnitude of an earthquake. The figure drawn by the needle during shaking is an outcome of earthquake's energy. This energy is what results in seismic waves travelling through various layers of earth causing shaking on the surface.

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Answer:

8m/s

Explanation:

Vavg= 16-0/2=8m/s

Answer:

a) 8.99*10³ V  b) 4.5*10⁻² J c) 0 d) 0

Explanation:

a)

• The electrostatic potential V, is the work done per unit charge, by the electrostatic force, producing a displacement d from infinity (assumed to be the reference zero level).
• For a point charge, it can be expressed as follows:

• As the electrostatic force is linear with the charge (it is raised to first power), we can apply superposition principle.
• This means that the total potential at a given point, is just the sum of the individual potentials due to the different charges, as if the others were not there.
• In our case, due to symmetry, the potential, at any corner of the triangle, is just the double of the potential due to the charge located at  any other corner, as follows:

• The potential at point C is 8.99*10³ V

b)

• The work required to bring a positive charge of 5μC from infinity to the point C, is just the product of the potential at this point times the charge, as follows:

• The work needed is 0.045 J.

c)

• If we replace one of the charges creating the potential at the point  C, by one of the same magnitude, but opposite sign, we will have the following equation:

• This means that the potential due to both charges is 0, at point C.

d)

• If the potential at point C is 0, assuming that at infinity V=0 also, we conclude that there is no work required to bring the charge of 5μC from infinity to the point C, as no potential difference exists between both points.

Answer:

5N

Explanation:

Given parameters:

Original length = 22cm

Spring constant, K  = 50N/m

New length = 32cm

Unknown

Force applied  = ?

Solution:

The force applied on a spring can be derived using the expression below;

   Force  = KE

 k is the spring constant

 E is the extension

  extension = new length - original length

  extension  = 32cm  - 22cm  = 10cm

convert the extension from cm to m;  

   100cm  = 1m;

    10cm will give 0.1m

So;

  Force  = 50N/m x 0.1m  = 5N

Final answer:

To calculate the force used to stretch the spring, Hooke's Law is utilized, which leads to the conclusion that a force of 5 N was exerted to stretch the spring from its original length of 22 cm to a final length of 32 cm.

Explanation:

The force exerted by a spring is governed by Hooke's Law, which states that the force required to stretch or compress a spring by a certain distance is proportional to that distance. In this case, the spring constant, k, is given as 50 N/m and the spring is stretched from its original length of 22 cm to a final length of 32 cm. This represents a stretch, or displacement, of 10 cm (or 0.1 m when converted to the standard unit).

The force (F) can be calculated using Hooke's law: F = kx, where x is the displacement of the spring. Substituting the given values, the force amounts to F = (50 N/m) * (0.1 m) = 5 N. Therefore, the force used to stretch the spring to its final length of 32 cm is 5 N.

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Answer:

22.26 years

, 15.585 light years  , 11.13 light years

Explanation:

a)

=

= 22.26 years

b)

0.7*c*22.26 years

=15.585 light years  

c)

0.7*c*15.9

=11.13 light years