This statement is TRUE.
Answer:
r= 3.2 cm
Explanation:
Given that
I= 8.7 A
B= 5.4 x 10⁻⁵ T
μo=1.25664 x 10⁻⁶
We know that magnetic filed in wire at a distance r given as
By putting the values
r=0.032 m
r= 3.2 cm
The distance from a long straight wire at which the magnetic field equals the strength of Earth’s field, given a current of 8.7 A and Earth's field of 5.4 × 10−5 T, can be calculated using the formula for the magnetic field around a current-carrying wire. Substituting the given values, the answer is approximately 37.22 cm.
To solve this physics problem, we will use the formula for the magnetic field produced by a current carrying long, straight wire. The formula is: B = μI / (2πr), where 'B' is the magnetic field strength, 'μ' is the permeability of free space, 'I' is the current, and 'r' is the radial distance away from the wire.
In this case, Earth’s magnetic field, 'B', is given as 5.4 × 10−5 T, the current, 'I', is given as 8.7 A, and the permeability of free space, 'μ', is given as 1.25664 × 10−6 T · m/A. We need to find 'r', the distance away from the wire, and we want this answer in centimeters.
So, rearrange the formula to solve for 'r': r = μI / (2πB).
Substitute our known values into the equation: r = (1.25664 × 10−6 T · m/A × 8.7 A) / (2π × 5.4 × 10^-5 T). After calculating, we need to convert from meters to centimeters by multiplying by 100. The final answer is approximately 37.22 cm.
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The conservation of mechanical energy allows to find the results for the questions of the motion of mass in a conservative force are;
a) the velocity at x = 4 m is: v = 16.9 m / s
b) The acceleration at x = 4m is: a = 17.8 m / s²
c) The maximum elongations is: x = 6.67 m
Given parameters
To find
a) The speed
b) The acceleration
c) The maximum value of the distance
The conservation of mechanical energy is one of the most important concepts in physics, stable that if there is not friction the mechanical energy remains constant at all points.
Em = K + U
Where Em mechanical energy, K the kinetical energy ang U the potential energy.
a) Let's find the velocity using the conservation of mechanical energy
Starting point. Where the mass is released.
Em₀ = U (0)
Final point. When for a distance of x = 4 m here we have potential and kinetic energy.
= K + U (4)
They indicate that the only force is conservative, therefore mechanicalenergy is conserved
Em₀ =
0 = ½ m v² + U (4)
½ m v² = -U (4)
v² = 2 / m (αx² - β x³)
Let's calculate
v² = (2 4² - 0.3 4³)
v =
v = 16.9 m / s
b) Acceleration is requested at this point.
We use that potential energy and force are related
F =
We carry out the derivatives
F = 2αx - 3βx²
Let's calculate
F = 2 2 4 - 3 0.3 4²
F = 1.6 N
Now we use Newton's second law that relates the net force with the product of the mass and the acceleration of the body.
F = ma
a =
a =
a = 17.8 m / s²
c) At maximum displacement.
Let's use conservation of mechanical energy
Starting point. Where x = 0 is released
Emo = U (0) = 0
Final point. Point of maximum elongation, kinetic energy is zero
= U (xmax)
Energy is conserved
Em₀ =
-αx² + βx³ = 0
x² (-α + βx) = 0
the solutions of this equation is:
x = 0
-α + βx = 0
x =
Let's calculate
x =
x = 6.67 m
In conclusion using the conservation of mechanical energy we can find the results for the questions of the motion of mass in a conservative force are;
a) the velocity at x = 4 m is: v = 16.9 m / s
b) The acceleration at x = 4m is: a = 17.8 m / s²
c) The maximum elongations is: x = 6.67 m
Learn more here: brainly.com/question/2615468
Answer:
a) v= 284.44
b) a=17.78
c) x=6.67m
Explanation:
a).
b).
c).
Value x,0
Inside the square root is the value of maximum value of x
but that value is not real so:
How high up must the 7th floor be?
If you had thrown it at the same speed but at the 28th floor, how far from the base of the building would it land?
1) 31.1 m/s
The rock has been thrown straight out of the window: its motion on the horizontal direction is simply a uniform motion, with constant speed , because no forces act in the horizontal direction. The speed in a uniform motion is given by
where S is the distance traveled and t the time taken.
In this case, the distance by the rock before hitting the ground is and the time taken is , so the initial speed is given by
2) 67.1 m
In this part of the problem we are only interested in the vertical motion of the rock. The vertical motion is a uniformly accelerated motion, with constant acceleration (acceleration of gravity) towards the ground. In a uniformly accelerated motion, the distance traveled by the object is given by
where t is the time. Substituting a=9.8 m/s^2 and t=3.7 s, we can find S, the vertical distance covered by the rock, which corresponds to the height of the 7th floor:
3) 230.1 m
The height of the 7th floor is 67.1 m. So we can assume that the height of each floor is
And so, the height of the 28th floor is
We can find the total time of the fall in this case by using the same formula of the previous part:
In this case, S=268.8 m, so we can re-arrange the formula to find t
And now we can consider the motion of the rock on the horizontal direction: we know that the rock travels at a constant speed of v=31.1 m/s, so the distance traveled is
And this is how far from the building the rock lands.