Answer:
F = 7.68 10¹¹ N, θ = 45º
Explanation:
In this exercise we ask for the net electric force. Let's start by writing the configuration of the charges, the charges of the same sign must be on the diagonal of the cube so that the net force is directed towards the interior of the cube, see in the attached numbering and sign of the charges
The net force is
F_ {net} = F₂₁ + F₂₃ + F₂₄
bold letters indicate vectors. The easiest method to solve this exercise is by using the components of each force.
let's use trigonometry
cos 45 = F₂₄ₓ / F₂₄
sin 45 = F_{24y) / F₂₄
F₂₄ₓ = F₂₄ cos 45
F_{24y} = F₂₄ sin 45
let's do the sum on each axis
X axis
Fₓ = -F₂₁ + F₂₄ₓ
Fₓ = -F₂₁₁ + F₂₄ cos 45
Y axis
F_y = - F₂₃ + F_{24y}
F_y = -F₂₃ + F₂₄ sin 45
They indicate that the magnitude of all charges is the same, therefore
F₂₁ = F₂₃
Let's use Coulomb's law
F₂₁ = k q₁ q₂ / r₁₂²
the distance between the two charges is
r = a
F₂₁ = k q² / a²
we calculate F₂₄
F₂₄ = k q₂ q₄ / r₂₄²
the distance is
r² = a² + a²
r² = 2 a²
we substitute
F₂₄ = k q² / 2 a²
we substitute in the components of the forces
Fx = 
Fx = 
( -1 + ½ cos 45)
F_y = k \frac{q^2}{a^2} ( -1 + ½ sin 45)
We calculate
F₀ = 9 10⁹ 4.25² / 0.440²
F₀ = 8.40 10¹¹ N
Fₓ = 8.40 10¹¹ (½ 0.707 - 1)
Fₓ = -5.43 10¹¹ N
remember cos 45 = sin 45
F_y = - 5.43 10¹¹ N
We can give the resultant force in two ways
a) F = Fₓ î + F_y ^j
F = -5.43 10¹¹ (i + j) N
b) In the form of module and angle.
For the module we use the Pythagorean theorem
F = 
F = 5.43 10¹¹ √2
F = 7.68 10¹¹ N
in angle is
θ = 45º
Answer:
x = 76.5 m
Explanation:
Let's use Newton's second law at the point of contact between the wheel and the floor.
fr = m a
fr = miy N
N-W = 0
N = W
μ mg = m a
a = miu g
a = 0.600 9.8
a = 5.88 m / s²
Having the acceleration we can use the kinematic relationships to find the distance
² = v₀² + 2 a x
= 0
x = -v₀² / 2 a
Acceleration opposes the movement by which negative
x = - 30²/2 (-5.88)
x = 76.5 m
The net force acting on the car is 65 N to the left
The net force acting on an object is simply defined as the resultant force acting on the object.
From the question given, we obtained the following data:
- Force applied to the right (Fᵣ) = 250 N
- Force applied to the left (Fₗ) = 315 N
- Net force (Fₙ) =?
The net force acting on the car can be obtained as follow:
Fₙ = Fₗ – Fᵣ
Fₙ = 315 – 250
<h3>Fₙ = 65 N to the left </h3>
Therefore, the net force acting on the car is 65 N to the left
Learn more on net force: brainly.com/question/19549734
Answer:
15.07 ksi
Explanation:
Given that:
Pitch (P) = 5 teeth/in
Pressure angle (
) = 20°
Pinion speed (
) = 2000 rev/min
Power (H) = 30 hp
Teeth on gear (
) = 50
Teeth on pinion (
) = 20
Face width (F) = 1 in
Let us first determine the diameter (d) of the pinion.
Diameter (d) = 
=
= 4 in
From the values of Lewis Form Factor Y for ( ) = 20 ; at 20°
Y = 0.321
To find the velocity (V); we use the formula:
V = 2094.40 ft/min
For cut or milled profile; the velocity factor 
can be determined as follows:
= 2.0472
However, there is need to get the value of the tangential load
, in order to achieve that, we have the following expression
Finally, the bending stress is calculated via the formula:
15.07 ksi
∴ The estimate of the bending stress = 15.07 ksi
Answer:
Weight on Earth = We = 186.2 N
Weight on Mars = Wm = 70.94 N
Explanation:
The weight of an object is defined as the force applied on the object by the gravitational field. The magnitude of weight is given by the following formula:
W = mg
were,
W= Weight of Eric
m = mass of Eric
g = acceleration due to gravity
ON EARTH:
W = We = Eric's Weight on Earth = ?
m = Eric's Mass on Earth = 19 kg
ge = acceleration due to gravity on Earth = 9.8 m/s²
Therefore,
We = (19 kg)(9.8 m/s²)
<u>We = 186.2 N</u>
<u></u>
ON MARS:
W = Wm = Eric's Weight on Mars = ?
m = Eric's Mass on Mars = 19 kg
gm = acceleration due to gravity on Mars = 0.381(ge) = (0.381)9.8 m/s² = 3.733 m/s²
Therefore,
Wm = (19 kg)(3.733 m/s²)
<u>Wm = 70.94 N</u>
