What happens when a force exerted on an object cause the object to move?
2 answers:
You might be interested in
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:
(a)Therefore the highest altitude attained by the object is =576 ft .
(b)Therefore the object takes 6 sec to fall to the ground.
Explanation:
Initial velocity: Initial velocity is a velocity from which an object starts to move.
u is usually used for notation of initial notation.
Final velocity: Final velocity is a velocity of an object after certain second from starting.
The final velocity is denoted by v.
Acceleration: The difference of final velocity and initial velocity per unit time
The S.I unit of acceleration is m/s².
(a)
Given that u= 128 ft\sec and g = 32 ft/sec².
At highest point the velocity of the object is 0 i.e v=0
Since the displacement is opposite to the gravity.
Therefore acceleration( a)= -g = -32 ft/sec².
To find the time this to happen we use the following formula
Here v=0
⇒0=128+(-32) t
⇒32t=128
⇒t = 4 sec
To determine the height we use the following formula
⇒s= 256 ft
Therefore the highest altitude attained by the object is =(320+256)ft=576 ft .
(b)
At the highest point the velocity of the object is 0.
so u=0. a=g= 32 ft/sec² [ since the direction of gravity and the displacement are same] s= 576 ft
To determine the time to fall we use the following formula
⇒t=6 sec
Therefore the object takes 6 sec to fall to the ground.