Answer:
A) K / K₀ = 4 b) v / v₀ = 4
Explanation:
A) For this exercise we can use the conservation of mechanical energy
in the problem it indicates that the displacement was doubled (x = 2xo)
starting point. At the position of maximum displacement
Em₀ = Ke = ½ k (2x₀)²
final point. In the equilibrium position
= K = ½ m v²
Em₀ = Em_{f}
½ k 4 x₀² = K
(½ K x₀²) = K₀
K = 4 K₀
K / K₀ = 4
B) the speed value
½ k 4 x₀² = ½ m v²
v = 4 (k / m) x₀
if we call
v₀ = k / m x₀
v = 4 v₀
v / v₀ = 4
Answer:
-9.46 N
Explanation:
In order to get the value of the x component of the resultant force, we need to get the value of the x component of each force.
This value will be the projection of the force vector, on the x-axis.
For F₁, as it is directed at an angle of 55.0º above the negative x axis, we can find F₁ₓ just applying the definition of cosine of an angle, as follows:
cos θ =
In this case, x = F₁ₓ, and r = F₁
θ, measured from the positive x axis counterclockwise, is as follows:
θ= 180º-55º = 125º
⇒ F₁ₓ = F₁* cosθ = 9.2 N * cos 125º = -5.28 N
We can repeat the process for F₂, as follows:
For F₂, as it is directed at an angle of 53.3º below the negative x axis, we can find F₂ₓ just applying the definition of cosine of an angle, as follows:
cos θ =
In this case, x = F₂ₓ, and r = F₂
θ, measured from the positive x axis counterclockwise, is as follows:
θ= 180º + 53.3º = 233.3º
⇒ F₂ₓ = F₂* cosθ = 7.00 N * cos 233.3º = -4.18 N
The total component of both forces along the x axis, can be found just adding both components, as follows:
Fₓ = F₁ₓ + F₂ₓ = -5.28 N + -4.18 N = -9.46 N