Answer:
Explanation:
Given two vectors as follows
E₁ = 13.5 i -12 j
E₂ = -7.4 i - 4.7 j
Resultant E = E₁ + E₂
= 13.5 i -12 j -7.4 i - 4.7 j
E = 6.1 i - 16.7 j
a ) X component of resultant = 6.1 N
b ) y component of resultant = -16.7 N
Magnitude of resultant = √ ( 6.1² + 16.7² )
= 17.75 N
d ) If θ be the required angle
tanθ = 16.7 / 6.1 = 2.73
θ = 70° .
counterclockwise = 360 - 70 = 290°
Using the formula A squared plus B squared equals C squared, we can find the solution by substituting 5 for A and 12 for B.
By squaring 5, we get 25, and by squaring 12, we get 144. Adding these, we get 169. The square root of this is 13.
Answer:
b ≈ 64 Kg/s
Explanation:
Given
Fd = −bv
m = 2.5 kg
y = 6.0 cm = 0.06 m
g = 9.81 m/s²
The object in the pan comes to rest in the minimum time without overshoot. this means that damping is critical (b² = 4*k*m).
m is given and we find k from the equilibrium extension of 6.0 cm (0.06 m):
∑Fy = 0 (↑)
k*y - W = 0 ⇒ k*y - m*g = 0 ⇒ k = m*g / y
⇒ k = (2.5 kg)*(9.81 m/s²) / (0.06 m)
⇒ k = 408.75 N/m
Hence, if
b² = 4*k*m ⇒ b = √(4*k*m) = 2*√(k*m)
⇒ b = 2*√(k*m) = 2*√(408.75 N/m*2.5 kg)
⇒ b = 63.9335 Kg/s ≈ 64 Kg/s
