Answer:
v = 2.029 m/s
Explanation:
Given
L = 84.0 cm ⇒ R = 0.5*L = 0.5*84 cm = 42 cm = 0.42 m
m₁ = 0.600 kg
m₂ = 0.200 kg
g = 9.8 m/s²
u₁ = u₂ = 0 m/s
v₁ = ?
v₂ = ?
Due to gravity, the bar oscillates and becomes vertical. The mass that occupies the lower position is the one with the highest torque. The one that reduces the potential energy (the system tends to the position of minimum energy). This is achieved if the mass that goes down is 0.6kg (that goes down 42cm) and the one that goes up is 0.2kg (goes up 42cm).
In this system mechanical energy is conserved, so we can match its value in the horizontal position with the one in the vertical.
then
Ei = Ki + Ui = 0.5*(m₁+m₂)*(0)² + (m₁+m₂)*9.8*(0) = 0 J
Ef = Kf + Uf
⇒ Kf = 0.5*(m₁+m₂)*v² = 0.5*(0.6+0.2)*v² = 0.4*v²
⇒ Uf = m₁*g*h₁ + m₂*g*h₂ = 0.6*9.8*(-0.42) + 0.2*9.8*0.42 = - 1.6464
⇒ Ef = Kf + Uf = 0.4*v² - 1.6464
Since
0 = 0.4*v² - 1.6464 ⇒ v = 2.029 m/s
v is the same value due to the wooden rod is pivoted about a horizontal axis through its center and the masses are on opposite ends.
v₁ = v₂ = v ⇒ ω₁*R₁ = ω₂*R₂ ⇒ ω₁*R = ω₂*R ⇒ ω₁ = ω₂ = ω
⇒ v = ω*R
Answer:
Explanation:
As we know that magnitude of two vectors is given as
here we know that
A = magnitude of vector A
B = magnitude of vector B
= angle between two vectors
so here we know that
A = 30 units
B = 40 units
angle = 90 degree
so we have
No person shall be judged by their financial status in the process of applying for a job or position of power in the government.
A decagram is 1000 times bigger than a centigram
Answer:
159.38 Watts
Explanation:
Initially;
- Mass on the spring is 8.5 kg
- Therefore, compression force is 85 N
- Compression distance is 15 cm or 0.15 m
But;
F = kx
where F is the force of compression, k is the spring constant and x is the compression distance.
Thus;
k = F/x
= 85 N ÷0.15
= 566.67 N/m
We are required to determine the power needed to stretch the same spring for 1.5 m in 4 secs.
Power = Work done ÷ time
Work done is given by 0.5kx²
Therefore;
Power = 0.5kx²÷ t
= (0.5×566.67 N/m × 1.5² ) ÷ 4 seconds
= 159.38 Watts
Thus, the power needed is 159.38 watts
