Answer:
speed for last lap is 247.89 km/h
Explanation:
given data
velocity v1 = 203 km/h
velocity v2 = 199 km/h
no of lap n = 10
to find out
average speed for last lap
solution
we consider here distance d for 1 lap
so in first 9 lap time taken is
t1 = distance / velocity v2
t1 = 9d / 199 ...............1
and
for 10 lap time is
t2 = 10d / 203 .............2
so from 1 and 2 equation time for last lap
last lap time t3 = t2 - t1
t3 = 10d / 203 - 9d / 199
t3 = 0.004034 d
so speed for last lap is
speed = distance / time
speed = d / 0.004034 d
speed = 247.89 km/h
so speed for last lap is 247.89 km/h
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:
The moment of inertia about the rotation axis is 117.45 kg-m²
Explanation:
Given that,
Mass of one child = 16 kg
Mass of second child = 24 kg
Suppose a playground toy has two seats, each 6.1 kg, attached to very light rods of length r = 1.5 m.
We need to calculate the moment of inertia
Using formula of moment of inertia


m = mass of seat
m₁ =mass of one child
m₂ = mass of second child
r = radius of rod
Put the value into the formula


Hence, The moment of inertia about the rotation axis is 117.45 kg-m²